武汉大学公司金融课件(一)

A FRAMEWORK OF CORPORATE FINANCEThe goal of financial management: to maximize the shareholders’ wealth.Three questions:1.What should the company invest (so as to earn good returns)?2.What is the lowest cost to get money (borrow or issue equity) in order to invest?3.How much cash needed to keep the company running?Work Map.Assets (investment):1.EvaluationCompounding & discountingBond valuationStock valuation2. Capital BudgetingPaybackNet present valueInternal rate of return3. Return & riskCapital market efficiency(SML)Expected returns and varianceRisks: systematic & unsystematic (Betacoefficient)Diversification & portfolios4. Financial StatementCashflowRatio analysisFinancial PlanningLiabilities & equity1.Cost of capitalCost of long-term debtFlotation costsCapital structureWeighted average cost of capital(WACC)2.Financial Leverage & capital structureModigliani & Miller Proposition I & IITrade-off theoryPecking order theory3.Raising CapitalCash offer, rights offer, private placementCash & stock dividendsWarrantsConvertible BondsThe dividend policy controversyFinancial leasing4.Merger & AcquisitionsEstimating gains and lossesLeveraged buy-outsBootsWorking capital management(e.g. p3 )From the balance-sheet, we can see net working capital is defined as current assets minus current liabilities. This part covers the topic of how to manage the gaps between cash inflows and outflows in order to keep the business running.1.Operating and cash cycles2.Cash budgeting3.Flexible & restrictive strategiesTIME V ALUE OF MONEYBASIC PRINCIPLE:A dollar today is worth more than a dollar tomorrow.WHY?COMPOUNDING: FUTURE VALUE▪Borrow---$500 for one year▪Interest rate per year--- 9%FV1 = $500 + (.09)(500) = $545FV1 = $500 * ( 1 + .09)FV1 = $500 ( 1 + r)$500 is the principal$45 is the simple interestCOMPOUNDING: MULTIPLE YEARS▪Borrow--- $500 for two yearsFV1 = 500 ( 1 + r)FV2 = FV1 ( 1 + r)= 500 ( 1 + r)( 1 + r) = 500 ( 1 + r )2FV2 = 500 ( 1.09)2 = 500 ( 1.1881 )FV2 = $594.05Principal---$500.00Total interest---$ 94.05Simple interest--- $45 + $45 = $90Compound interest = $4.05(Interest on interest)(.09)($45) = $4.05Generally:FV t = Principal * ( 1 + r )tFUTURE V ALUE INTERESTFACTOR = ( 1 + r )tNotation:FVIF(r,t)The future value interest factor at an interest rate of r over tperiods.DETERMINING THE FUTURE VALUE OF THE INVESTMENT OR DEBTYou run your credit card to the limit of $3,000. The interest rate is 1.75% permonth. How much will you owe at the end of 12 months?POWER OF COMPOUNDINGAbout 374 years ago, Manhattan Island was sold for $24. What would be the value today (the Future Value) if that money had been invested at a compound interest rate of 5% per year?DISCOUNTING: PRESENT VALUEPresent Value: value today of a futurecash flow at an appropriatediscount (interest) rate.▪You will receive a scholarship of $1,000 one year from now.▪7% interest rateThe Present Value ($934.58) is today’s value of $1,000 to be received in one year’s time.Given the opportunity cost created by the 7% interest rate, a value of a future dollar has to be discounted to be comparable to a current dollar.DISCOUNTING: MULTIPLE YEARSFV t = PV * ( 1 + r )tPV = FV t / ( 1 + r )tPV = FV t * 1/(1 + r)t▪You will receive the $1,000 scholarship in three years---what is its value today. Generally:PV = FV t * 1/( 1 + r )tPRESENT V ALUE INTERESTFACTOR = 1/( 1 + r )tNotation:PVIF(r,t)The present value interest factor at a discount rate of r over tperiods.DETERMINING THE PRESENT VALUEYou buy a type of bond called a “strip bond” with a future value of $250,000 foryour retirement 35 years from now. The current interest rate (discount rate) is7.5%. How much will you pay for the strip bond?Overview:PV = FV t * 1/( 1 + r )tFV t = PV * ( 1 + r )tFour factors:▪Present value (PV)▪Future value (FV t)▪Discount rate (r)▪Life of the investment (t)Given any 3 of the factors, you can always determine the 4th.DETERMINING THE DISCOUNT RATE▪If you give me $4,000 today, I will give you $5,000 in three years. What rate of interest will you earn with this investment, if interest is compounded annually?You will earn about 7.72% per year with this opportunity.EXAMPLE: DETERMINING THE DISCOUNT RATEYou are still trying to buy the $250,000 strip bond coming due in 35 years. Your broker states that you must pay $21,000. What interest rate will you earn over the 35 years if you pay this price, if interest is compounded annually?EXAMPLE: DETERMINING THE LIFE OF THE INVESTMENTYou have $2,000 set aside in a savings account earning ½ of 1% interest per month, compounded monthly. When you