公司理财精要版第10版 Chap05-06
Chap5财务管理,公司金融,罗斯第十版
5C-5
终值-基本公式
• FV = PV(1 + r)t
FV = 终值 PV = 现值 r = 每期利率，表示为百分比或小数 t = 期间数
• 终值利息因子= (1 + r)t
5C-6
复利的效应
• 单利 • 复利 • 考虑上一个例子
单利时的终值PV= 1,000 + 50 + 50 = 1,100 复利时的终值FV = 1,102.50 额外的2.5美元利息是在第一笔利息的基础之上 赚取的 .05(50) = 2.50
• • • • N=5 PV = -1,000 (本年支付1000元) FV = 1,200 (5年后收到1200元) CPT I/Y = 3.714%
5C-22
贴现率 – 例 2
• 假设你有10000美元可以投资6年，6年后 你的投资价值会翻倍。隐含报酬率是多少？
公式：r = (20,000 / 10,000)1/6 – 1 = .122462 = 12.25%
N = 10; I/Y = 7; FV = 19,671.51 CPT PV = -10,000
5C-16
现值-重要的关系式I
• 给定报酬率时，投资期数越长，则现值越少。
5年后将收到的500美元的现值是多少？10年呢？ 贴现率是10%。 5 年: N = 5; I/Y = 10; FV = 500 CPT PV = -310.46 10 年: N = 10; I/Y = 10; FV = 500 CPT PV = -192.77
• 使用公式:
t = ln(21,750 / 15,000) / ln(1.075) = 5.14 年
5C-29
公司理财精要版参考答案
公司理财精要版参考答案公司理财精要版参考答案在当今竞争激烈的商业环境中，公司理财是确保企业可持续发展的关键要素之一。
良好的财务管理和有效的资金运作可以帮助企业实现利润最大化，并提供稳定的财务基础。
本文将探讨公司理财的精要版参考答案，以帮助企业管理者更好地理解和应用这一概念。
1. 财务规划与预算控制公司理财的核心是财务规划和预算控制。
财务规划是指根据企业的长期战略目标和短期业务需求，制定合理的财务目标和计划。
预算控制则是通过制定详细的预算和监控实际支出，确保企业在财务方面的稳定和可持续发展。
企业管理者应该根据市场环境和经济状况，合理制定财务目标和预算，并根据实际情况及时调整。
2. 资金管理与风险控制资金管理是公司理财的重要组成部分。
企业应该合理规划和运用资金，确保流动性和盈利能力。
资金管理包括现金流量管理、资本结构管理和投资决策等。
同时，风险控制也是资金管理的重要内容。
企业应该通过风险评估和控制措施，降低经营风险，保护企业的财务安全。
3. 资本运作与融资策略资本运作是公司理财的重要环节。
企业可以通过资本运作来优化资本结构，提高资金利用效率。
资本运作包括股权融资、债务融资和资产重组等。
企业管理者应该根据企业的实际情况和市场需求，选择适合的融资策略，并合理运用各种融资工具。
4. 利润管理与税务筹划利润管理是公司理财的核心目标之一。
企业应该通过成本控制、价格管理和销售策略等手段，提高利润水平。
同时，税务筹划也是利润管理的重要组成部分。
企业应该合法合规地进行税务筹划，降低税务成本，提高税务效益。
5. 绩效评估与报告披露绩效评估是公司理财的重要环节。
企业应该建立科学合理的绩效评估体系，对企业的财务状况和经营业绩进行定期评估和报告。
同时，企业还应该及时披露财务信息，提高透明度和信任度，为投资者和利益相关者提供准确可靠的财务数据。
综上所述，公司理财是企业管理中不可或缺的一部分。
良好的财务管理和有效的资金运作可以帮助企业实现利润最大化，并提供稳定的财务基础。
公司理财第十版PPTChap.ppt
PV = -917.56
7-11
Interest Rate Risk
• Price Risk
▪ Change in price due to changes in interest rates ▪ Long-term bonds have more price risk than short-term
rates • Understand the term structure of interest rates
and the determinants of bond yields
7-2
Chapter Outline
• Bonds and Bond Valuation • More about Bond Features • Bond Ratings • Some Different Types of Bonds • Bond Markets • Inflation and Interest Rates • Determinants of Bond Yields
7-12
Figure 7.2
7-13
Computing Yield to Maturity
• Yield to Maturity (YTM) is the rate implied by the current bond price
• Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity
公司理财精要版第10版Chap05-06
5.1 终值和复利
$1.10(1.40)5 $1.10(1.40)4 $1.10(1.40)3 $1.10(1.40)2 $1.10 (1.40)
$1.10 $1.54 $2.16 $3.02 $4.23 $5.92
0
1
2
3
4
5
5.1 终值和复利
终值和复利计算
如果资金按复利（compound interest）计算，利息将被进 行再投资；而在单利（simple interest）情况下，利息没有 进行再投资，每期只赚取初始本金的利息。 $1×( 1 + r )2=1+2r+r2>1+2r
其中， $500 是利息 ($10,000 ×0.05)
$10,000 是本金偿还 ($10,000 × 1) $10,500 是本息合计，可由下式计算得到：
$10,500 = $10,000×(1.05) 该投资在期末的本息合计金额被称为终值。
5.1 终值和复利：多期投资的情形
终值和复利计算
《公司财务》 Corporate Finance
1-1
第三部分 折现现金流量估价
第5章 货币的时间价值 第6章 贴现现金流量估价
1-2
第5章 货币的时间价值
5.1 终值与复利 5.2 现值与贴现 5.3 现值与终值的进一步讲解
快速阅读
现金流量的终值是如何计算的? 现金流量的现值是如何计算的？ 如何计算投资回报率？ 如何计算一项投资的价值增长到期望值所需要的
PV CT (1 r)T
其中： CT 是在T期的现金流量 r 是适用的利率
1/(1 + r)T被叫做现值系数（Present Value Factor），缩写为PVIF(r,t)。 附录表A-2给出了“T期后得到的1元钱的现值（现值系数）”。
公司理财精要版第十版课后答案
CHAPTER 18VALUATION AND CAPITAL BUDGETING FOR THE LEVERED FIRM Answers to Concepts Review and Critical Thinking Questions1.APV is equal to the NPV of the project (i.e. the value of the project for an unlevered firm) plus theNPV of financing side effects.2. The WACC is based on a target debt level while the APV is based on the amount of debt.3.FTE uses levered cash flow and other methods use unlevered cash flow.4.The WACC method does not explicitly include the interest cash flows, but it does implicitly includethe interest cost in the WACC. If he insists that the interest payments are explicitly shown, you should use the FTE method.5. You can estimate the unlevered beta from a levered beta. The unlevered beta is the beta of the assetsof the firm; as such, it is a measure of the business risk. Note that the unlevered beta will always be lower than the levered beta (assuming the betas are positive). The difference is due to the leverage of the company. Thus, the second risk factor measured by a levered beta is the financial risk of the company.