Chapter7PropertiesofStockOptionPrices(期权期
Ch07_Properties of Stock Option Prices(金融工程学,华东师大).
7.11
Puts: An Arbitrage Possibility?
• Suppose that p= 3 S0= 48 T= 0.25 r= 5% X= 50 D= 0 • Is there an arbitrage possibility?
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University
• C : American Call option
• • • price P : American Put option price ST :Stock price at time T D : Present value of dividends during option’s life r : Risk-free rate for maturity T with cont comp
7.6
(NO Dividends)
• A is worth more than B, so it must cost more to set it up initially. So c + Xe-rT > S0
c > max[S0 -Xe-rT, 0]
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University
7.13
Call Early Exercise on Non-Dividend Paying Stock
国际会计第七版英文版课后答案（第七章）
国际会计第七版英文版课后答案（第七章）预览说明:预览图片所展示的格式为文档的源格式展示,下载源文件没有水印,内容可编辑和复制Chapter 7Financial Reporting and Changing PricesDiscussion Questions Solutions1.Historical-based financial statements may be misleading during periods of significant inflation.Many resources may have been acquired in periods when the purchasing power of the monetary unit was much higher. These expenses then typically are deducted from revenues that reflect current purchasing power. The resulting income number is unintelligible. Another problem for statement readers is that the value of assets recorded at their historical acquisition cost is typically understated as a result of inflation. Understated asset values produce understated expenses and overstated earnings.Financial trends are also difficult to interpret, as trend statistics generally include monetary units of different purchasing power. A positive trend in sales may be due to price changes, not real increases in sales.2. A price index is a cost ratio, that is, the ratio of a representative “basket” of goods and servicesconsumed by an average family, compared to the price of that same basket in a benchmark (“base”) year. The price index is invaluable in enabling a statement reader to translate sums of money paid in the past to their current purchasing power equivalents.3.This statement is partly true and shows the confusion thatsurrounds inflation accounting. Inaccounting for changing prices, users must distinguish between general price changes and specific price changes. General prices refer to the prices of all goods and services in the economy. The object of accounting for general price level changes is to preserve the general purchasing power of a company’s money capital. Specific price changes refer to changes in the prices of specific commodities. The object of accounting for specific price changes is to preserve a company’s productive capacity or operating capability.4.The congressman is wrong. The object of inflation accounting is to clarify the distinction betweencapital and income, not to minimize corporate taxes. Inflation accounting shows how much money the company can pay in expenses, taxes, and dividends, while keeping enough resources to maintain its capital.5.Although it is generally conceded in principle that price level-adjusted financial statements are moreuseful than conventional accounting statements during periods of significant inflation, it is a judgment call to identify exactly when price level-adjusted statements become more meaningful. Asa rule of thumb, executives in Brazil use an inflation rate greater than 10 % per month. Investors inGermany or Switzerland may believe that 5 % inflation per year is alarming. Unfortunately, no one has yet developed a formal, rigorous, easy-to-apply definition of meaningfulness.How does one determine whether the benefits of price level-adjusted accounting information exceed the costs? While the costs to generate such information can be measured, it is muchharder to quantify the benefits. Financial accounting deals with information produced by business enterprises for use by external decision makers. Consequently, measurement of the benefits of price level-adjusted information must cover all user groups in an economy. Multiple user groups, uneven distributions of benefits (both within and between groups), and favorable economy-wide spillover effects of price level information complicate the task. Adding international dimensions makes the problem even worse.6.The U.S. approach resembles the price-level adjusted current cost model, whereas the U.K.approach embraces the current cost model. While both require disclosure of the impact ofchanging prices on monetary items, the U.S. approach basically uses the general price level index to compute monetary gains and losses, whereas the U.K. employs specific prices changes by way of its gearing adjustment.1.The International Accounting Standards Board sanctions use of the general price level model orthe current cost framework. Whichever method is employed, these inflation adjustments must be expressed in terms of constant purchasing power as of the balance sheet date. Purchasing powergains or losses are to be included in current income. Firms adjusting their accounts for changingprices must disclose, at a minimum: a) the fact that end-of-period purchasing power adjustmentshave been made, b) the asset valuation framework employed in the primary financial statements,c) the type of inflation index or indexes employed and theirlevel at the end of the period as wellas their movements during the period, and d) the net purchasing power gain or loss on netmonetary items held during the period. Given the options that are available, analysts mustunderstand the differences between the approved inflation accounting methods to be able tocompare companies choosing one option over the other and to assure proper interpretation ofinflation adjusted amounts.2.The historical cost-constant dollar model measures the impact of general price level changes on afirm's reported performance and financial position. The current cost model examines the impact of specific price changes on enterprise income and wealth.The two measurement frameworks are similar in that both attempt to clarify the distinction between capital and income. They differ in reporting objectives. Whereas the historical cost/constant dollar model attempts to preserve the general purchasing power of a firm's original money capital, the current cost model attempts to preserve an entity's physical capital or productive capacity.3.Your authors think that restating foreign and domestic accounts to their current cost equivalentsproduces information that is far more helpful to investor decisions than historical cost methods, whether or not adjusted for changes in general price levels. Such information provides a performance measure that signals the maximum amount of resources that enterprises can distribute without reducing their productive capacity. It also facilitates comparisons ofconsolidated data.10. The gearing adjustment is an inflation adjustment that partially offsets the additional charges toincome associated with assets whose values are restated for inflation (e.g., higher depreciation and cost of sales). This adjustment recognizes that borrowers generally gain from inflation because they can repay their debts with currency of reduced purchasing power. Hence, it is unnecessary to recognize the higher replacement cost of inventory and plant and equipment in the income statement so far as they are financed by debt.11. Accounting for foreign inflation differs from accounting for domestic inflation in two major ways.First, foreign rates of inflation often are higher than domestic rates, which increases potential distortions in an entity's reported results from changing prices. Second, as foreign exchange rates and differential national rates of inflation are seldom perfectly negatively correlated, care must be taken to avoid double-dipping when consolidating the results of foreign operations.12.Double-dipping refers to methods that count the effects of foreign inflation twice in reportedearnings. Earnings are reduced once when cost of sales is adjusted upwards for inflation, andagain when inventories are translated to domestic currency using a current exchange rate, whichyields a translation loss. Since the change in the exchange rate itself was caused by inflation, the result is a double charge for inflation.Exercise Solutions1.This exercise is a good way to test students’ understanding of the various approaches toaccounting for changin g prices. Vestel’s earnings numbers are based on the general price levelmodel whereas Infosys is measuring its performance based on a current cost framework. Modello goes a step further and adjusts its current cost statements for changes in the general price level.Some may feel that current cost data, which is based on the notion of replacement costs, is toosubjective a notion to be reliable. Since general price level data are based on general price level indices, the numbers appearing in Vestel’s income statement are much more objective andfacilitates comparisons among companies using a similar methodology. Moreover, Vestel’sstatements do not violate the historical cost doctrine. Others will argue that the value of stockinvestments are based on discounted future cash flows. Accordingly, the current cost framework provided by Infosys is more germane to investor decisions as it measures the amount of earnings that could be distributed as dividends without reducing the firm’s future dividend gen eratingpotential. Moreover, current cost earnings, including the gearing adjustment , reflects how thefirm is impacted by prices that are more germane to the firm, as opposed to the general public.Some will argue that Modello’s income statement combin es the best of both worlds. However,there is merit to the argument that the income statementshould measure the performance of thefirm and that this is best accomplished with the current cost framework. Since individualinvestors are affected by the g eneral price level, they should adjust their share of a firm’s current cost earnings distributions for general inflation.2. a.Income Statement Historical Price Level Historical Cost-Cost Adjustment Constant Dollar Revenue MXP 144,000,000 420/340 MXP 177,882,353 Operating expenses (86,400,000) 420/340 (106,729,412) Depreciation (36,000,000) 420/263 (57,490,494)Operating income MXP 21,600,000 MXP 13,662,447a Monetary gains(losses) - (73,248,759)Net income MXP 53,280,000 MXP(59,586,312)Balance SheetCash MX(P 157,600,000 420/420 MXP 157,600,000Land 180,000,000 420/263 287,452,471Building 720,000,000 420/263 1,149,809,885Acc. Depreciation (36,000,000) 420/263 (57,490,494)Total MXP 1,021,600,000 MXP 1,537,371,862Owners' equity(beg.) MXP1,000,000,000 rolled forward b MXP 1,596,958,174Net income (loss) 21,600,000 (59,586,312)Owner's equity MXP 1,021,600,000 MXP 1,537,371,862(end)a Monetary loss:CashBeginning balance 1,000,000,000 420/263 1,596,958,174 Purchase ofreal estate ( 900,000,000) 420/263 (1,437,262,356)Rental revenues 144,000,000 420/340 177,882,353Operating expenses (86,400,000) 420/340 106,729,412)157,600,000 230,848,759-157,600,000 Monetary loss (73,248,759)b Beginning equity x price level adjustment = adjusted amount= P 1,000,000,000 x 420/263 = P 1,596,958,1742.b.Cost HC/Constant DollarReturn on Assets 21,600,000 (59,586,312)1,021,600,000 1,537,371,862= 2.1% = -3.9%Cost-based profitability ratios tend to provide a distorted (overstated) picture of a company's operating performance during a period of inflation.3.20X7 20X8Cash MJR 2,500 MJR 5,100Current liabilities (1,000) (1,200)LT-Debt (3,000) (4,000)Net monetary liabilities MJR (1,500) MJR (100)Zonolia Enterprise’s net monetary liability position changed by MJR1,400 during the year (MJR100) –(MJR1,500).4.Nominal Restate for ConstantMJR’s Majikstan GPL MJR’sNet monetary liab.'s MJR 1,500 x 32,900/30,000 = MJR1,645 12/31/X7Decrease during year (1,400) = (1,400)Net monetary liab.'s MJR 100 x 32,900/36,000 = MJR 9112/31/X8Monetary (general purchasing power) gain MJR 