hav e $3,000, you’re off to Mexico to lie in the sun. How many months must you wait?MULTIPLE CASH FLOWSUse our basic compounding and discounting techniques to determine the present or future value of a series of uneven payments, over a number of compounding periods.Understand the importance of the timing of payments.Calculated the present and future values of streams of cash payments, where the payments are all the same amounts, e.g., annuities, loan payments, or perpetuities.Compare interest rates to determine which are the highest and which are the lowest.Illustrate how interest rates can be quoted in different and often deceptive ways. FVIF(r,t) = (1 + r)t PVIF(r,t) = 1/(1 + r)tFUTURE VALUEThe Value at 10th year from now(i) One year at a time at a 7% discount rateEnd ofYear 1 Year 2 Year 3 Year 4750 800 700 900*1.07= 802.501,602.50*1.07= 1,714.682,414.68*1.07=2,583.713,483.71FV4 = $3,483.71FV10 = $3,483.71 * FVIF7%,6FV10 = $5,228.11(ii)Each cash flow separately at a 7% discount rateEnd ofYear 1 Year 2 Year 3 Year 4750 800 700 900750 * FVIF7%,3 = 918.78800 * FVIF7%,2= 915.92700 * FVIF7%,1= 749.00FV4= 3,483.70FV10 = $3,483.71 * FVIF7%,6FV10 = $5,228.11PRESENT VALUE(i)One Year at a time at a 7% discount rateEnd of0 Year 1 Year 2 Year 3 Year 4750 800 700 900/1.07841.121,541.12 /1.071,440.302,240.30/1.072,093.742,843.74 /1.072,657.70PV = $2,657.70(ii)Each cash flow separately at a 7% discount rateEnd of0 Year 1 Year 2 Year 3 Year 4 750 800 700 900750 * PVIF7%,1= 700.93800 * PVIF7%,2= 698.75700 * PVIF7%,3= 571.41900 * PVIF7%,4= 686.61PV = $2,657.70EXAMPLEYou have just received your first job offer from a large investment banking firm. They want to test your skills and have offered you either a $200,000 signing bonus with no salary for 4 years or a $60,000 salary at the end of each year for 4 years.Ignoring taxes, which would you prefer if you could earn 9% on investments?PV bonus = $200,000PV sal = (60,000 *PVIF9%,1)+ (60,000*PVIF9%,2)+(60,000 *PVIF9%,3) + (60,000 * PVIF9%,4)= (60,000 * .91743) + (60,000 * .84168) + (60,000 * .77218) + (60,000 * .70843)= 55,046 + 50,501 + 46,331 + 42,506 == $194,384The signing bonus of $200,000 has a greater present value.IMPORTANT: TIMING OF PAYMENTSAll preset calculations assume that payments occur at the end of each period.In our example, the assumption is that the annual salary occurs at the end of each year.Since many payments, such as rent payments, occur at the beginning of a period it is very important to pay attention to the timing of the payments…ANNUITIES :a level stream of cash payments for a fixed period of time.Examples:▪Car loans▪Mortgages▪Rent payments▪Fixed costs▪Pension paymentPresent Value of = C * 1 – PVIFan Annuity rPV A (r,t)= C * 1 - (1/( 1 + r )t)rNotationPVIFA(r,t)= 1 - 1/( 1 + r )trPREVIOUS EXAMPLESalary of $60,000 per year for 4 years with a 9% discount rate.PV A (9%,4) = 60,000 * ( 1 – (1/(1.09)4).09= 60,000 * 3.23972PV A = $194,383.19Three Methods:compute the equationuse present value of an annuity tableuse PV function on a business calculatorEXAMPLE:You win the “million dollar” lottery but find that you will receive $50,000 per year for 20 years.You could earn 7.5% on an investment.What is the present value of your winnings?EXAMPLE: CALCULATING THEMONTHL Y PAYMENTYou’ve grad uated, have a new job, and have the student loan paid off.Now, the fine car! Used but fine.Price: $37,500Interest rate: 1% compounded monthlyTerm: 60 monthsWHAT WILL YOUR MONTHL Y PAYMENT BE?EXAMPLE: CALCULATING THEINTEREST RATE ON ANANNUITYMore on the carPrice: $37,500Term: 60 months; compounded monthlyPayment per month; $950WHAT MONTHL Y INTEREST RA TE WILL YOU BE PAYING?FUTURE VALUE OF AN ANNUITYFV A(r,t) = PV A * FVIF(r,t)ORFV A(r,t) = C * FVIF – 1rFVA(r,t) = C * (1 + r)t –1rNotationFVIFA(r,t) = (1 + r)t –1rEXAMPLEYou won $50,000 per year for 20 years. You can earn 7.5% per year on an investment. We showed earlier that the Present Value is $509,724.57.What is the Future Value of this Annuity?EXAMPLEYou set aside $3,500 per year for 40 years in an RRSP in preparation for your retirement. If you earn 7.32% per annum, what is the future value of this constant stream of contributions? PERPETUITYAn annuity in which the cash flow continues forever.PVIFA = 1 – 1/(1 + r)tr-if t becomes very large, then 1/(1+r)tapproaches zeroSo: PVIFA perpetuity = 1/rPV perpetuity = C * 1/r = C/rEXAMPLEA preferred stock has a $7.50 dividend in perpetuity and the interest rate is 6.9%. What is the value of the preferred stock?PV perpetuity = C/r = 7.50/.069Price of the preferred stock = $108.70。