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. a.The maximum price that the company should be willing to pay for the fleet of cars with all-equity funding is the price that makes the NPV of the transaction equal to zero. The NPV equation for the project is:NPV = –Purchase Price + PV[(1 –t C )(EBTD)] + PV(Depreciation Tax Shield)If we let P equal the purchase price of the fleet, then the NPV is:NPV = –P + (1 – .35)($175,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5Setting the NPV equal to zero and solving for the purchase price, we find:0 = –P + (1 – .35)($175,000)PVIFA13%,5 + (.35)(P/5)PVIFA13%,5P = $400,085.06 + (P)(.35/5)PVIFA13%,5P = $400,085.06 + .2462P.7538P = $400,085.06P = $530,761.93b.The adjusted present value (APV) of a project equals the net present value of the project if itwere funded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:APV = NPV(All-Equity) + NPV(Financing Side Effects)So, the NPV of each part of the APV equation is:NPV(All-Equity)NPV = –Purchase Price + PV[(1 – t C )(EBTD)] + PV(Depreciation Tax Shield)The company paid $480,000 for the fleet of cars. Because this fleet will be fully depreciated over five years using the straight-line method, annual depreciation expense equals:Depreciation = $480,000/5Depreciation = $96,000So, the NPV of an all-equity project is:NPV = –$480,000 + (1 – .35)($175,000)PVIFA13%,5 + (.35)($96,000)PVIFA13%,5NPV = $38,264.03NPV(Financing Side Effects)The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt, so:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt R B. So, the NPV of the financing side effects are:NPV = $390,000 – (1 – .35)(.08)($390,000)PVIFA8%,5– $390,000/1.085NPV = $43,600.39So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = $38,264.03 + 43,600.39APV = $81,864.422.The adjusted present value (APV) of a project equals the net present value of the project if it werefunded completely by equity plus the net present value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt, so:APV = NPV(All-Equity) + NPV(Financing Side Effects)So, the NPV of each part of the APV equation is:NPV(All-Equity)NPV = –Purchase Price + PV[(1 –t C)(EBTD)] + PV(Depreciation Tax Shield)Since the initial investment of $1.7 million will be fully depreciated over four years using thestraight-line method, annual depreciation expense is:Depreciation = $1,700,000/4Depreciation = $425,000NPV = –$1,700,000 + (1 – .30)($595,000)PVIFA13%,4 + (.30)($425,000)PVIFA9.5%,4NPV (All-equity) = –$52,561.35NPV(Financing Side Effects)The net present value of financing side effects equals the aftertax present value of cash flowsresulting from the firm’s debt. So, the NPV of the financing side effects are:NPV = Proceeds(Net of flotation) – Aftertax PV(Interest Payments) – PV(Principal Payments) + PV(Flotation Cost Tax Shield)Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, R B.Since the flotation costs will be amortized over the life of the loan, the annual flotation costs that will be expensed each year are:Annual flotation expense = $45,000/4Annual flotation expense = $11,250NPV = ($1,700,000 – 45,000) – (1 – .30)(.095)($1,700,000)PVIFA9.5%,4– $1,700,000/1.0954 + .30($11,250) PVIFA9.5%,4NPV = $121,072.23So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$52,561.35 + 121,072.23APV = $68,510.883. a.In order to value a firm’s equity using the flow-to-equity approach, discount the cash flowsavailable to equity holders at the cost of the firm’s levered equity. The cash flows to equity holders will be the firm’s net income. Remembering that the company has three stores, we find:Sales $3,900,000COGS 2,010,000G & A costs 1,215,000Interest 123,000EBT $ 552,000Taxes 220,800NI $ 331,200Since this cash flow will remain the same forever, the present value of cash flows available tothe firm’s equity holders is a perpetuity. We can discount at the levered cost of equity, so, thevalue of the company’s equity is:PV(Flow-to-equity) = $331,200 / .19PV(Flow-to-equity) = $1,743,157.89b.The value of a firm is equal to the sum of the market values of its debt and equity, or:V L = B + SWe calculated the value of the company’s equity in part a, so now we need to calculate the value of debt. The company has a debt-to-equity ratio of .40, which can be written algebraically as:B / S = .40We can substitute the value of equity and solve for the value of debt, doing so, we find:B / $1,743,157.89 = .40B = $697,263.16So, the value of the company is:V = $1,743,157.89 + 697,263.16V = $2,440,421.054. a.In order to determine the cost of the firm’s debt, we need to find the yield to maturity on itscurrent bonds. With semiannual coupon payments, the yield to maturity of the company’s bonds is:$1,080 = $35 (PVIFA R%,40) + $1,000(PVIF R%,40)R = .03145, or 3.145%Since the coupon payments are semiannual, the YTM on the bonds is:YTM = 3.145%× 2YTM = 6.29%b.We can use the Capital Asset Pricing Model to find the return on unlevered equity. Accordingto the Capital Asset Pricing Model:R0 = R F+ βUnlevered(R M–R F)R0 = 4% + .85(11% – 4%)R0 = 9.95%Now we can find the cost of levered equity. According to Modigliani-Miller Proposition II with corporate taxesR S = R0 + (B/S)(R0–R B)(1 –t C)R S = .0995 + (.40)(.0995 – .0629)(1 – .34)R