1545. Historical Current Cost Current Income Statement Cost Adjustment Cost Revenues MXP 144,000,000 - MXP 144,000,000 Operating expenses 86,400,000 - 86,400,000 Depreciation (36,000.000) 1.8 64,800,000 Net Income (loss) MXP 21,600,000 MXP (7,200,000)Balance SheetCash MXP 157,600,000 - P 157,600,000 Land 180,000,000 1.9 342,000,000 Building 720,000,000 1.8 1,296,000,000 Acc. Depreciation (36,000,000) 1.8 (64,800,000) Total MXP1,021,600,000 MXP 1,730,800,000 Owners' Equity Beg. Balance MXP1,000,000,000 MXP 1,000,000,000 OE revaluation a - 738,000,000Net income (loss) 21,600,000 (7,200,000) Total MXP1,021,600,000 MXP 1,730,800,000a Revaluation of land MXP 162,000,000Revaluation of building 576,000,000MXP 738,000,0006. Solution in 000,000's:MJR8,000 X 137.5/100.0 = MJR11,00020X7 20X8Current cost MJR8,000 MJR11,000Acc. depreciation (1,600) (3,300)aNet current cost MJR6,400 MJR7,700a Current cost depreciation = MJR800 X 137.5/100.0 = 1,100per year for 3 years.7. As no new assets were acquired during the year, we must determine to what extent the MJR3,000 increase in the current cost of Zonolia's equipment exceeded the change in the general price level during the year. The appropriate calculation follows: MJR11,000 - [MJR8,000 X 36,000/30,000]= MJR11,000 - MJR9,600= MJR1,400Alternatively, if we follow the FASB’s sug gested methodology, where calculations are expressed in average (20X8) dollars, current cost depreciation would be computed by reference to the average current cost of the related assets. Thus, Current cost, 12/31/X7 MJR8,000,000Current cost, 12/31/X8 11,000,000MJR19,000,000Average current cost MJR19,000,000/2 = MJR9,500,000Current cost depreciation at 10% = MJR950,000Increase in current cost of equipment, net of inflation (000's): Current Restate for Current cost/Cost Inflation Constant Zonos Current cost, net12/31/X7 MJR6,400 X 32,900/30,000 MJR7,019Depreciation (950) (950)Current cost, net12/31/X8 7,700 X 32,900/36,000 7,037MJR 2,250 MJR968The increase in the current cost of equipment, net of inflation is MJR968. The difference between the nominal renge amount (MJR2,250) and constant renges (MJR968) is the inflation component of the equipment's current cost increase.8. Restate-translate method:Constant Translate $ Equivalentsrenges of constantrengesIncrease in currentcost of equip., netof inflation MJR968,000 X 1/4,800 = $202Translate-restate method:CC (MJR) Translate CC ($) Restate CC/ Constant $U.S. GPLCC, net MJR 6,400,000 x 1/4,800 = $1,333 x 292.5/281.5 = $1,38512/31/X7Dep. (950,000) x 1/4,800 = (198) = (198)CC, net 7,700,000 x 1/4,800 = 1,604 x 292.5/303.5 = 1,54612/31/X8MJR 2,250,000 $ 469 $ 3599.20X7 20X8￡m ￡mTrade receivables 242 270-Trade payables (170) (160)Net monetary working capital 72 110Change in monetary working capital = ￡38 (￡110 - ￡72) Nominal Restate for Constant￡British PPI ￡Net monetary W/C 72 X 110/100 = 79.212/31/20X7Increase during year 38 = 38.0Net monetary W/C 110 X 110/120 = 100.812/31/20X8Monetary working capital adjustment = (16.4)aa This amount is added to the current cost adjustments for depreciation and cost of sales because trade receivables exceeded trade payables, thus tying up working capital in an asset that lost purchasing power.Gearing adjustment:[(TL – CA)/(FA + I + MWC)] [CC Dep. Adj. + CC Sales Adj. + MWCA]where TL = total liabilities other than trade payablesCA = current assets other than trade receivables and inventoryFA = fixed assets including investmentsI = inventoryMWC = monetary working capitalCC Dep. Adj. = current cost depreciation adjustmentCC Sales adj. = current cost of sales adjustmentMWCA = monetary working capital adjustment= [(128 – 75)/(479 + 220 + 110] [￡m 216]= [.066 ] [216]= ￡14.3The only number I could readily identify in problem 9 is inventory of 220. The next number I could come close on is fixed assets. Looks like the solution above says 479, the text for 08 indicates 473. I could not see where the 110 (MWC) came from. Neither is it clear where the other 3 items in brackets came from. The solution needs to be clearer before I can check the numbers.This gearing adjustment of ￡14.3 million is subtracted from the current cost of sales and depreciation adjustments. It represents the purchasing power gain from using debt to finance part of the firm's operating assets.a.Nominal Thai Historical Translation U.S.baht inflation c ost/constant rate dollaradjustment baht equivalentInven-tory BHT500,000 x 100/200 = BHT250,000 x .02 = $5,000b.Nominal Translation U.S. U.S. Historicalbaht rate dollar inflation c ost/constantequivalent adjustment dollarsInven-tory BHT500,000 x .02 = 10,000 x 180/198 = $9,090Sorry this seems confusing compared to number 2 where the year end index was in the numerator and either the beginning or average index was in the denominator (e.g. 420/340 or 420/263). It is not clear why we do the opposite here where the Thai price level doubles and we put the 200 in the denominator and 100 in the numerator.c. Most students will prefer the restate-translate method. This approach has merit if general and specific pricelevels move in tandem. If not, neither approach is satisfactory as both are based on a historical cost valuation framework that is generally irrelevant for investment decisions.d. For reasons enumerated in this chapter, we favor restating local currency assets for specific price changesand then translating these current cost equivalents to dollars using the current exchange rate.11. We assume that Doosan Enterprises translates its inventory at the current rate and adjusts its cost ofsales for inflation by simulating what it would have been ona LIFO basis. Two adjustments are necessarybecause local inflation impacts exchange rates used to translate foreign currency inventory balances to dollars.With FIFO inventories, a translation loss is recorded in "as reported" earnings when it is originally translatedto U.S. dollars by a current exchange rate that changed (devalued) during the period. This translation loss isan indirect charge for local inflation. The inflation adjustment (simulated LIFO charge) to increase "as reported" cost of sales to a current cost basis is an additional charge for inflation. Absent some offsettingentry, consolidated results would be charged twice for inflation. To avoid this double charge, the translation loss embodied in reported earnings is deducted from the simulated LIFO charge to arrive at a net U.S. dollarcurrent cost of sales adjustment. Steps in the adjustment process are as follows:1. FIFO inventory subject to simulated LIFO charge KRW10,920,0002. Restate line 1 to January 1 currency units(KRW10,920,000 x 100/120). The result is anapproximation of December 31 LIFO inventory KRW9,100,0003. Difference between FIFO and LIFO inventorybalances (line 1 minus line 2) is the additionallira LIFO expense (current cost adjustment)for the current year. KRW1,820,0004. Translate line 3 to dollars at the January 1exchange rate (KRW1,820,000 ÷ 900). The resultis the additional dollar LIFO expense for thecurrent year $ 2,0225. Calculate the translation loss on FIFO inventory(line 1) that has already been reflected in "asreported" results:a. Translate line 1 at Januaryexchange rate (KRW10,920,000 ÷ KRW900) $ 12,133b. Translate line 1 at December 31exchange rate (L 10,920,000 ÷ KRW1,170) $ 9,333c. The difference is the translationloss in “as reported” results $ (2,800)6. The difference between lines 4 and 5c isthe cost of sales adjustment in dollars:a. Additional dollar LIFO expense fromline 4. $ 2,022b. Less: Inventory translation loss alreadyreflected in "as reported” results (fromline 5c) $ (2,800)c. The difference is the net dollar currentcost of sales adjustment $ (778)Here, the current cost of sales adjustment is negative (i.e., reduces the dollar cost of sales adjustment). This is because the won devalued by more than the differential inflation rate (assuming a U.S. inflation rate close to zero). If the lira devalued by less than the differential inflation rate, the cost of sales adjustment would have been positive.12.1. Cost of fixed assets at 12/31 EUR20,0002. FIFO inventory at 12/31 EUR 8,0003. Total EUR28,0004. Less: Owners' equity at 12/31 EUR 2,0005. Liabilities used to financefixed assets and inventory EUR26,0006. Restate liabilities to beginningof period markka (EUR26,000 X300/390) EUR20,0007. Purchasing power gain EUR 6,0008. Purchasing power gain inpounds (EUR 6,000/EUR 1.5) ￡4,0009. Translation gain on appliedliabilities(EUR 26,000/EUR 1.5 -EUR26,000/EUR1.95) ￡4,00010. Net purchasing power gain ￡ -0-In this case the translation gain on liabilities used to finance nonmonetary assets equals the purchasing power gain because the currency devaluation matched the differential inflation of 30%. Hence, no purchasing power gains would be recognized.Case 7-1 SolutionCase 7.1 Kashmir Enterprises1.a–cHistorical Price Level HistoricalCost Adjustment Cost ConstantIncome Statement RupeesRevenues INR6,000,000 160/144 I NR6,666,667Cost of Sales 2,560,000 160/128 3,200,000Selling & Admin. 1,200,000 160/144 1,333,333Depreciation 160,000 160/128 200,000Interest 240,000 160/160 240,000Monetary gains (losses)a - 741,666Net Income INR1,840,000 INR2,435,000Balance SheetCash INR2,480,000 160/160 I NR2,480,000 Inventory 480,000 160/128 600,000Building 3,200,000 160/128 4,000,000Accu. depreciation (160,000) 160/128 (200,000) Total INR6,000,000 INR6,880,000Accounts payable INR 620,000 160/160 I NR 620,000 Notes payable 2,400,000 160/160 2,400,000 Owners' equity 2,980,000 3,860,000INR 6,000,000 INR6,880,000a Monetary gains/(losses):CashBeg. balance INR 720,000 160/128 INR1,150,000 Down payment (800,000) 160/128 (1,000,000) Sales 6,000,000 160/144 6,666,667Selling & Adm. exp. (1,200,000) 160/144 (1,333,333) Payment on account (2,200,000) 160/144 (2,444,444) Interest (240,000) 160/160 (240,000)INR 2,480,000 INR2,798,890-2,480,000Monetary loss INR (318,890)a Monetary gains and losses:Accounts PayableBeg. balance INR 420,000 160/128 INR525,000 Purchases 2,400,000 160/128 3,000,000Payments on account (2,200,000) 160/144 (2,444,444) INR 620,000 INR1,080,556- 620,000Monetary gain INR 460,556a Monetary gains/(losses):Notes PayablePurchase warehouse INR 2,400,000 160/128 INR 3,000,000 - 2,400,000Monetary gain INR 600,000Net monetary loss: INR(318,890) + INR460,556 + INR600,000 = INR741,666.Current Cost Financial StatementsHistorical Adjustment Current Cost Income Statement Cost F actor EquivalentsRevenues INR6,000,000 - INR 6,000,000Cost of Sales 2,560,000 1.3 3,328,000Selling and adm. 1,200,000 - 1,200,000Depreciation 160,000 1.4 224,000Interest 240,000 - 240,000Net Income INR 1,840,000 INR1,008,000Balance SheetCash INR 2,480,000 - INR 2,480,000Inventory 480,000 1.3 624,000Building 3,200,000 1.4 4,480,000Acc. depreciation 160,000 1.4 224,000Total INR 6,000,000 INR 7,360,000Accounts payable INR 620,000 - INR 620,000Notes payable 2,400,000 - 2,400,000Owners' equity 2,980,000 4,340,000INR 6,000,000 INR 7,360,0002. Your authors favor current cost over historical or historical cost/constant dollar financial statements. Finance theory states that investors are interested in a firm's dividend-generating potential, as the value of their investment depends on future cash flows. A firm's dividend-generating potential, in turn, is directly related to its productive capacity. Unless a firm preserves itsproductive capacity or physical capital(e.g.,plant, equipment, inventories), dividends can’t be sustained over time. Under these circumstances, current cost financial statements give investors information important to their decisions. They show the maximum resources that a firm can distribute to investors without impairing its operating capability.3.Translate-Restate MethodBalance Sheet, Jan. 1Local Currency Trans. Dollar Inflation Historical costRate Equivalents Adjustment Constant $Cash INR 920,000 .025 $23,000 - $23,000Inventory 640,000 .025 16,000 - 16,000 Total INR1,560,000 $39,000 $39,000A/P INR 420,000 .025 $10,500 - $10,500 Owners' equity 1,140,000 .025 28,500 - 28,500 Total INR 1,560,000 $39,000 $ 39,000Income StatementDec. 