S = .1092, or 10.92%c.In a world with corporate taxes, a firm’s weighted average cost of capital is equal to:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SThe problem does not provide either the debt-value ratio or equity-value ratio. However, the firm’s debt-equity ratio is:B/S = .40Solving for B:B = .4SSubstituting this in the debt-value ratio, we get:B/V = .4S / (.4S + S)B/V = .4 / 1.4B/V = .29And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .29S/V = .71So, the WACC for the company is:R WACC = .29(1 – .34)(.0629) + .71(.1092)R WACC = .0898, or 8.98%5. a.The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since eachfirm has an unlevered beta of 1.10, we can find the equity beta for each. Doing so, we find:North PoleβEquity = [1 + (1 –t C)(B/S)]βUnleveredβEquity = [1 + (1 – .35)($2,900,000/$3,800,000](1.10)βEquity = 1.65South PoleβEquity = [1 + (1 –t C)(B/S)]βUnleveredβEquity = [1 + (1 – .35)($3,800,000/$2,900,000](1.10)βEquity = 2.04b.We can use the Capital Asset Pricing Model to find the required return on each firm’s equity.Doing so, we find:North Pole:R S = R F+ βEquity(R M–R F)R S = 3.20% + 1.65(10.90% – 3.20%)R S = 15.87%South Pole:R S = R F+ βEquity(R M–R F)R S = 3.20% + 2.04(10.90% – 3.20%)R S = 18.88%6. a.If flotation costs are not taken into account, the net present value of a loan equals:NPV Loan = Gross Proceeds – Aftertax present value of interest and principal paymentsNPV Loan = $5,850,000 – .08($5,850,000)(1 – .40)PVIFA8%,10– $5,850,000/1.0810NPV Loan = $1,256,127.24b.The flotation costs of the loan will be:Flotation costs = $5,850,000(.025)Flotation costs = $146,250So, the annual flotation expense will be:Annual flotation expense = $146,250 / 10Annual flotation expense = $14,625If flotation costs are taken into account, the net present value of a loan equals:NPV Loan = Proceeds net of flotation costs – Aftertax present value of interest and principalpayments + Present value of the flotation cost tax shieldNPV Loan = ($5,850,000 – 146,250) – .08($5,850,000)(1 – .40)(PVIFA8%,10)– $5,850,000/1.0810 + $14,625(.40)(PVIFA8%,10)NPV Loan = $1,149,131.217.First we need to find the aftertax value of the revenues minus expenses. The aftertax value is:Aftertax revenue = $3,200,000(1 – .40)Aftertax revenue = $1,920,000Next, we need to find the depreciation tax shield. The depreciation tax shield each year is:Depreciation tax shield = Depreciation(t C)Depreciation tax shield = ($11,400,000 / 6)(.40)Depreciation tax shield = $760,000Now we can find the NPV of the project, which is:NPV = Initial cost + PV of depreciation tax shield + PV of aftertax revenueTo find the present value of the depreciation tax shield, we should discount at the risk-free rate, and we need to discount the aftertax revenues at the cost of equity, so:NPV = –$11,400,000 + $760,000(PVIFA3.5%,6) + $1,920,000(PVIFA11%,6)NPV = $772,332.978.Whether the company issues stock or issues equity to finance the project is irrelevant. Thecompany’s optimal capital structure determines the WACC. In a world with corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SR WACC = .80(1 – .34)(.069) + .20(.1080)R WACC = .0580, or 5.80%Now we can use the weighted average cost of capital to discount NEC’s unlevered cash flows. Doing so, we find the NPV of the project is:NPV = –$45,000,000 + $3,100,000 / .0580NPV = $8,418,803.429. a.The company has a capital structure with three parts: long-term debt, short-term debt, andequity. Since interest payments on both long-term and short-term debt are tax-deductible, multiply the pretax costs by (1 –t C) to determine the aftertax costs to be used in the weighted average cost of capital calculation. The WACC using the book value weights is:R WACC = (X STD)(R STD)(1 –t C) + (X LTD)(R LTD)(1 –t C) + (X Equity)(R Equity)R WACC = ($10 / $19)(.041)(1 – .35) + ($3 / $19)(.072)(1 – .35) + ($6 / $19)(.138)R WACC = .0650, or 6.50%ing the market value weights, the company’s WACC is:R WACC = (X STD)(R STD)(1 –t C) + (X LTD)(R LTD)(1 –t C) + (X Equity)(R Equity)R WACC = ($11 / $40)(.041)(1 – .35) + ($10 / $40)(.072)(1 – .35) + ($26 / $40)(.138)R WACC = .1005, or 10.05%ing the target debt-equity ratio, the target debt-value ratio for the company is:B/S = .60B = .6SSubstituting this in the debt-value ratio, we get:B/V = .6S / (.6S + S)B/V = .6 / 1.6B/V = .375And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .375S/V = .625We can use the ratio of short-term debt to long-term debt in a similar manner to find the short-term debt to total debt and long-term debt to total debt. Using the short-term debt to long-term debt ratio, we get:STD/LTD = .20STD = .2LTDSubstituting