31Revenues INR 6,000,000 .022 $ 132,000 108/104 $ 137,077 Cost of sales 2,560,000 .022 56,320 108/100 60,825Selling & Adm. 1,200,000 .022 26,400 108/104 27,415 Depreciation 160,000 .022 3,520 108/100 3,802 Interest 240,000 .022 5,280 108/108 5,280Net Income INR 1,840,000 $ 40,480 $ 39,755 Monetary gains (losses)a - - 4,468$44,223a Monetary gains/(losses):CashBeg. Bal INR 920,000 .02 $ 18,400 108/100 $ 19,872Downpayment (800,000) .02 (16,000) 108/100 (17,280) Sales 6,000,000 .02 120,000 108/104 124,615Selling & Adm. (1,200,000) .02 (24,000) 108/104 (24,923)Payments on Acc. (2,200,000) .02 (44,000) 108/104 (45,692) Interest (240,000) .02 (4,800) 108/108 (4,800)INR 2,480,000 $ 49,600 51,792-49,600Monetary loss $ (2,192) Accounts PayableBeg. Bal. INR 420,000 .02 $ 8,400 108/100 $ 9,072Purchases 2,400,000 .02 48,000 108/100 51,840Pmt. on acc. (2,200,000) .02 (44,000) 108/104 45,692INR 620,000 $ 12,400 $ 15,592- 12,400Monetary gain $ 2,820Notes payablePur. W/house Rpe 2,400,000 .02 $ 48,000 108/100 $ 51,840 48,000Monetary gain $ 3,840Netmonetary gain: $(2,192) + $2,820 + $3,840 = $4,468.Balance Sheet Local Trans. Dollar Inflation Historical cost- Dec. 31 Currency Rate Equiv. Adjustment Constant $Cash INR 2,480,000 .02 48,600 108/108 $ 48,600 Inventory 480,000 .02 9,600 108/100 10,368 Building 3,200,000 .02 64,000 108/100 69,120Acc. Dep. 160,000 .02 3,200 108/100 3,456Total INR 6,000,000 $120,000 $ 124,632Acc. payable 620,000 .02 12,400 108/108 $ 12,400Notes payable 2,400,000 .02 48,000 108/108 48,000Trans. adj.b - (9,380) (9,978)Owners' equity c 2,980,000 68,980 74,210Total INR 6,000,000 $120,000 $124,632________________________________________________________________ __b Translation adjustment:Beginning net assets Rpe 1,140,000 (.02 - .025) = $ (5,700) X 108/100 = $(6,156)Increase in net assets Rpe 1,840,000 (.02 - .022) = (3,680) X 108/104 = $(3,822)$(9,380) $(9,978) c Balancing residualRestate - Translate MethodBalance Sheet Local Inflation Historical Cost- Trans. D ollar Jan 1. Currency Adjustment Constant rupee Rate equivalents Cash INR 920,000 128/128 INR 920,000 .025 $ 23,000 Inventory d 640,000 128/128 640,000 .025 16,000Total INR1,560,000 INR1,560,000 $ 39,000Acct. payable INR 420,000 128/128 INR 420,000 .025 $ 10,500Owner's equity 1,140,000 1,140,000 28,500Total INR 1,560,000 INR 1,560,000 $ 39,000d Assumes inventory acquired near year-end.Income StatementYear ended Dec. 31Revenues INR 6,000,000 160/144 INR 6,666,666 .022 $ 146,667Cost of Sales 2,560,000 160/128 3,200,000 .022 70,400 Selling & Adm. 1,200,000 160/144 1,333,333 .022 29,333 Depreciation 160,000 160/128 200,000 .022 4,400Interest 240,000 160/160 240,000 .022 5,280Net Income INR1,840,000 INR1,693,334 $ 37,254 Monetary gains(losses)a- 741,666 .022 16,317INR2,435,000 $ 53,571Balance SheetDec. 31Cash INR 2,480,000 160/160 INR 2,480,000 .02 $ 49,600Inventory 480,000 160/128 600,000 .02 12,000Building 3,200,000 160/128 4,000,000 .02 80,000Acc. deprec. 160,000 160/128 200,000 .02 4,000Total INR 6,000,000 INR 6,880,000 $137,600Acc. payable INR620,000 160/160 INR 620,000 .02 $ 12,400 Notes payable 2,400,000 160/160 2,400,000 .02 48,000Owner's equity 2,980,000 3,860,000 87,770 Translation adj.b - (10,570)Total INR 6,000,000 INR 6,880,000 $137,600________________________________________b Beginning net assets INR1,140,000 (.02 - .025) = $ (5,700)Change in net assets 2,435,000 ).02 - .022) = $(4,870)$(10,570)Both methods are inadequate for American investors because they are based on the historical cost valuation framework. A better reporting procedure is to restate local accounts to their current cost equivalents, then translate these amounts to the reporting currency using the year-end (current) foreign exchange rate. This is illustrated here.Restate (current cost)/Translate (current rate)Cash INR 920,000 - INR 920,000 .025 $ 23,000Inventory 640,000 - 640,000 .025 16,000Total INR 1,560,000 INR1,560,000 $ 39,000Acc. payable INR 420,000 - INR 420,000 .025 $ 10,500Owner's equity 1,140,000 - 1,140,000 28,500。
高级职员优资料新先认股权物产定价(英文)
CP
S0 X
–+
– +
–+
– +
T
? ? ++
r D
–++
–+ +
–++
–+ +
Options, Futures, and Other Derivatives, 4th edition © 1999 by John C. Hull
7.4
American vs European Options
An American option is worth at least as much as the corresponding European option
7.11
Early Exercise
• Usually there is some chance that an American option will be exercised early
• An exception is an American call on a non-dividend paying stock
• Consider the following 2 portfolios: – Portfolio A: European call on a stock + PV of the strike price in cash – Portfolio B: European put on the stock + the stock
insurance against stock price falling below strike price
资产定价 chapter7
}
Firm-specific risk
◦ The risk that can be eliminated by diversification. ◦ Also called unique risk, nonsystematic risk, or diversifiable risk.
9
}
Efficient diversification
◦ Since the portfolio’s expected return is the weighted average of its component expected returns, and is unaffected by correlation between them. ◦ But the portfolio’s SD is less than the weighted average of the component SD.
2
}
Asset allocation and security selection are technically identical; both aim at identifying that optimal risky portfolio, namely, the combination of risky assets that provides the best risk-return trade-off.
Alice Ouyang
1
}
The investment decision can be viewed as a top-down process:
1. Capital allocation between the risky portfolio and risk-free assets. 2. Asset allocation across broad asset classes (ex: US stocks, international stocks, and long-term bonds). 3. Security selection of individual assets within each asset class.
债券及股票的定价策略(英文版)
债券及股票的定价策略(英文版)In finance, pricing strategies for bonds and stocks are crucial for investors and financial institutions to determine the fair value of these financial securities. This helps in making informed investment decisions and managing investment portfolios effectively. Let's explore the pricing strategies for bonds and stocks.Bond Pricing Strategy:1. Discounted Cash Flow (DCF) Analysis: This strategy involves calculating the present value of future cash flows generated by the bond. The cash flows include periodic interest payments and the bond's face value at maturity. The present value is determined by discounting these cash flows using an appropriate discount rate, usually the bond's yield to maturity (YTM).2. Comparable Bond Analysis: This strategy relies on comparing the bond in question with similar bonds in the market. By analyzing similar bonds' yields and prices, investors can assess whether the bond is overvalued or undervalued. Factors considered in this analysis include credit rating, coupon rate, maturity, and market conditions.3. Yield Spread Analysis: This strategy involves analyzing the yield spread between a particular bond and a benchmark bond with similar characteristics but different credit ratings. If the yield spread is wider than historical levels, indicating higher risk, the bond may be priced at a discount. Conversely, a narrower yield spread implies a premium.Stock Pricing Strategy:1. Dividend Discount Model (DDM): This strategy focuses on estimating the intrinsic value of a stock based on its future dividends. The DDM involves discounting expected future dividends to the present value using an appropriate discount rate, such as the stock's required rate of return or the dividend growth rate.2. Price-to-Earnings (P/E) Ratio Analysis: This strategy evaluates a stock's value by comparing its market price to its earnings per share (EPS). A low P/E ratio may suggest an undervalued stock, while a high P/E ratio could indicate an overvalued stock. This analysis considers industry P/E ratios, earnings growth prospects, and other relevant factors.3. Comparable Company Analysis: This strategy involves comparing the valuation metrics of a company with its industry peers or similar companies. Parameters such as price-to-sales ratio, price-to-book ratio, or enterprise value-to-EBITDA ratio are compared to identify relative valuation. If a company's valuation is significantly lower than its peers with similar fundamentals, it may be considered undervalued.Both bond and stock pricing strategies require careful analysis of various quantitative and qualitative factors. It is crucial for investors to consider the fundamental characteristics of the security, market conditions, economic indicators, interest rates, and other relevant factors. Additionally, incorporating risk assessment and future market expectations into these pricing strategies enhances their accuracy.Bond Pricing Strategy (Continued):4. Term Structure of Interest Rates Analysis: This strategy takes into account the term structure of interest rates, which shows the relationship between the yields and maturity dates of bonds. By comparing the yields of bonds with different maturities, investors can assess the expectations of future interest rate movements. If the current bond's yield is higher than the expected future rates, it may be undervalued, and vice versa.5. Credit Rating Analysis: Credit ratings assigned by rating agencies provide an indication of a bond's creditworthiness. Higher-rated bonds typically have lower yields due to lower perceived risk. Investors can analyze the bond's credit rating and compare it to similar rated bonds to determine whether the bond is priced appropriately.Stock Pricing Strategy (Continued):4. Discounted Free Cash Flow (DCF) Analysis: This strategy estimates the intrinsic value of a stock by forecasting its future cash flows. The future cash flows are projected based on expected revenue, expenses, and capital expenditures. These cash flows are discounted to their present value using an appropriate discount rate, such as the company's cost of capital. The resulting value represents the fair value of the stock.5. Price-to-Book (P/B) Ratio Analysis: This strategy compares a company's market price per share to its book value per share. The book value represents the net assets of the company, calculated by subtracting liabilities from assets. A low P/B ratio may indicate anundervalued stock, suggesting that the market is not fully recognizing the company's tangible assets.6. Earnings Growth Analysis: This strategy looks at the growth potential of a company's earnings. Investors analyze historical earnings growth rates and projected future growth rates to assess the stock's value. A higher expected earnings growth rate may justify a higher valuation for the stock.7. Technical Analysis: This pricing strategy focuses on analyzing historical price and volume patterns of a stock to predict future price movements. Technical analysts use various tools and techniques such as charts, moving averages, and oscillators to identify trends, support and resistance levels, and other patterns that can guide investment decisions.It is important to note that these pricing strategies serve as a guide and should not be considered definitive methods of valuation. Market conditions, investor sentiment, and unforeseen events can impact the fair value of bonds and stocks. It is recommended to use a combination of these strategies and exercise caution while interpreting the results. Regular monitoring and reassessment of pricing strategies are necessary to adapt to changing market dynamics. Ultimately, investors should conduct thorough research and seek professional advice before making investment decisions.。
期货期权及其衍生品配套(全34章)Ch(22)
16
整理ppt
2
Effect of Variables on Option Pricing (Table
9.1, page 202)
Variable c
p
CP
S0 K
–+
– +
–+
– +
T
? ? ++
r D
–++
–+ +
–++
–+ +
整理ppt
3
American vs European Options
Suppose that
c =3 T = 0.25
S0 = 31 r = 10%
K = 30
D= 0
What are the arbitrage possibilities when p = 2.25 ?
p= 1 ?