this in the short-term debt to total debt ratio, we get:STD/B = .2LTD / (.2LTD + LTD)STD/B = .2 / 1.2STD/B = .167And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or: LTD/B = 1 – .167LTD/B = .833Now we can find the short-term debt to value ratio and long-term debt to value ratio bymultiplying the respective ratio by the debt-value ratio. So:STD/V = (STD/B)(B/V)STD/V = .167(.375)STD/V = .063And the long-term debt to value ratio is:LTD/V = (LTD/B)(B/V)LTD/V = .833(.375)LTD/V = .313So, using the target capital structure weights, the company’s WACC is:R WACC = (X STD)(R STD)(1 –t C) + (X LTD)(R LTD)(1 – t C) + (X Equity)(R Equity)R WACC = (.063)(.041)(1 – .35) + (.313)(.072)(1 – .35) + (.625)(.138)R WACC = .1025, or 10.25%d.The differences in the WACCs are due to the different weighting schemes. The company’sWACC will most closely resemble the WACC calculated using target weights since futureprojects will be financed at the target ratio. Therefore, the WACC computed with targetweights should be used for project evaluation.Intermediate10.The adjusted present value of a project equals the net present value of the project under all-equityfinancing plus the net present value of any financing side effects. In the joint venture’s case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firms’ debt. So, the APV is:APV = NPV(All-Equity) + NPV(Financing Side Effects)The NPV for an all-equity firm is:NPV(All-Equity)NPV = –Initial Investment + PV[(1 –t C)(EBITD)] + PV(Depreciation Tax Shield)Since the initial investment will be fully depreciated over five years using the straight-line method, annual depreciation expense is:Annual depreciation = $80,000,000/5Annual depreciation = $16,000,000NPV = –$80,000,000 + (1 – .35)($12,100,000)PVIFA13%,20 + (.35)($16,000,000)PVIFA13%,5NPV = –$5,053,833.77NPV(Financing Side Effects)The NPV of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the financing effects is:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments)NPV = $25,000,000 – (1 – .35)(.05)($25,000,000)PVIFA8.5%,15– $25,000,000/1.08515NPV = $10,899,310.51So, the APV of the project is:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$5,053,833.77 + $10,899,310.51APV = $5,845,476.7311.If the company had to issue debt under the terms it would normally receive, the interest rate on thedebt would increase to the company’s normal cost of debt. The NPV of an all-equity project would remain unchanged, but the NPV of the financing side effects would change. The NPV of the financing side effects would be:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Repayments)NPV = $25,000,000 – (1 – .35)(.085)($25,000,000)PVIFA8.5%,15– $25,000,000/1.08515NPV = $6,176,275.95Using the NPV of an all-equity project from the previous problem, the new APV of the project would be:APV = NPV(All-Equity) + NPV(Financing Side Effects)APV = –$5,053,833.77 + $6,176,275.95APV = $1,122,442.18The gain to the company from issuing subsidized debt is the difference between the two APVs, so: Gain from subsidized debt = $5,845,476.73 – 1,122,442.18Gain from subsidized debt = $4,723,034.55Most of the value of the project is in the form of the subsidized interest rate on the debt issue.12.The adjusted present value of a project equals the net present value of the project under all-equityfinancing plus the net present value of any financing side effects. First, we need to calculate the unlevered cost of equity. According to Modigliani-Miller Proposition II with corporate taxes:R S = R0 + (B/S)(R0–R B)(1 –t C).16 = R0 + (.50)(R0– .09)(1 – .40)R0 = .1438 or 14.38%Now we can find the NPV of an all-equity project, which is:NPV = PV(Unlevered Cash Flows)NPV = –$18,000,000 + $5,700,000/1.1438 + $9,500,000/(1.1438)2 + $8,800,000/1.14383NPV = $124,086.62Next, we need to find the net present value of financing side effects. This is equal the aftertax present value of cash flows resulting from the firm’s debt. So:NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments)Each year, an equal principal payment will be made, which will reduce the interest accrued during the year. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so the NPV of the financing effects is:NPV = $9,300,000 – (1 – .40)(.09)($9,300,000) / 1.09 – $3,100,000/1.09– (1 – .40)(.09)($6,200,000)/1.092– $3,100,000/1.092– (1 – .40)(.09)($3,100,000)/1.093– $3,100,000/1.093NPV = $581,194.61So, the APV of project is:APV = NPV(All-equity) + NPV(Financing side effects)APV = $124,086.62 + 581,194.61APV = $705,281.2313. a.To calculate the NPV of the project, we first need to find the company’s WACC. In a worldwith corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SThe market value of the company’s equity is:Market value of equity = 4,500,000($25)Market value of equity = $112,500,000So, the debt-value ratio and equity-value ratio are:Debt-value = $55,000,000 / ($55,000,000 + 112,500,000)Debt-value = .3284Equity-value = $112,500,000 / ($55,000,000 + 112,500,000)Equity-value = .6716Since the CEO believes its current capital structure is optimal, these values can be used as the target w eights in the firm’s weighted average cost of capital calculation. The yield to maturity of the company’s debt is its pretax cost of debt. To find the company’s cost of equity, we need to calculate the stock beta. The stock beta can be calculated as:β = σS,M / σ2Mβ = .0415 / .202β = 1.04Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is:R S = R F+ β(R M–R F)R S = 3.4% + 1.04(7.50%)R S = 11.18%Now, we can calculate the company’s WACC, which is:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SR WACC = .3284(1 – .35)(.065) + .6716(.1118)R WACC = .0890, or 8.90%Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = –$42,000,000 + $11,800,000(PVIFA8.90%,5)NPV = $4,020,681.28b.The weighted average cost of capital used in part a will not change if the firm chooses to fundthe project entirely with debt. The weighted average cost of capital is based on optimal capital structure weights. Since the current capital structure is optimal, all-debt funding for the project simply implies that the firm will have to use more equity in the future to bring the capital structure back towards the target.14.We have four companies with comparable operations, so the industry average beta can be used as thebeta for this project. So, the average unlevered beta is:βUnlevered = (1.15 + 1.08 + 1.30 + 1.25) / 4βUnlevered = 1.20A debt-to-value ratio of .40 means that the equity-to-value ratio is .60. This implies a debt-equityratio of .67{=.40/.60}. Since the project will be levered, we need to calculate the levered beta, which is:βLevered = [1 + (1 –t C)(Debt/Equity)]βUnleveredβLevered = [1 + (1 – .34)(.67)]1.20βLevered = 1.72Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is:R S = R F+ β(R M–R F)R S = 3.8% + 1.72(7.00%)R S = 15.85%Now, we can calculate the company’s WACC, which is:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SR WACC = .40(1 – .35)(.068) + .60(.1585)R WACC = .1130, or 11.30%Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = –$4,500,000 + $675,000(PVIFA11.30%,20)NPV = $770,604.48Challenge15. a.The company is currently an all-equity firm, so the value as an all-equity firm equals thepresent value of aftertax cash flows, discounted at the cost of the firm’s unlevered cost of equity. So, the current value of the company is:V U = [(Pretax earnings)(1 –t C)] / R0V U = [($21,000,000)(1 – .35)] / .16V U = $85,312,500The price per share is the total value of the company divided by the shares outstanding, or:Price per share = $85,312,500 / 1,300,000Price per share = $65.63b.The adjusted present value of a firm equals its value under all-equity financing plus the netpresent value of any financing side effects. In this case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firm’s debt. Given a known level of debt, debt cash flows can be discounted at the pretax cost of debt, so the NPV of the financing effects are:NPV = Proceeds – Aftertax PV(Interest Payments)NPV = $30,000,000 – (1 – .35)(.09)($30,000,000) / .09NPV = $10,500,000So, the value of the company after the recapitalization using the APV approach is:V = $85,312,500 + 10,500,000V = $95,812,500Since the company has not yet issued the debt, this is also the value of equity after the announcement. So, the new price per share will be:New share price = $95,812,500 / 1,300,000New share price = $73.70c.The company will use the entire proceeds to repurchase equity. Using the share price wecalculated in part b, the number of shares repurchased will be:Shares repurchased = $30,000,000 / $73.70Shares repurchased = 407,045And the new number of shares outstanding will be:New shares outstanding = 1,300,000 – 407,045New shares outstanding = 892,955The value of the company increased, but part of that increase will be funded by the new debt.The value of equity after recapitalization is the total value of the company minus the value of debt, or:New value of equity = $95,812,500 – 30,000,000New value of equity = $65,812,500So, the price per share of the company after recapitalization will be:New share price = $65,812,500 / 892,955New share price = $73.70The price per share is unchanged.d.In order to value a firm’s equity using the flow-to-equity approach, we must discount