整理ppt
10
Early Exercise
Usually there is some chance that an American option will be exercised early An exception is an American call on a nondividend paying stock This should never be exercised early
Both are worth max(ST , K ) at the maturity of the options They must therefore be worth the same today. This means that
c + Ke -rT = p + S0
国际财务管理课后习题答案chapter 7
CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGESUGGESTED ANSWERS AND SOLUTIONS TO END-OF—CHAPTERQUESTIONS AND PROBLEMSQUESTIONS1。
Explain the basic differences between the operation of a currency forward market and a futures market.Answer: The forward market is an OTC market where the forward contract for purchase or sale of foreign currency is tailor-made between the client and its international bank. No money changes hands until the maturity date of the contract when delivery and receipt are typically made. A futures contract is an exchange-traded instrument with standardized features specifying contract size and delivery date。
Futures contracts are marked-to—market daily to reflect changes in the settlement price。
Delivery is seldom made in a futures market。
Rather a reversing trade is made to close out a long or short position。
Properties of Stock Options
The Impact of Dividends on Lower Bounds to Option Prices
c S 0 D Ke
rT
p D Ke
rT
S0
18
Early Exercise
Usually there is some chance that an American option will be exercised early An exception is an American call on a nondividend paying stock This should never be exercised early
Equation 10.10 p. 244
American options; D > 0 S0 - D - K < C - P < S0 - Ke -rT
Equation 10.11 p. 244 26
Summary
Options
An American option is worth at least as much as the corresponding European option Cc&Pp
Call option can never be worth more than the stock price today S Put option can never be worth more than the present value of strike price K
Properties of Stock Options
Notation
C : American Call option c : European call option price
高二经济学原理英语阅读理解30题
A. The quality of a product.
B. The price ofa product.
C. The production cost.
D. The market size.
答案解析：B。供求关系相互作用决定产品价格。A选项质量不是由供求直接决定；C选项生产成本影响供给但不是供求直接决定；D选项市场规模不是供求直接决定。本题涉及的经济学原理是供求关系对价格的影响，英语阅读技巧是理解“interact”这个词的含义。
15. Economic growth is often measured by...
A. Changes in inflation rates
B. The level of government spending
C. Increases in gross domestic product
D. Fluctuations in interest rates
18. During an economic recession, which of the following is likely to happen?
A. Increased employment
B. Higher economic growth
C. Decreased government spending
2. In a monopoly market, who sets the price?
A. The government.
B. The consumers.
C. The producer.
D. The competitors.
投资学第7版TestBank答案21
投资学第7版TestBank答案21Multiple Choice Questions1. Before expiration, the time value of an in the money call option is alwaysA) equal to zero.B) positive.C) negative.D) equal to the stock price minus the exercise price.E) none of the above.Answer: B Difficulty: EasyRationale: The difference between the actual option price and the intrinsic value is called the time value of the option.2. Before expiration, the time value of an in the money put option is alwaysA) equal to zero.B) negative.C) positive.D) equal to the stock price minus the exercise price.E) none of the above.Answer: C Difficulty: EasyRationale: The difference between the actual option price and the intrinsic value is called the time value of the option.3. Before expiration, the time value of an at the money call option is alwaysA) positive.B) equal to zero.C) negative.D) equal to the stock price minus the exercise price.E) none of the above.Answer: A Difficulty: EasyRationale: The difference between the actual option price and the intrinsic value is called the time value of the option.4. Before expiration, the time value of an at the money put option is alwaysA) equal to zero.B) equal to the stock price minus the exercise price.C) negative.D) positive.E) none of the above.Answer: D Difficulty: EasyRationale: The difference between the actual option price and the intrinsic value is called the time value of the option.5. A call option has an intrinsic value of zero if the option isA) at the money.B) out of the money.C) in the money.D) A and C.E) A and B.Answer: E Difficulty: EasyRationale: Intrinsic value can never be negative; thus it is set equal to zero for out of the money and at the money options.6. A put option has an intrinsic value of zero if the option isA) at the money.B) out of the money.C) in the money.D) A and C.E) A and B.Answer: E Difficulty: EasyRationale: Intrinsic value can never be negative; thus it is setequal to zero for out of the money and at the money options.7. Prior to expirationA) the intrinsic value of a call option is greater than its actual value.B) the intrinsic value of a call option is always positive.C) the actual value of call option is greater than the intrinsic value.D) the intrinsic value of a call option is always greater than its time value.E) none of the above.Answer: C Difficulty: ModerateRationale: Prior to expiration, any option will be selling for a positive price, thus the actual value is greater than the intrinsic value.8. Prior to expirationA) the intrinsic value of a put option is greater than its actual value.B) the intrinsic value of a put option is always positive.C) the actual value of put option is greater than the intrinsic value.D) the intrinsic value of a put option is always greater than its time value.E) none of the above.Answer: C Difficulty: ModerateRationale: Prior to expiration, any option will be selling for a positive price, thus the actual value is greater than the intrinsic value.9. If the stock price increases, the price of a put option on that stock __________ and thatof a call option __________.A) decreases, increasesB) decreases, decreasesC) increases, decreasesD) increases, increasesE) does not change, does not changeAnswer: A Difficulty: ModerateRationale: As stock prices increases, call options become more valuable (the owner can buy the stock at a bargain price). As stock prices increase, put options become less valuable (the owner can sell the stock at a price less than market price).10. If the stock price decreases, the price of a put option on that stock __________ and thatof a call option __________.A) decreases, increasesB) decreases, decreasesC) increases, decreasesD) increases, increasesE) does not change, does not changeAnswer: C Difficulty: ModerateRationale: As stock prices decreases, call options become less valuable (the owner can buy the stock at a bargain price). As stock prices decreases, put options become more valuable (the owner can sell the stock at a price less than market price).11. Other things equal, the price of a stock call option is positively correlated with thefollowing factors exceptA) the stock price.B) the time to expiration.C) the stock volatility.D) the exercise price.E) none of the above.Answer: D Difficulty: ModerateRationale: The exercise price is negatively correlated with the call option price.12. Other things equal, the price of a stock put option is positively correlated with thefollowing factors exceptA) the stock price.B) the time to expiration.C) the stock volatility.D) the exercise price.E) none of the above.Answer: A Difficulty: ModerateRationale: The exercise price is negatively correlated with the stock price.13. The price of a stock put option is __________ correlated with the stock price and__________ correlated with the striking price.A) positively, positivelyB) negatively, positivelyC) negatively, negativelyD) positively, negativelyE) not, notAnswer: B Difficulty: ModerateRationale: The lower the stock price, the more valuable the call option. The higher the striking price, the more valuable the put option.14. The price of a stock call option is __________ correlated with the stock price and__________ correlated with the striking price.A) positively, positivelyB) negatively, positivelyC) negatively, negativelyD) positively, negativelyE) not, notAnswer: D Difficulty: ModerateRationale: The lower the stock price, the more valuable the call option. The higher the striking price, the more valuable the put option.15. All the inputs in the Black-Scholes Option Pricing Model are directly observable exceptA) the price of the underlying security.B) the risk free rate of interest.C) the time to expiration.D) the variance of returns of the underlying asset return.E) none of the above.Answer: D Difficulty: ModerateRationale: The variance of the returns of the underlying asset is not directly observable, but must be estimated from historical data, from scenario analysis, or from the prices of other options.16. Delta is defined asA) the change in the value of an option for a dollar change in the price of the underlyingasset.B) the change in the value of the underlying asset for a dollar change in the call price.C) the percentage change in the value of an option for a one percent change in the valueof the underlying asset.D) the change in the volatility of the underlying stock price.E) none of the above.Answer: A Difficulty: ModerateRationale: An option's hedge ratio (delta) is the change in the price of an option for $1 increase in the stock price.17. A hedge ratio of 0.70 implies that a hedged portfolio should consist ofA) long 0.70 calls for each short stock.B) short 0.70 calls for each long stock.C) long 0.70 shares for each short call.D) long 0.70 shares for each long call.E) none of the above.Answer: C Difficulty: ModerateRationale: The hedge ratio is the slope of the option value as a function of the stock value. A slope of 0.70 means that as the stock increases in value by $1, the optionincreases by approximately $0.70. Thus, for every call written, 0.70 shares of stock would be needed to hedge the investor's portfolio.18. A hedge ratio for a call option is ________ and a hedge ratio for a put option is ______.A) negative, positiveB) negative, negativeC) positive, negativeD) positive, positiveE) zero, zeroAnswer: C Difficulty: ModerateRationale: Call option hedge ratios must be positive and less than 1.0, and put option ratios must be negative, with a smaller absolute value than 1.0.19. A hedge ratio for a call is alwaysA) equal to one.B) greater than one.C) between zero and oneD) between minus one and zero.E) of no restricted valueAnswer: C Difficulty: ModerateRationale: See rationale for test bank question 21.18.20. A hedge ratio for a put is alwaysA) equal to one.B) greater than one.C) between zero and oneD) between minus one and zero.E) of no restricted valueAnswer: D Difficulty: ModerateRationale: See rationale for test bank question 21.18.21. The dollar change in the value of a stock call option is alwaysA) lower than the dollar change in the value of the stock.B) higher than the dollar change in the value of the stock.C) negatively correlated with the change in the value of the stock.D) B and C.E) A and C.Answer: A Difficulty: ModerateRationale: The slope of the call option valuation function is less than one.22. The percentage change in the stock call option price divided by the percentage change inthe stock price is calledA) the elasticity of the option.B) the delta of the option.C) the theta of the option.D) the gamma of the option.E) none of the above.Answer: A Difficulty: ModerateRationale: Option price elasticity measures the percent change in the option price as a function of the percent change in the stock price.23. The elasticity of a stock call option is alwaysA) greater than one.B) smaller than one.C) negative.D) infinite.E) none of the above.Answer: A Difficulty: ModerateRationale: Option prices are much more volatile than stock prices, as option premiums are much lower than stock prices.24. The elasticity of a stock put option is alwaysA) positive.B) smaller than one.C) negativeD) infiniteE) none of the above.Answer: C Difficulty: ModerateRationale: As put options become more valuable as stock prices decline, the elasticity ofa put option must be negative.25. Portfolio A consists of 150 shares of stock and 300 calls on that stock. Portfolio Bconsists of 575 shares of stock. The call delta is 0.7. Whichportfolio has a higher dollar exposure to a change in stock price?A) Portfolio BB) Portfolio AC) The two portfolios have the same exposureD) A if the stock price increases and B if it decreases.E) B if the stock price decreases and A if it increases.Answer: A Difficulty: DifficultRationale: 300 calls (0.7) = 210 shares + 150 shares = 360 shares; 575 shares = 575 shares.26. Portfolio A consists of 500 shares of stock and 500 calls on that stock. Portfolio Bconsists of 800 shares of stock. The call delta is 0.6. Which portfolio has a higher dollar exposure to a change in stock price?A) Portfolio BB) Portfolio AC) The two portfolios have the same exposureD) A if the stock price increases and B if it decreases.E) B if the stock price decreases and A if it increases.Answer: C Difficulty: DifficultRationale: 500 calls (0.6) = 300 shares + 500 shares = 800 shares; 800 shares = 800 shares.27. Portfolio A consists of 400 shares of stock and 400 calls on that stock. Portfolio Bconsists of 500 shares of stock. The call delta is 0.5. Which portfolio has a higher dollar exposure to a change in stock price?A) Portfolio BB) Portfolio AC) The two portfolios have the same exposureD) A if the stock price increases and B if it decreases.E) B if the stock price decreases and A if it increases.Answer: B Difficulty: DifficultRationale: 400 calls (0.5) = 200 shares + 400 shares = 600 shares; 500 shares = 500 shares.28. Portfolio A consists of 600 shares of stock and 300 calls on that stock. Portfolio Bconsists of 685 shares of stock. The call delta is 0.3. Which portfolio has a higher dollar exposure to a change in stock price?A) Portfolio BB) Portfolio AC) The two portfolios have the same exposureD) A if the stock price increases and B if it decreases.E) B if the stock price decreases and A if it increases.Answer: B Difficulty: DifficultRationale: 300 calls (0.3) = 90 shares + 600 shares = 690 shares; 685 shares = 685shares.29. A portfolio consists