the cashflows available to equity holders at the cost of the firm’s levered equity. According to Modigliani-Miller Proposition II with corporate taxes, the required return of levered equity is: R S = R0 + (B/S)(R0–R B)(1 –t C)R S = .16 + ($30,000,000 / $65,812,500)(.16 – .09)(1 – .35)R S = .1807, or 18.07%After the recapitalization, the net income of the company will be:EBIT $21,000,000Interest 2,700,000EBT $18,300,000Taxes 6,405,000Net income $11,895,000The firm pays all of its earnings as dividends, so the entire net income is available toshareholders. Using the flow-to-equity approach, the value of the equity is:S = Cash flows available to equity holders / R SS = $11,895,000 / .1807S = $65,812,50016. a.If the company were financed entirely by equity, the value of the firm would be equal to thepresent value of its unlevered after-tax earnings, discounted at its unlevered cost of capital.First, we need to find the company’s unlevered cash flows, which are:Sales $17,500,000Variable costs 10,500,000EBT $7,000,000Tax 2,800,000Net income $4,200,000So, the value of the unlevered company is:V U = $4,200,000 / .13V U = $32,307,692.31b.According to Modigliani-Miller Proposition II with corporate taxes, the value of levered equityis:R S = R0 + (B/S)(R0–R B)(1 –t C)R S = .13 + (.35)(.13 – .07)(1 – .40)R S = .1426 or 14.26%c.In a world with corporate taxes, a firm’s weighted average cost of capital equals:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SSo we need the debt-value and equity-value ratios for the company. The debt-equity ratio forthe company is:B/S = .35B = .35SSubstituting this in the debt-value ratio, we get:B/V = .35S / (.35S + S)B/V = .35 / 1.35B/V = .26And the equity-value ratio is one minus the debt-value ratio, or:S/V = 1 – .26S/V = .74So, using the capital structure weights, the company’s WACC is:R WACC = [B / (B + S)](1 –t C)R B + [S / (B + S)]R SR WACC = .26(1 – .40)(.07) + .74(.1426)R WACC = .1165, or 11.65%We can use the weighted average cost of capital to discount the firm’s unlevered aftertax earnings to value the company. Doing so, we find:V L = $4,200,000 / .1165V L = $36,045,772.41Now we can use the debt-value ratio and equity-value ratio to find the value of debt and equity, which are:B = V L(Debt-value)B = $36,045,772.41(.26)B = $9,345,200.25S = V L(Equity-value)S = $36,045,772.41(.74)S = $26,700,572.16d.In order to value a firm’s equity using the flow-to-equity approach, we can discount the cashflows available to equity holders at the cost of the firm’s levered equity. First, we need to calculate the levered cash flows available to shareholders, which are:Sales $17,500,000Variable costs 10,500,000EBIT $7,000,000Interest 654,164EBT $6,345,836Tax 2,538,334Net income $3,807,502So, the value of equity with the flow-to-equity method is:S = Cash flows available to equity holders / R SS = $3,807,502 / .1426S = $26,700,572.1617. a.Since the company is currently an all-equity firm, its value equals the present value of itsunlevered after-tax earnings, discounted at its unlevered cost of capital. The cash flows to shareholders for the unlevered firm are:EBIT $118,000Tax 47,200Net income $70,800So, the value of the company is:V U = $70,800 / .14V U = $505,714.29b.The adjusted present value of a firm equals its value under all-equity financing plus the netpresent value of any financing side effects. In this case, the NPV of financing side effects equals the after-tax present value of cash flows resulting from debt. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so:NPV = Proceeds – Aftertax PV(Interest payments)NPV = $235,000 – (1 – .40)(.08)($235,000) / .08NPV = $94,000So, using the APV method, the value of the company is:APV = V U + NPV(Financing side effects)APV = $505,714.29 + 94,000APV = $599,714.29The value of the debt is given, so the value of equity is the value of the company minus the value of the debt, or:S = V–BS = $599,714.29 – 235,000S = $364,714.29c.According to Modigliani-Miller Proposition II with corporate taxes, the required return oflevered equity is:R S = R0 + (B/S)(R0–R B)(1 –t C)R S = .14 + ($235,000 / $364,714.29)(.14 – .08)(1 – .40)R S = .1632, or 16.32%d.In order to value a firm’s equity using the flow-to-equity approach, we can discount the cashflows available to equity holders at the cost of the firm’s levered equity. First, we need to calculate the levered cash flows available to shareholders, which are:EBIT $118,000Interest 18,800EBT $99,200Tax 39,680Net income $59,520。
Chap5财务管理,公司金融,罗斯第十版概要
终值-例3
• 假设你的祖先在200年前以5.5%的利率存了10美 元。这项投资今天的价值是多少？ ▪ Formula: FV = 10(1.055)200 = 10(44,718.9838) = 447,189.84
• 复利的效应是多少?
▪ 单利= 10 + 200(10)(.055) = 120.00 ▪ 复利使得投资价值额外增加了447,069.84 美元。
• 终值利息因子= (1 + r)t
5C-6
复利的效应
• 单利 • 复利 • 考虑上一个例子
▪ 单利时的终值PV= 1,000 + 50 + 50 = 1,100 ▪ 复利时的终值FV = 1,102.50 ▪ 额外的2.5美元利息是在第一笔利息的基础之上
赚取的 .05(50) = 2.50
5C-7
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
关键概念和技能
• 理解怎样计算一个投资项目的终值 • 理解怎样计算未来收益的现值 • 理解怎样计算投资回报 • 理解怎样计算一项投资的价值增长到期望值所需要
5C-10
终值-作为一般的增长公式
• 假设你的公司预期产品的销售量在接下来 的5年中每年将增长15%。若今年售出3百 万个产品，则第五年预期售出多少个？
▪ 5 N;15 I/Y; 3,000,000 PV ▪ CPT FV = -6,034,072 单位
5C-11
小测验-第1部分
• 单利和复利的区别是什么？ • 假设你将500美元以8%的报酬率投资15年。
率”
▪ 贴现率 ▪ 资本成本率 ▪ 资本的机会成本率 ▪ 必要报酬
公司理财精要版第10版Chap.ppt
1-0
第3-4章
财务报表分析与长期计划
1-1
快速阅读
怎样标准化资产负债表和利润表？ 为什么标准化后的信息更加有用？ 财务比率有哪些主要类别？是如何进行计算的？ 什么是杜邦恒等式？ 财务报表分析存在哪些可能的问题？
本章结构
3.1 现金流量和财务报表 3.2 标准财务报表 3.3 比率分析 3.4 杜邦恒等式 3.5 财务模型 3.6 外部融资与增长 3.7 财务计划模型的一些注意事项
Sample Balance Sheet
XYZ Corporation December 31, 201X (Figures in millions of dollars)
2011
2010
2011
Cash
696
58 A/P
307
A/R
956
992 N/P
26
Inventory Other CA Total CA
丰田 日元编制财务报表
通用
资产规模相对较大
美元编制财务报表
3.2 财务报表分析
不同公司财务报表之间的对比
方法一：报表的标准化 方法二：比率分析
3.2 财务报表分析
报表的标准化
共同比资产负债表
将所有项目表示为总资产的百分比
共同比利润表
将表中每个项目表示为销售额的百分比
标准化财务报表使财务信息的可比性增强，特别是当 公司还在不断成长时（纵向比较）。
+ 68.1
所有者权益小计
-------99.8
P32
把
利 润
共
销 售
表 中
同
额每比
的 百
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5-6
5.1 终值和复利：单期投资的情形
终值（Future Value, FV）：
指在一定的利率水平下，现在一定量的资金在未来某一时
点上的价值。
如果你投资$10,000，收益率为5%，一年后你的投资将增长为
$10,500。 其中，
$500 是利息 ($10,000 ×0.05) $10,000 是本金偿还 ($10,000 × 1) $10,500 是本息合计，可由下式计算得到： $10,500 = $10,000×(1.05) 该投资在期末的本息合计金额被称为终值。
5
$1.10
0
$1.54 $2.16 $3.02
1 2 3
$4.23
4
$5.92
5
5.1 终值和复利
终值和复利计算
如果资金按复利（compound interest）计算，利息将被进
行再投资；而在单利（simple interest）情况下，利息没有 进行再投资，每期只赚取初始本金的利息。 $1×( 1 + r )2=1+2r+r2>1+2r 如果投资金额越大，期限越长，复利的威力就越大。 $V×( 1 + r )n >>V + V×r×n 附录表A-1给出了“1元钱在T期末的复利值（终值系数）”。
计算公式：r = (FV / PV)1/t – 1
FV C0 (1 r)T
$ 5 0 ,0 0 0 ( 1r) 1 0 $ 5 ,0 0 0
1 2
$50,000 $5,000 (1 r )12 (1 r) 10
1 12
r 10
1 12
1 1 .2115 1 .2115
复利计算的相反过程。 一项多期投资的现值的一般计算公式可以写为：
CT PV (1 r )T
其中： CT 是在T期的现金流量 r 是适用的利率 1/(1 + r)T被叫做现值系数（Present Value Factor），缩写为PVIF(r,t)。 附录表A-2给出了“T期后得到的1元钱的现值（现值系数）”。
T
$ 1 0 ,0 0 0 ( 1 .1 0 ) 2 $ 5 ,0 0 0
T
ln(1.10)T ln 2
l n2 0 .6 9 3 1 T 7 .2 7y ears l n (1 .1 0 ) 0 .0 9 5 3
Quick Quiz
You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest? r = (1,200 / 1,000)1/5 – 1 = .03714 = 3.714%
知道如何计算现值、终值、贴现率、期数
FV = PV(1 + r)t PV = FV / (1 + r)t
r = (FV / PV)1/t – 1
t = ln(FV / PV) / ln(1 + r)
第6章 贴现现金流量估值
6.1 6.2 6.3 6.4 多期现金流量的现值和终值 评估均衡现金流量：年金和永续年金 比较利率：复利的影响 贷款种类与分期偿还贷款
You want to purchase a new car, and you are willing to pay $20,000. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?