of 100 shares of stock and 1500 calls on that stock. If the hedgeratio for the call is 0.7, what would be the dollar change in the value of the portfolio in response to a one dollar decline in the stock price?A) +$700B) +$500C) -$1,150D) -$520E) none of the aboveAnswer: C Difficulty: DifficultRationale: -$100 + [-$1,500(0.7)] = -$1,150.30. A portfolio consists of 800 shares of stock and 100 calls on that stock. If the hedge ratiofor the call is 0.5. What would be the dollar change in the value of the portfolio inresponse to a one dollar decline in the stock price?A) +$700B) -$850C) -$580D) -$520E) none of the aboveAnswer: B Difficulty: DifficultRationale: -$800 + [-$100(0.5)] = -$850.31. A portfolio consists of 225 shares of stock and 300 calls on that stock. If the hedge ratiofor the call is 0.4, what would be the dollar change in the value of the portfolio inresponse to a one dollar decline in the stock price?A) -$345B) +$500C) -$580D) -$520E) none of the aboveAnswer: A Difficulty: DifficultRationale: -$225 + [-$300(0.4)] = -$345.32. A portfolio consists of 400 shares of stock and 200 calls on that stock. If the hedge ratiofor the call is 0.6, what would be the dollar change in the value of the portfolio inresponse to a one dollar decline in the stock price?A) +$700B) +$500C) -$580D) -$520E) none of the aboveAnswer: D Difficulty: DifficultRationale: -$400 + [-$200(0.6)] = -$520.33. If the hedge ratio for a stock call is 0.30, the hedge ratio for a put with the sameexpiration date and exercise price as the call would be ________.A) 0.70B) 0.30C) -0.70D) -0.30E) -.17Answer: C Difficulty: DifficultRationale: Call hedge ratio = N(d1); Put hedge ratio = N(d1) - 1; 0.3 - 1.0 = -0.7.34. If the hedge ratio for a stock call is 0.50, the hedge ratio for a put with the sameexpiration date and exercise price as the call would be ________.A) 0.30B) 0.50C) -0.60D) -0.50E) -.17Answer: D Difficulty: DifficultRationale: Call hedge ratio = N(d1); Put hedge ratio = N(d1) - 1; 0.5 - 1.0 = -0.5.35. If the hedge ratio for a stock call is 0.60, the hedge ratio for a put with the sameexpiration date and exercise price as the call would be _______.A) 0.60B) 0.40C) -0.60D) -0.40E) -.17Answer: D Difficulty: DifficultRationale: Call hedge ratio = N(d1); Put hedge ratio = N(d1) - 1; 0.6 - 1.0 = -0.4.36. If the hedge ratio for a stock call is 0.70, the hedge ratio for a put with the sameexpiration date and exercise price as the call would be _______.A) 0.70B) 0.30C) -0.70D) -0.30E) -.17Answer: D Difficulty: DifficultRationale: Call hedge ratio = N(d1); Put hedge ratio = N(d1) - 1; 0.7 - 1.0 = -0.3.37. A put option is currently selling for $6 with an exercise price of $50. If the hedge ratiofor the put is -0.30 and the stock is currently selling for $46, what is the elasticity of the put?A) 2.76B) 2.30C) -7.67D) -2.76E) -2.30Answer: E Difficulty: DifficultRationale: % stock price change = ($47 - $46)/$46 = 0.021739; % option price change = $5.70 - $6.00)/$6 = - 0.05; - 0.05/0.021739 = - 2.30.38. A put option on the S&P 500 index will best protect ________A) a portfolio of 100 shares of IBM stock.B) a portfolio of 50 bonds.C) a portfolio that corresponds to the S&P 500.D) a portfolio of 50 shares of AT&T and 50 shares of Xerox stocks.E) a portfolio that replicates the Dow.Answer: C Difficulty: EasyRationale: The S&P 500 index is more like a portfolio that corresponds to the S&P 500 and thus is more protective of sucha portfolio than of any of the other assets.39. Higher dividend payout policies have a __________ impact on the value of the call anda __________ impact on the value of the put.A) negative, negativeB) positive, positiveC) positive, negativeD) negative, positiveE) zero, zeroAnswer: D Difficulty: ModerateRationale: Dividends lower the expected stock price, and thus lower the current call option value and increase the current put option value.40. Lower dividend payout policies have a __________ impact on the value of the call anda __________ impact on the value of the put.A) negative, negativeB) positive, positiveC) positive, negativeD) negative, positiveE) zero, zeroAnswer: C Difficulty: ModerateRationale: Dividends lower the expected stock price, and thus lower the current call option value and increase the current put option value.41. A one dollar decrease in a call option's exercise price would result in a(n) __________in the call option's value of __________ one dollar.A) increase, more thanB) decrease, more thanC) decrease, less thanD) increase, less thanE) increase, exactlyAnswer: D Difficulty: ModerateRationale: Option prices are less than stock prices, thus changes in stock prices (market or exercise) are greater (in absolute terms) than are changes in prices of options.42. Which one of the following variables influences the value of call options?I)Level of interest rates.II)Time to expiration of the option.III)Dividend yield of underlying stock.IV)Stock price volatility.A) I and IV only.B) II and III only.C) I, II, and IV only.D) I, II, III, and IV.E) I, II and III only.Answer: D Difficulty: ModerateRationale: All of the above variables affect call option prices.43. Which one of the following variables influences the value of put options?I)Level of interest rates.II)Time to expiration of the option.III)Dividend yield of underlying stock.IV)Stock price volatility.A) I and IV only.B) II and III only.C) I, II, and IV only.D) I, II, III, and IV.E) I, II and III only.Answer: D Difficulty: ModerateRationale: All of the above variables affect put option prices.44. An American call option buyer on a non-dividend paying stock willA) always exercise the call as soon as it is in the money.B) only exercise the call when the stock price exceeds the previous highC) never exercise the call early.D) buy an offsetting put whenever the stock price drops below the strike price.E) none of the above.Answer: C Difficulty: ModerateRationale: An American call option buyer will not exercise early if the stock does not pay dividends; exercising forfeits the time value. Rather, the option buyer will sell the option to collectboth the intrinsic value and the time value.45. Relative to European puts, otherwise identical American put optionsA) are less valuable.B) are more valuable.C) are equal in value.D) will always be exercised earlier.E) none of the above.Answer: B Difficulty: ModerateRationale: It is valuable to exercise a put option early if the stock drops below athreshold price; thus American puts should sell for more than European puts.46. Use the two-state put option value in this problem. S O = $100; X = $120; the twopossibilities for S T are $150 and $80. The range of P across the two states is _____; the hedge ratio is _______.A) $0 and $40; -4/7B) $0 and $50; +4/7C) $0 and $40; +4/7D) $0 and $50; -4/7E) $20 and $40; +1/2Answer: A Difficulty: DifficultRationale: When S T = $150; P = $0; when S T =$80: P = $40; ($0 - $40)/($150 - $80) = -4/7.47. Use the Black-Scholes Option Pricing Model for the following problem. Given: S O =$70; X = $70; T = 70 days; r = 0.06 annually (0.0001648 daily); σ = 0.020506 (daily).No dividends will be paid before option expires. The value ofthe call option is_______.A) $10.16.B) $5.16.C) $0.00.D) $2.16.E) none of the above.Answer: B Difficulty: DifficultRationale: d2 = 0.1530277 - (0.020506)(70)1/2 = -0.01853781; N(d1) = 0.5600; N(d2) = 0.4919; C = 0.5600($70) - $70[e-(0.0001648)(70)]0.4919 = $5.16.48. Empirical tests of the Black-Scholes option pricing modelA) show that the model generates values fairly close to the prices at which optionstrade.B) show that the model tends to overvalue deep in the money calls and undervaluedeep out of the money calls.C) indicate that the mispricing that does occur is due to the possible early exercise ofAmerican options on dividend-paying stocks.D) A and C.E) A, B, and C.Answer: D Difficulty: DifficultRationale: Studies have shown that the model tends to undervalue deep in the money calls and to overvalue deep out of the money calls. The other statements are true.49. Options sellers who are delta-hedging would most likelyA) sell when markets are fallingB) buy when markets are risingC) both A and B.D) sell whether markets are falling or rising.E) buy whether markets are falling or rising.Answer: C Difficulty: ModerateUse the following to answer questions 50-54:An American-style call option with six months to maturity has a strike price of $35. The underlying stock now sells for $43. The call premium is $12.50. What is the intrinsic value of the call?A) $12B) $8C) $0D) $23E) none of the above.Answer: B Difficulty: EasyRationale: 43 - 35 = $8.51. What is the time value of the call?A) $8B) $12C) $0D) $4E) cannot be determined without more information.Answer: D Difficulty: ModerateRationale: 12 - (43 - 35) = $4.52. If the option has delta of .5, what is its elasticity?A) 4.17B) 2.32C) 1.79D) 0.5E) 1.5Answer: C Difficulty: DifficultRationale: [(12.50 - 12)/12] / [(44 - 43)/43] = 1.79.53. If the risk-free rate is 6%, what should be the value of a put option on the same stockwith the same strike price and expiration date?A) $3.00B) $2.02C) $12.00D) $5.25E) $8.00Answer: A Difficulty: DifficultRationale: P = 12 - 43 + 35/(1.06).5; P = $3.0054. If the company unexpectedly announces it will pay its first-ever dividend 3 months fromtoday, you would expect thatA) the call price would increase.B) the call price would decrease.C) the call price would not change.D) the put price would decrease.E) the put price would not change.Answer: B Difficulty: ModerateRationale: As an approximation, subtract the present value of the dividend from the stock price and recompute the Black-Scholes value with this adjusted stock price. Since the stock price is lower, the option value will be lower.55. Since deltas change as stock values change, portfolio hedge ratios must be constantlyupdated in active markets. This process is referred to asA) portfolio insurance.B) rebalancing.C) option elasticity.D) gamma hedging.E) dynamic hedging.Answer: E Difficulty: ModerateRationale: Dynamic hedgers will convert equity into cash in market declines to adjust for changes in option deltas.56. In volatile markets, dynamic hedging may be difficult to implement becauseA) prices move too quickly for effective rebalancing.B) as volatility increases, historical deltas are too low.C) price quotes may be delayed so that correct hedge ratios cannot be computed.D) volatile markets may cause trading halts.E) all of the above.Answer: E Difficulty: EasyRationale: All of the above correctly describe the problems associated with dynamic hedging in volatile markets.57. Rubinstein (1994) observed that the performance of the Black-Scholes model haddeteriorated in recent years, and he attributed this toA) investor fears of another market crash.B) higher than normal dividend payouts.C) early exercise of American call options.D) decreases in transaction costs.E) none of the above.Answer: A Difficulty: ModerateRationale: Options on the same stock with the same strike price should have the same implied volatility, but the exhibit progressively different implied volatilities.Rubinstein believes this is due to fear of another marketcrash.58. The time value of a call option isI)the difference between the option's price and the value it would have if it wereexpiring immediately.II)the same as the present value of the option's expected future cash flows.III)the difference between the option's price and its expected future value.IV)different from the usual time value of money concept.A) IB) I and IIC) II and IIID) IIE) I and IVAnswer: E Difficulty: EasyRationale: The time value of an option is described by I, and is different from the time value of money concept frequently used in finance.59. The time value of a put option isI)the difference between the option's price and the value it would have if it wereexpiring immediately.II)the same as the present value of the option's expected future cash flows.III)the difference between the option's price and its expected future value.IV)different from the usual time value of money concept.A) IB) I and IIC) II and IIID) IIE) I and IVAnswer: E Difficulty: EasyRationale: The time value of an option is described by I, and is different from the time value of money concept frequently used in finance.60. You purchased a call option for a premium of $4. The call has an exercise price of $29and is expiring today. The current stock price is $31. What would be your best course of action?A) Exercise the call because the stock price is greater than the exercise price.B) Do not exercise the call because the stock price is greater than the exercise price.C) Do not exercise the call because the difference between the exercise price and thestock price is not enough to cover the amount of the premium.D) Exercise the call to get a positive net return on the investment.E) Do not exercise the call to avoid a negative net return on the investment.Answer: A Difficulty: ModerateRationale: If you exercise the call, your return will be ($31-29-4)/$4 = -50%. But if you don't exercise the call your return will be -$4/4 = -100%.61. As the underlying stock's price increased, the call option valuation function's slopeapproachesA) zero.B) one.C) two times the value of the stock.D) one-half time s the value of the stock.E) infinityAnswer: B Difficulty: ModerateRationale: As the stock price increases the value of the call option increases in price one for one with the stock price. The option is very likely to be exercised.。
衍生品市场基础10章
Parity and Other Option Relationships
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
IBM Option Quotes
Table 9.1 IBM option prices, dollars per share, October 16, 2007. The closing price of IBM on that day was $119.60.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
9-10
Properties of Option Prices (cont’d)
• Different strike prices (K1 < K2 < K3), for both European and American options
Table 9.2 Payoff table demonstrating that there is an arbitrage opportunity unless −C(St , Qt , T − t) + P(St , Qt, T − t) + F P t ,T (S) − FP t ,T (Q) = 0.