5.1 终值和复利：多期投资的情形
终值和复利计算
一项多期投资的终值的一般计算公式可以写为：
FV = C0×(1 + r)T 其中： C0 是时间0的现金流量 r 是适用的利率 T 是现金投资的时期数 (1 + r)T被叫做终值系数（Future Value Factor），缩写为FVIF(r,t)。
6-28
6.1 多期现金流的终值
• 直接将第2年末的资金复利到第5年末
Today0 700
$2,354
$2,803
6-29
6.1 多期现金流的终值
• 计算每笔现金流在第5年末的终值，再汇总。
Today
1
2
3
4
5
$1,000 500 700
6-30
$1,338 $ 631 $ 833 $2,803
r = 10; PV = -15,000; FV = 20,000 T= 3.02 years
5-19
Finance Formulas
5-20
关键概念与技能
概念
终值Future Value；现值Present Value；
复利Compound Interest；单利Simple Interest 贴现Discounting；贴现率Discount Rate
时间？ 复利和单利的含义
Time and Money
Which would you rather receive: A or B?
Today
1 Year 2 Years
Today
1 Year
2 Years
Time and Money
Money received over time is not equal in value. So how do we “value” future money?
5.1 终值和复利：多期投资的情形
假定 Jay Ritter 投资 Modigliani company 首次公开发行的
新股。Modigliani 当前支付了 $1.10 的股利，预期未来五 年里股利将每年增长40%。 在五年后股利将为多少？ FV = C0×(1 + r)T $5.92 = $1.10×(1.40)5
5-12
5.2现值和贴现： 单期现值
现值（Present Value, PV）：
现值就是资金折算至基准年的数值。 我们经常用现值来估算债券、股票等金融资产的价值，也
用现值估算项目的价值。
如果你想在一年后保证得到 $10,000，假定利率为
5%，你的投资在今天的价值是 $9,523.81。
快速阅读
多期现金流量的现值和终值是如何计算的？
什么是实际利率（EAR）？年利率（APR）和实
际年利率（EAR）之间的关系？ 什么是永续年金？什么是年金？如何计算其现值 和终值。 如何计算贷款的支付额以及贷款的利率。
单期现金流量
• 在前面的章节中，我们介绍了单期现金流量的现值和终 值。 • 但现实生活中，大多数投资都涉及多期现金流的问题。
《公司财务》 Corporate Finance
1-1
第三部分 折现现金流量估价
第5章 货币的时间价值 第6章 贴现现金流量估价
1-2
第5章 货币的时间价值
5.1 终值与复利 5.2 现值与贴现 5.3 现值与终值的进一步讲解
快速阅读
现金流量的终值是如何计算的?
现金流量的现值是如何计算的？ 如何计算投资回报率？ 如何计算一项投资的价值增长到期望值所需要的
$ 10 ,0 00 $ 9,52 3.8 1 1 .0 5
一位借款者今天需要预留以便在一年后能够满足承诺 的 $10,000 支付的金额被称作 $10,000 的现值 (PV)。
注意，$10,000 = $9,523.81×(1.05)
5.2 现值和贴现：
现值和贴现
计算未来现金流量的现值的过程叫做“贴现”。它是
5.2 现值和贴现：
如果当前利率为15%，一个投资者为了在五年后能
获得 $20,000，现在必须投资多少？
PV
0 1 2 3 4
$20,000
5
$ 2 0 ,0 0 0 $ 9 ,9 4 3 .5 3 5 ( 1 .1 5 )
5.3 现值和终值的关系
在利率和期数相同时，现值系数恰好是终值系数的
Today
1
2
3
4
5
PV
Today
复利(Compounding)
1
2
3
4
FV
5
6-24
PV
贴现(Discounting)
FV
6.1 多期现金流的终值
假定你今天在一个利率为 6%的账户中存入了$1,000。
1年后你将再存入$500，2年后你将再次存入$700。
Today
1 Year
2 Years
我们可以由最初的投资额、利率，计算终值，也可以由初
始投资额、终值，求利率。
Quick Quiz
Suppose you have $500 to invest and you believe that
you can earn 8% per year over the next 15 years.
大约 21.15%.
5.3 求解期数
如果我们今天将 $5,000 存在一个支付 10% 利率的账
户里，它需要经过多长时间能增值到 $10,000？
计算公式：t = ln(FV / PV) / ln(1 + r)
FV C0 (1 r)
T
$10,000 $5,000 (1.10)
1
2
3
4
6-32
178.57 318.88 427.07 508.41 1,432.93