C(K1 ) C(K2 ) K2 K1
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
9-11
Properties of Option Prices (cont’d)
• Different strike prices (K1 < K2 < K3), for both European and American options
公司理财英文版第七章
7-10
Example 7.1
• Find present values based on the payment period
– – – – How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? B = 70[1 – 1/(1.08)14] / .08 + 1,000 / (1.08)14 = 917.56 – Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -917.56
– – – – Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?) – YTM = 4%*2 = 8%
– Why? Higher coupon rate causes value above par – Price above par value, called a premium bond
7-9
The Bond Pricing Equation
1 1 (1 r) t Bond Value C r FV t (1 r)
• Bond Value = PV of coupons + PV of par • Bond Value = PV of annuity + PV of lump sum • As interest rates increase, present values decrease • So, as interest rates increase, bond prices decrease and vice versa
{财务管理财务知识}高盛财经词典英汉对照
{财务管理财务知识}高盛财经词典英汉对照ActualReturn 实际回报一名投资者的实际收益或损失，可用以下公式表示：预期回报加上公司特殊消息及总体经济消息Actuary 精算保险公司的专业人员，负责评估申请人及其医疗纪录，以预测申请人的寿命Acquisition 收购一家公司收购另一家公司的多数股权AcquisitionPremium 收购溢价收购一家公司的实际成本与该公司收购前估值之间的差额AffiliatedCompanies 联营公司一家公司拥有另一家公司少数权益（低于50%）的情况，或指两家公司之间存在某些关联AffiliatedPerson 关联人士能影响一家企业活动的人士，包括董事、行政人员及股东等AfterHoursTrading 收盘后交易主要大型交易所正常交易时间以外进行的买卖交易AfterTaxOperatingIne-ATOI 税后营运收入一家公司除税后的总营运收入。
计算方法为将总营运收入减税项AfterTaxProfitMargin 税后利润率一种财务比率，计算方法为税后净利润除以净销售额AfterTheBell 收盘铃后股票市场收盘后Agent 代理人1.为客户进行证券买卖的人士或机构2.持有销售保险许可证的人士3.代表证券经纪行或发行人向公众出售或尝试出售证券的证券销售人员AgencyBonds 机构债券由政府机构发行的债券AgencyCross 交叉代理人一项由一名代理人同时代表买方与卖方的交易，也称为撍卮砣藬("DualAgency"。
AgencyProblem 代理问题债券人、股东及管理人员因目标不同而产生的利益冲突AgencySecurities 机构证券由美国政府支持的企业发行的低风险债务AggregateExercisePrice 总行使价格出售或买入期权的行使价格乘以合约金额AggressiveAccounting 激进会计不当地编制损益表以取悦投资者及提高股价法AggressiveInvestmentStrategy 进取投资策略投资组合经理尝试争取最高的回报。
罗斯《公司理财》第9版精要版英文原书课后部分章节答案
CH5 11，13，18，19，2011.To find the PV of a lump sum, we use:PV = FV / (1 + r)tPV = $1,000,000 / (1.10)80 = $488.1913.To answer this question, we can use either the FV or the PV formula. Both will give the sameanswer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for r, we get:r = (FV / PV)1 / t– 1r = ($1,260,000 / $150)1/112– 1 = .0840 or 8.40%To find the FV of the first prize, we use:FV = PV(1 + r)tFV = $1,260,000(1.0840)33 = $18,056,409.9418.To find the FV of a lump sum, we use:FV = PV(1 + r)tFV = $4,000(1.11)45 = $438,120.97FV = $4,000(1.11)35 = $154,299.40Better start early!19. We need to find the FV of a lump sum. However, the money will only be invested for six years,so the number of periods is six.FV = PV(1 + r)tFV = $20,000(1.084)6 = $32,449.3320.To answer this question, we can use either the FV or the PV formula. Both will give the sameanswer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for t, we get:t = ln(FV / PV) / ln(1 + r)t = ln($75,000 / $10,000) / ln(1.11) = 19.31So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. Fro m now, you’ll wait:2 years + 19.31 years = 21.31 yearsCH6 16，24，27，42，5816.For this problem, we simply need to find the FV of a lump sum using the equation:FV = PV(1 + r)tIt is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get:FV = $2,100[1 + (.084/2)]34 = $8,505.9324.This problem requires us to find the FVA. The equation to find the FVA is:FVA = C{[(1 + r)t– 1] / r}FVA = $300[{[1 + (.10/12) ]360 – 1} / (.10/12)] = $678,146.3827.The cash flows are annual and the compounding period is quarterly, so we need to calculate theEAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get:EAR = [1 + (APR / m)]m– 1EAR = [1 + (.11/4)]4– 1 = .1146 or 11.46%And now we use the EAR to find the PV of each cash flow as a lump sum and add them together: PV = $725 / 1.1146 + $980 / 1.11462 + $1,360 / 1.11464 = $2,320.3642.The amount of principal paid on the loan is the PV of the monthly payments you make. So, thepresent value of the $1,150 monthly payments is:PVA = $1,150[(1 – {1 / [1 + (.0635/12)]}360) / (.0635/12)] = $184,817.42The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is:$240,000 – 184,817.42 = $55,182.58This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be:Balloon payment = $55,182.58[1 + (.0635/12)]360 = $368,936.5458.To answer this question, we should find the PV of both options, and compare them. Since we arepurchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is thesame as the interest rate of the loan. The PV of leasing is:PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is:PV = $23,000 / [1 + (.07/12)]12(3) = $18,654.82The PV of the decision to purchase is:$32,000 – 18,654.82 = $13,345.18In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be:$32,000 – PV of resale price = $14,672.91PV of resale price = $17,327.09The resale price that would make the PV of the lease versus buy decision is the FV of this value, so:Breakeven resale price = $17,327.09[1 + (.07/12)]12(3) = $21,363.01CH7 3，18，21，22，313.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice thisproblem assumes an annual coupon. The price of the bond will be:P = $75({1 – [1/(1 + .0875)]10 } / .0875) + $1,000[1 / (1 + .0875)10] = $918.89We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:PVIF R,t = 1 / (1 + r)twhich stands for Present Value Interest FactorPVIFA R,t= ({1 – [1/(1 + r)]t } / r )which stands for Present Value Interest Factor of an AnnuityThese abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key.18.The bond price equation for this bond is:P0 = $1,068 = $46(PVIFA R%,18) + $1,000(PVIF R%,18)Using a spreadsheet, financial calculator, or trial and error we find:R = 4.06%This is the semiannual interest rate, so the YTM is:YTM = 2 4.06% = 8.12%The current yield is:Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61%The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter:Effective annual yield = (1 + 0.0406)2– 1 = .0829 or 8.29%20. Accrued interest is the coupon payment for the period times the fraction of the period that haspassed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $74/2 × 2/6 = $12.33And we calculate the clean price as:Clean price = Dirty price – Accrued interest = $968 – 12.33 = $955.6721. Accrued interest is the coupon payment for the period times the fraction of the period that haspassed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $68/2 × 4/6 = $22.67And we calculate the dirty price as:Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.6722.To find the number of years to maturity for the bond, we need to find the price of the bond. Sincewe already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P0P0 = $80/.0755 = $1,059.60Now that we have the price of the bond, the bond price equation is:P = $1,059.60 = $80[(1 – (1/1.072)t ) / .072 ] + $1,000/1.072tWe can solve this equation for t as follows:$1,059.60(1.072)t = $1,111.11(1.072)t– 1,111.11 + 1,000111.11 = 51.51(1.072)t2.1570 = 1.072tt = log 2.1570 / log 1.072 = 11.06 11 yearsThe bond has 11 years to maturity.31.The price of any bond (or financial instrument) is the PV of the future cash flows. Even thoughBond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is:P M= $1,100(PVIFA3.5%,16)(PVIF3.5%,12) + $1,400(PVIFA3.5%,12)(PVIF3.5%,28) + $20,000(PVIF3.5%,40)P M= $19,018.78Notice that for the coupon payments of $1,400, we found the PVA for the coupon payments, and then discounted the lump sum back to today.Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par, or:P N= $20,000(PVIF3.5%,40) = $5,051.45CH8 4，18，20，22，24ing the constant growth model, we find the price of the stock today is:P0 = D1 / (R– g) = $3.04 / (.11 – .038) = $42.2218.The price of a share of preferred stock is the dividend payment divided by the required return.We know the dividend payment in Year 20, so we can find the price of the stock in Year 19, one year before the first dividend payment. Doing so, we get:P19 = $20.00 / .064P19 = $312.50The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = $312.50 / (1.064)19P0 = $96.1520.We can use the two-stage dividend growth model for this problem, which is:P0 = [D0(1 + g1)/(R –g1)]{1 – [(1 + g1)/(1 + R)]T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R –g2)]P0= [$1.25(1.28)/(.13 – .28)][1 – (1.28/1.13)8] + [(1.28)/(1.13)]8[$1.25(1.06)/(.13 – .06)]P0= $69.5522.We are asked to find the dividend yield and capital gains yield for each of the stocks. All of thestocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield.W: P0 = D0(1 + g) / (R–g) = $4.50(1.10)/(.19 – .10) = $55.00Dividend yield = D1/P0 = $4.50(1.10)/$55.00 = .09 or 9%Capital gains yield = .19 – .09 = .10 or 10%X: P0 = D0(1 + g) / (R–g) = $4.50/(.19 – 0) = $23.68Dividend yield = D1/P0 = $4.50/$23.68 = .19 or 19%Capital gains yield = .19 – .19 = 0%Y: P0 = D0(1 + g) / (R–g) = $4.50(1 – .05)/(.19 + .05) = $17.81Dividend yield = D1/P0 = $4.50(0.95)/$17.81 = .24 or 24%Capital gains yield = .19 – .24 = –.05 or –5%Z: P2 = D2(1 + g) / (R–g) = D0(1 + g1)2(1 + g2)/(R–g2) = $4.50(1.20)2(1.12)/(.19 – .12) = $103.68P0 = $4.50 (1.20) / (1.19) + $4.50 (1.20)2/ (1.19)2 + $103.68 / (1.19)2 = $82.33Dividend yield = D1/P0 = $4.50(1.20)/$82.33 = .066 or 6.6%Capital gains yield = .19 – .066 = .124 or 12.4%In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time.24.Here we have a stock with supernormal growth, but the dividend growth changes every year forthe first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be:P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so:P0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.112 + $2.45(1.20)(1.15)(1.10)/1.113 + $65.08/1.113 P0 = $55.70CH9 3，4，6，9，153.Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 ofrecapturing the initial investment, so the payback for Project A is:Payback = 1 + ($21,000 / $25,000) = 1.84 yearsProject B has cash flows of:Cash flows = $14,000 + 17,000 + 24,000 = $55,000during this first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is:B: Payback = 3 + ($5,000 / $270,000) = 3.019 yearsUsing the payback criterion and a cutoff of 3 years, accept project A and reject project B.4.When we use discounted payback, we need to find the value of all cash flows today. The valuetoday of the project cash flows for the first four years is:Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21Value today of Year 2 cash flow = $5,300/1.142 = $4,078.18Value today of Year 3 cash flow = $6,100/1.143 = $4,117.33Value today of Year 4 cash flow = $7,400/1.144 = $4,381.39To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is:Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 yearsFor an initial cost of $10,000, the discounted payback is:Discounted payback = 2 + ($10,000 – 3,684.21 – 4,078.18)/$4,117.33 = 2.54 yearsNotice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback.If the initial cost is $13,000, the discounted payback is:Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years6.Our definition of AAR is the average net income divided by the average book value. The averagenet income for this project is:Average net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325And the average book value is:Average book value = ($15,000,000 + 0) / 2 = $7,500,000So, the AAR for this project is:AAR = Average net income / Average book value = $1,836,325 / $7,500,000 = .2448 or 24.48%9.The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cashinflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA8%, 9) = $40,036.31At an 8 percent required return, the NPV is positive, so we would accept the project.The equation for the NPV of the project at a 20 percent required return is:NPV = –$138,000 + $28,500(PVIFA20%, 9) = –$23,117.45At a 20 percent required return, the NPV is negative, so we would reject the project.We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is:0 = –$138,000 + $28,500(PVIFA IRR, 9)IRR = 14.59%15.The profitability index is defined as the PV of the cash inflows divided by the PV of the cashoutflows. The equation for the profitability index at a required return of 10 percent is:PI = [$7,300/1.1 + $6,900/1.12 + $5,700/1.13] / $14,000 = 1.187The equation for the profitability index at a required return of 15 percent is:PI = [$7,300/1.15 + $6,900/1.152 + $5,700/1.153] / $14,000 = 1.094The equation for the profitability index at a required return of 22 percent is:PI = [$7,300/1.22 + $6,900/1.222 + $5,700/1.223] / $14,000 = 0.983We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI is less than one.CH10 9，13，14，17，18ing the tax shield approach to calculating OCF (Remember the approach is irrelevant; the finalanswer will be the same no matter which of the four methods you use.), we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = ($2,650,000 – 840,000)(1 – 0.35) + 0.35($3,900,000/3)OCF = $1,631,50013.First we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation = $560,000/5Annual depreciation = $112,000Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:Aftertax salvage value = MV + (BV – MV)t cVery often the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:Aftertax salvage value = MV + (0 – MV)t cAftertax salvage value = MV(1 – t c)We will use this equation to find the aftertax salvage value since we know the book value is zero.So, the aftertax salvage value is:Aftertax salvage value = $85,000(1 – 0.34)Aftertax salvage value = $56,100Using the tax shield approach, we find the OCF for the project is:OCF = $165,000(1 – 0.34) + 0.34($112,000)OCF = $146,980Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.NPV = –$560,000 – 29,000 + $146,980(PVIFA10%,5) + [($56,100 + 29,000) / 1.105]NPV = $21,010.2414.First we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation charge = $720,000/5Annual depreciation charge = $144,000The aftertax salvage value of the equipment is:Aftertax salvage value = $75,000(1 – 0.35)Aftertax salvage value = $48,750Using the tax shield approach, the OCF is:OCF = $260,000(1 – 0.35) + 0.35($144,000)OCF = $219,400Now we can find the project IRR. There is an unusual feature that is a part of this project.Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –$720,000 + 110,000 + $219,400(PVIFA IRR%,5) + [($48,750 – 110,000) / (1+IRR)5]IRR = 21.65%17.We will need the aftertax salvage value of the equipment to compute the EAC. Even though theequipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:Both cases: aftertax salvage value = $40,000(1 – 0.35) = $26,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:OCF = –$67,000(1 – 0.35) + 0.35($290,000/3) = –9,716.67NPV = –$290,000 – $9,716.67(PVIFA10%,3) + ($26,000/1.103) = –$294,629.73EAC = –$294,629.73 / (PVIFA10%,3) = –$118,474.97And the OCF and NPV for Techron II is:OCF = –$35,000(1 – 0.35) + 0.35($510,000/5) = $12,950NPV = –$510,000 + $12,950(PVIFA10%,5) + ($26,000/1.105) = –$444,765.36EAC = –$444,765.36 / (PVIFA10%,5) = –$117,327.98The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.18.To find the bid price, we need to calculate all other cash flows for the project, and then solve forthe bid price. The aftertax salvage value of the equipment is:Aftertax salvage value = $70,000(1 – 0.35) = $45,500Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is:NPV = 0 = –$940,000 – 75,000 + OCF(PVIFA12%,5) + [($75,000 + 45,500) / 1.125]Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:OCF = $946,625.06 / PVIFA12%,5 = $262,603.01The easiest way to calculate the bid price is the tax shield approach, so:OCF = $262,603.01 = [(P – v)Q – FC ](1 – t c) + t c D$262,603.01 = [(P – $9.25)(185,000) – $305,000 ](1 – 0.35) + 0.35($940,000/5)P = $12.54CH14 6、9、20、23、246. The pretax cost of debt is the YTM of the company’s bonds, so:P0 = $1,070 = $35(PVIFA R%,30) + $1,000(PVIF R%,30)R = 3.137%YTM = 2 × 3.137% = 6.27%And the aftertax cost of debt is:R D = .0627(1 – .35) = .0408 or 4.08%9. ing the equation to calculate the WACC, we find:WACC = .60(.14) + .05(.06) + .35(.08)(1 – .35) = .1052 or 10.52%b.Since interest is tax deductible and dividends are not, we must look at the after-tax cost ofdebt, which is:.08(1 – .35) = .0520 or 5.20%Hence, on an after-tax basis, debt is cheaper than the preferred stock.ing the debt-equity ratio to calculate the WACC, we find:WACC = (.90/1.90)(.048) + (1/1.90)(.13) = .0912 or 9.12%Since the project is riskier than the company, we need to adjust the project discount rate for the additional risk. Using the subjective risk factor given, we find:Project discount rate = 9.12% + 2.00% = 11.12%We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus the PV of the cash inflows. Since we have the costs, we just need to find the PV of inflows. The cash inflows are a growing perpetuity. If you remember, the equation for the PV of a growing perpetuity is the same as the dividend growth equation, so:PV of future CF = $2,700,000/(.1112 – .04) = $37,943,787The project should only be undertaken if its cost is less than $37,943,787 since costs less than this amount will result in a positive NPV.23. ing the dividend discount model, the cost of equity is:R E = [(0.80)(1.05)/$61] + .05R E = .0638 or 6.38%ing the CAPM, the cost of equity is:R E = .055 + 1.50(.1200 – .0550)R E = .1525 or 15.25%c.When using the dividend growth model or the CAPM, you must remember that both areestimates for the cost of equity. Additionally, and perhaps more importantly, each methodof estimating the cost of equity depends upon different assumptions.Challenge24.We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of thecompany has a weight for long-term debt and a weight for accounts payable. We can use the weight given for accounts payable to calculate the weight of accounts payable and the weight of long-term debt. The weight of each will be:Accounts payable weight = .20/1.20 = .17Long-term debt weight = 1/1.20 = .83Since the accounts payable has the same cost as the overall WACC, we can write the equation for the WACC as:WACC = (1/1.7)(.14) + (0.7/1.7)[(.20/1.2)WACC + (1/1.2)(.08)(1 – .35)]Solving for WACC, we find:WACC = .0824 + .4118[(.20/1.2)WACC + .0433]WACC = .0824 + (.0686)WACC + .0178(.9314)WACC = .1002WACC = .1076 or 10.76%We will use basically the same equation to calculate the weighted average flotation cost, except we will use the flotation cost for each form of financing. Doing so, we get:Flotation costs = (1/1.7)(.08) + (0.7/1.7)[(.20/1.2)(0) + (1/1.2)(.04)] = .0608 or 6.08%The total amount we need to raise to fund the new equipment will be:Amount raised cost = $45,000,000/(1 – .0608)Amount raised = $47,912,317Since the cash flows go to perpetuity, we can calculate the present value using the equation for the PV of a perpetuity. The NPV is:NPV = –$47,912,317 + ($6,200,000/.1076)NPV = $9,719,777CH16 1，4，12，14，171. a. A table outlining the income statement for the three possible states of the economy isshown below. The EPS is the net income divided by the 5,000 shares outstanding. The lastrow shows the percentage change in EPS the company will experience in a recession or anexpansion economy.Recession Normal ExpansionEBIT $14,000 $28,000 $36,400Interest 0 0 0NI $14,000 $28,000 $36,400EPS $ 2.80 $ 5.60 $ 7.28%∆EPS –50 –––+30b.If the company undergoes the proposed recapitalization, it will repurchase:Share price = Equity / Shares outstandingShare price = $250,000/5,000Share price = $50Shares repurchased = Debt issued / Share priceShares repurchased =$90,000/$50Shares repurchased = 1,800The interest payment each year under all three scenarios will be:Interest payment = $90,000(.07) = $6,300The last row shows the percentage change in EPS the company will experience in arecession or an expansion economy under the proposed recapitalization.Recession Normal ExpansionEBIT $14,000 $28,000 $36,400Interest 6,300 6,300 6,300NI $7,700 $21,700 $30,100EPS $2.41 $ 6.78 $9.41%∆EPS –64.52 –––+38.714. a.Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax.The EPS under this capitalization will be:EPS = $350,000/160,000 sharesEPS = $2.19Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so:NI = $500,000 – .08($2,800,000)NI = $126,000And the EPS will be:EPS = $126,000/80,000 sharesEPS = $1.58Plan I has the higher EPS when EBIT is $350,000.b.Under Plan I, the net income is $500,000 and the EPS is:EPS = $500,000/160,000 sharesEPS = $3.13Under Plan II, the net income is:NI = $500,000 – .08($2,800,000)NI = $276,000And the EPS is:EPS = $276,000/80,000 sharesEPS = $3.45Plan II has the higher EPS when EBIT is $500,000.c.To find the breakeven EBIT for two different capital structures, we simply set the equationsfor EPS equal to each other and solve for EBIT. The breakeven EBIT is:EBIT/160,000 = [EBIT – .08($2,800,000)]/80,000EBIT = $448,00012. a.With the information provided, we can use the equation for calculating WACC to find thecost of equity. The equation for WACC is:WACC = (E/V)R E + (D/V)R D(1 – t C)The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, soWACC = .10 = (1/2.5)R E + (1.5/2.5)(.07)(1 – .35)R E = .1818 or 18.18%b.To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:R E = R U + (R U– R D)(D/E)(1 – t C).1818 = R U + (R U– .07)(1.5)(1 – .35)R U = .1266 or 12.66%c.To find the cost of equity under different capital structures, we can again use M&MProposition II with taxes. With a debt-equity ratio of 2, the cost of equity is:R E = R U + (R U– R D)(D/E)(1 – t C)R E = .1266 + (.1266 – .07)(2)(1 – .35)R E = .2001 or 20.01%With a debt-equity ratio of 1.0, the cost of equity is:R E = .1266 + (.1266 – .07)(1)(1 – .35)R E = .1634 or 16.34%And with a debt-equity ratio of 0, the cost of equity is:R E = .1266 + (.1266 – .07)(0)(1 – .35)R E = R U = .1266 or 12.66%14. a.The value of the unlevered firm is:V U = EBIT(1 – t C)/R UV U = $92,000(1 – .35)/.15V U = $398,666.67b.The value of the levered firm is:V U = V U + t C DV U = $398,666.67 + .35($60,000)V U = $419,666.6717.With no debt, we are finding the value of an unlevered firm, so:V U = EBIT(1 – t C)/R UV U = $14,000(1 – .35)/.16V U = $56,875With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, one-half of the firm value is debt, so the value of the levered firm is:V L = V U + t C(D/V)V UV L = $56,875 + .35(.50)($56,875)V L = $66,828.13And with 100 percent debt, the value of the firm is:V L = V U + t C(D/V)V UV L = $56,875 + .35(1.0)($56,875)V L = $76,781.25c.The net cash flows is the present value of the average daily collections times the daily interest rate, minus the transaction cost per day, so:Net cash flow per day = $1,276,275(.0002) – $0.50(385)Net cash flow per day = $62.76The net cash flow per check is the net cash flow per day divided by the number of checksreceived per day, or:Net cash flow per check = $62.76/385Net cash flow per check = $0.16Alternatively, we could find the net cash flow per check as the number of days the system reduces collection time times the average check amount times the daily interest rate, minusthe transaction cost per check. Doing so, we confirm our previous answer as:Net cash flow per check = 3($1,105)(.0002) – $0.50Net cash flow per check = $0.16 per checkThis makes the total costs:Total costs = $18,900,000 + 56,320,000 = $75,220,000The flotation costs as a percentage of the amount raised is the total cost divided by the amount raised, so:Flotation cost percentage = $75,220,000/$180,780,000 = .4161 or 41.61%8.The number of rights needed per new share is:Number of rights needed = 120,000 old shares/25,000 new shares = 4.8 rights per new share.Using P RO as the rights-on price, and P S as the subscription price, we can express the price per share of the stock ex-rights as:P X = [NP RO + P S]/(N + 1)a.P X = [4.8($94) + $94]/(4.80 + 1) = $94.00; No change.b. P X = [4.8($94) + $90]/(4.80 + 1) = $93.31; Price drops by $0.69 per share.。
投资学(双语)11
2. Types of agreements
Best-efforts agreement
— make best effort to sell securities — return all the unsold shares to the issuing firm — commission — the risk rests with the issuing company — limited to less well known firms
Stop-loss Order (止损交易指令) — Stop Price (止损价格). 止损卖出交易指令，止损价格要低 于交易指令时的市价；止损买入交易指令，止损价格必须高 于交易指令的市价。 — 只能保证成交，不能保证价格。 Stop Limit Order (止损限价交易指令) — 同时注明止损价和限价的交易指令。
The Issuing and Selling of New Securities
1. The Role of Investment Bankers in IPO
Brokerage firm: channal money from investors to firms, do not claims on themselves. Consultant: how to price and sell new stock Underwriting: 当一家发行人通过证券市场筹集资金时，就 要聘请证券经营机构来帮助它销售证券。证券经营机构借 助自己在证券市场上的信誉和营业网点，在规定的发行有 效期限内将证券销售出去，这一过程称为承销。承销分为 包销（firm commitment）和代销（best-efforts agreement）。投资银行在两种承销方式中承担的风险有 所区别。 Syndicate and lead underwriter
投资学第六版第7章课后答案
1. Because very few securities will exhibit perfectly positive correlation,diversification will tend to reduce portfolio risk. Thus, for any given level of expected return, one would expect that portfolios will exhibit lower risk (lie further to the west in the feasible set) than individual portfolios (which will therefore lie to the east in the feasible set).2. Diversified portfolios are more efficient than individual securities. That is,diversified portfolios provide the investor with higher expected returns for given levels of risk and/or lower risk for given levels of expected return when compared with individual securities.Diagrammatically, individual securities will lie in the eastern portion of the feasible set. Hence they are dominated by diversified portfolios, which lie in the northwestern portion of the feasible set, including those on the efficient set.3. The macroeconomic forces that impact the U.S. economy tend to have a strongeffect on the earnings (and, hence, stock prices) of all domestic corporations, although the magnitude of this effect will vary among industries and specific firms.For example, a recession causes most companies to experience a downturn in earnings. While some companies may be more severely affected than others, nevertheless, the broad influence of a recession on general economic activity likely results in most companies' stocks performing poorly.Companies whose stocks would be expected to have a high positive covariance are auto and steel companies. When auto sales are strong (weak), the demand for steel generally rises (falls). The earnings of companies in both industries would rise and fall at roughly the same time and this movement would likely be anticipated by the earlier rise and fall of their stocks' prices.Companies whose stocks would be expected to have a low covariance are banks and gold mining firms. Rising interest rates and poor business conditions generally produce declining bank earnings. At the same time, a pessimistic economic outlook often causes investors to increase their demand for gold, which increases the price of gold and, therefore, the earnings of gold mining firms. The result is that the stock prices of banks and gold mining firms will not likely move in the same direction.4. It is the fact that all stocks do not have high positive covariances that causesdiversification to benefit the investor. That is, by diversifying, investors can reduce portfolio risk and thereby create more efficient portfolios. If stocks did have high positive covariances, then holding a well-diversified portfolio would not result in meaningful reductions in risk relative to holding individual securities.5. If the security in question had significant negative correlation with the rest of thesecurities in the portfolio, Mule might consider purchasing it even though it had anegative expected return. The diversifying nature of the security might reduce the risk of the portfolio sufficiently to make it attractive despite its inferior return potential.6. Given the expected returns and variance-covariance estimates for all securities, aninvestor can construct the efficient set. This information, combined with the unique risk-return preferences of the investor, allows the investor to determine his or her optimal portfolio. Diagrammatically, this optimal portfolio lies at the point of tangency between the investor's indifference curves and the efficient set.7. The standard deviation of a two-security portfolio is given by:[]σσσρσσp A A B B A B AB A B X X X X =++22122/In Dode's case:= [(.35)²(20)² + (.65)²(25)² + 2(.35)(.65)(20)(25)12]½= [49 + 264 + 22812]½The portfolio's standard deviation will be at a minimum when the correlation between securities A and B is -1.0. That is:= [49 + 264 - 228]½= 9.2%The portfolio's standard deviation will be at a maximum when the correlation between securities A and B is +1.0. That is: = [49 + 264 + 228]½= 23.3%17. The beta of a portfolio is defined as the weighted average of the componentsecurities' betas. In the case of Siggy's portfolio:ββP i i i X ==∑13= (.30 ⨯ 1.20) + (.50 ⨯ 1.05) + (.20 ⨯ 0.90)= 1.07Further, the standard deviation of a portfolio can be expressed as:()σβσσεp P I p =+22212/= [(1.07)²(18)² + (.30)²(5.0)² +(.50)²(8.0)²+ (.20)²(2.0)²]½= [370.9 + 2.3 + 16.0 + 0.2]½= [389.4]½ = 19.7%18.The total risk of a portfolio can be expressed as: σβσσεp p I p =+222Further, the unique risk (σεp 2) is the weighted average of the unique risks of the portfolio's individual securities. In the case of the first portfolio with four equal-weighted securities:()()σεp i 2221430025=⨯=∑..= 56.25 ⨯ 4 = 225.0Therefore the total risk of the first portfolio is:0.225)20()00.1(2221+⨯=σ= 625.01 = 25.0%In the case of the second portfolio with ten equal-weighted securities:()()σεp i 22211030010=⨯=∑..= 9.0 ⨯ 10 = 90.0Therefore the total risk of the second portfolio is:σ222210020900=⨯+(.)().= 490.02 = 22.1%。
商务英语阅读(第三版)Chapter_7
Technological Environment Technological environment hold new technological innovation, new products, the state of technology, the utilization of technology for maximum inputs and outputs, the obsolescence of technology and the dynamic changes that frequently occur in technologies which enable firms to get a competitive advantage.
leverage (para.20) upstream (para.20) stoke (para.21) traction (para.21) merit (para.24)
preempt (para.25) substantive (para.25) retainer (para.25) stringer (para.25) emanate (para.26)
An environment can be defined as anything which surrounds a system. Therefore, the business environment is anything which surrounds the business organization. It affects the decisions, strategies, processes and performance of the business. The micro environment consists of different types of stakeholders - customers, employees, suppliers, board of directors and creditors.
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
无风险利率与期权价格(二)
其次我们可从动态的角度考察，即考察一个均衡被打 破到另一个均衡的过程。在标的资产价格与利率呈负 相关时（如股票、债券等），当无风险利率提高时， 原有均衡被打破，为了使标的资产预期收益率提高， 均衡过程通常是通过同时降低标的资产的期初价格和 预期未来价格，只是前者的降幅更大来实现的。同时 贴现率也随之上升。对于看涨期权来说，两种效应都 将使期权价格下降，而对于看跌期权来说，前者效应 为正，后者为负，由于前者效应通常大于后者，因此 其净效应是看跌期权价格上升。
Effect of Variables on Option Pricing (Table 7.1, page 141)
Variable c
p
CP
S0 X
–+
– +
–+
– +
T(无红利)+ + + +
s
r(静态)
D
–++
–+ +
–++
–++
边际时间价值
在一般情况下（即剔除标的资产支付大量收益 这一特殊情况），由于有效期越长，标的资产 的风险就越大，空头亏损的风险也越大，因此 即使是欧式期权，有效期越长，其期权价格也 越高，即期权的边际时间价值（Marginal Time Value）为正值。
此外，期权的时间价值还受期权内在价值的影 响。以无收益资产看涨期权为例，当S=X e-rT时， 期权的时间价值最大。当S-X e-rT的绝对值增大 时，期权的时间价值是递减的，如下图所示。
时间价值
Xe-rT
S0
Question
假设A股票（无红利）的市价为9.05元，A股票 有两种看涨期权，其协议价格分别为X1=10元， X2=8元，它们的有效期都是1年，1年期无风险 利率为10%（连续复利）。这两种期权的内在 价值分别为0和1.81元。那么这两种期权的时间 价值谁高呢？
Chapter 7
Properties of Stock Option Prices
Notation
c : European call option price p : European put option price C : American Call option price P : American Put option price S0 :Stock price today ST :Stock price at time T X : Strike price T : Life of option s: Volatility of stock price D : Present value of dividends during option’s
情也况亏3二.8：1eS0.T1=-21=02元.2。1元则。期期权权1亏1亏2e损0.1等=2于.21期元权，2期。权2 情亏况3.8三1 ：e0.1S=T4=.82元1元。。则期期权权11亏亏损2e少0.1于=2期.2权1元2。，而期权2 由此可见，无论未来A股票价格是涨是跌还是平，
期权1均优于或等于期权2。显然，期权1的时间价 值应高于期权2。
有收益资产欧式看涨期权的内在价值等于S0-DXe-rT。
当标的资产市价低于协议价格时，期权多方是 不会行使期权的，因此期权的内在价值应大于 等于0。
期权的时间价值
期权的时间价值（Time Value）是指在期权有效 期内标的资产价格波动为期权持有者带来收益 的可能性所隐含的价值。显然，标的资产价格 的波动率越高，期权的时间价值就越大。
另一种情形
我 X期3们权=11再2的元来内。比在其较价它如值条下为件两0与种，上期期例权权相。3的同X内。1=在显10价然元值，， 虽然也等于0，但S-X e-rT却等于-1.81元。 通过同样的分析，我们也可以得出期权1 的时间价值应高于期权3的结论。综合这 三种期权，我们就可以得出无收益资产 看涨期权的时间价值在S=X e-rT点最大的 结论。
首先我们可以从比较静态的角度考察，即比较 不同利率水平下的两种均衡状态。如果状态1 的无风险利率较高，则标的资产的预期收益率 也应较高，这意味着对应于标的资产现在特定 的时市 由价 于（ 贴S现o）率，较未高来，预未期来价同格样[预E(期ST盈)]较利高的。现同值 就较低。这两种效应都将减少看跌期权的价值。 但对于看涨期权来说，前者将使期权价格上升， 而后者将使 期权价格下降。由于前者的效应大 于后者，因此对应于较高的无风险利率，看涨 期权的价格也较高。
假设这两种期权的时间价值相等，都等于2元， 则第一种期权的价格为2元，第二种期权的价 格为3.81元。那么让读者从中挑一种期权，你 们愿意挑哪一种呢？
分析
为了比较这两种期权，我们T0.=1）14=元1.。79则元期，权可持从有期者权可2中从获期利权（1中14获-8利3.81e0.1）=1.79元。期权1获利金额等于期权2。
大家应注意到，从两个角度得到的结论刚好相反。因 此我们在具体运用时要注意区别分析的角度。
American vs European Options
An American option is worth at least as much as the corresponding European option C c P p
但随着时间的延长，期权时间价值的增幅是递 减的,这边际时间价值递减规律。换个角度说， 对于到期日确定的期权来说，在其它条件不变 时，随着时间的流逝，其时间价值的减小是递 增的。这意味着，当时间流逝同样长度，期限 长的期权的时间价值减小幅度将小于期限短的 期权时间价值的减小幅度。
无风险利率与期权价格(一)
life r : Risk-free rate for maturity T with cont comp
期权价格的特性
期权价格(或者说价值)等于期权的内在价 值加上时间价值。
期权的内在价值
期权的内在价值（Intrinsic Value）是指多方行 使期权时可以获得的收益的现值。
无收益资产欧式看涨期权的内在价值等于S0Xe-rT.