Corporate Finance Net Present Value.ppt

1、,Corporate Finance Ross Westerfield Jaffe,Sixth Edition,Chapter Outline,4.1 The One-Period Case 4.2 The Multiperiod Case 4.3 Compounding Periods 4.4 Simplifications 4.5 What Is a Firm Worth? 4.6 Summary and Conclusions,4.1 The One-Period Case: Future Value,If you were to invest $10,000 at 5-percent

2、interest for one year, your investment would grow to $10,500 $500 would be interest ($10,000 .05) $10,000 is the principal repayment ($10,000 1) $10,500 is the total due. It can be calculated as: $10,500 = $10,000(1.05). The total amount due at the end of the investment is call the Future Value (FV)

3、.,4.1 The One-Period Case: Future Value,In the one-period case, the formula for FV can be written as: FV = C1(1 + r) Where C1 is cash flow at date 1 and r is the appropriate interest rate.,4.1 The One-Period Case: Present Value,If you were to be promised $10,000 due in one year when interest rates a

4、re at 5-percent, your investment be worth $9,523.81 in todays dollars.,The amount that a borrower would need to set aside today to to able to meet the promised payment of $10,000 in one year is call the Present Value (PV) of $10,000.,Note that $10,000 = $9,523.81(1.05).,4.1 The One-Period Case: Pres

5、ent Value,In the one-period case, the formula for PV can be written as:,Where C1 is cash flow at date 1 and r is the appropriate interest rate.,4.1 The One-Period Case: Net Present Value,The Net Present Value (NPV) of an investment is the present value of the expected cash flows, less the cost of th

6、e investment. Suppose an investment that promises to pay $10,000 in one year is offered for sale for $9,500. Your interest rate is 5%. Should you buy?,Yes!,4.1 The One-Period Case: Net Present Value,In the one-period case, the formula for NPV can be written as:,If we had not undertaken the positive

7、NPV project considered on the last slide, and instead invested our $9,500 elsewhere at 5-percent, our FV would be less than the $10,000 the investment promised and we would be unambiguously worse off in FV terms as well: $9,500(1.05) = $9,975 $10,000.,4.2 The Multiperiod Case: Future Value,The gener

8、al formula for the future value of an investment over many periods can be written as: FV = C0(1 + r)T Where C0 is cash flow at date 0, r is the appropriate interest rate, and T is the number of periods over which the cash is invested.,4.2 The Multiperiod Case: Future Value,Suppose that Jay Ritter in

9、vested in the initial public offering of the Modigliani company. Modigliani pays a current dividend of $1.10, which is expected to grow at 40-percent per year for the next five years. What will the dividend be in five years? FV = C0(1 + r)T $5.92 = $1.10(1.40)5,Future Value and Compounding,Notice th

10、at the dividend in year five, $5.92, is considerably higher than the sum of the original dividend plus five increases of 40-percent on the original $1.10 dividend: $5.92 $1.10 + 5$1.10.40 = $3.30 This is due to compounding.,Future Value and Compounding,Present Value and Compounding,How much would an

11、 investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%?,$20,000,PV,How Long is the Wait?,If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000?,Assume the total cost of a college education will be $50,000 when

12、 your child enters college in 12 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your childs education? About 21.15%.,What Rate Is Enough?,4.3 Compounding Periods,Compounding an investment m times a year for T years provides for fut

13、ure value of wealth:,For example, if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow to,Effective Annual Interest Rates,A reasonable question to ask in the above example is what is the effective annual rate of interest on that investment?,The Effective Annual In

14、terest Rate (EAR) is the annual rate that would give us the same end-of-investment wealth after 3 years:,Effective Annual Interest Rates (continued),So, investing at 12.36% compounded annually is the same as investing at 12% compounded semiannually.,Continuous Compounding (Advanced),The general form

15、ula for the future value of an investment compounded continuously over many periods can be written as: FV = C0erT Where C0 is cash flow at date 0, r is the stated annual interest rate, T is the number of periods over which the cash is invested, and e is a transcendental number approximately equal to

16、 2.718. ex is a key on your calculator.,4.4 Simplifications,Perpetuity A constant stream of cash flows that lasts forever. Growing perpetuity A stream of cash flows that grows at a constant rate forever. Annuity A stream of constant cash flows that lasts for a fixed number of periods. Growing annuit

17、y A stream of cash flows that grows at a constant rate for a fixed number of periods.,Perpetuity,A constant stream of cash flows that lasts forever.,The formula for the present value of a perpetuity is:,Perpetuity: Example,What is the value of a British consol that promises to pay 15 each year, ever

18、y year until the sun turns into a red giant and burns the planet to a crisp? The interest rate is 10-percent.,Growing Perpetuity,A growing stream of cash flows that lasts forever.,The formula for the present value of a growing perpetuity is:,Growing Perpetuity: Example,The expected dividend next yea

19、r is $1.30 and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream?,Annuity,A constant stream of cash flows with a fixed maturity.,The formula for the present value of an annuity is:,Annuity: Example,If you can afford a $400 m

20、onthly car payment, how much car can you afford if interest rates are 7% on 36-month loans?,Growing Annuity,A growing stream of cash flows with a fixed maturity.,The formula for the present value of a growing annuity:,Growing Annuity,A defined-benefit retirement plan offers to pay $20,000 per year f

21、or 40 years and increase the annual payment by 3-percent each year. What is the present value at retirement if the discount rate is 10-percent?,4.5 What Is a Firm Worth?,Conceptually, a firm should be worth the present value of the firms cash flows. The tricky part is determining the size, timing an

22、d risk of those cash flows.,4.6 Summary and Conclusions,Two basic concepts, future value and present value are introduced in this chapter. Interest rates are commonly expressed on an annual basis, but semi-annual, quarterly, monthly and even continuously compounded interest rate arrangements exist.

23、The formula for the net present value of an investment that pays $C for N periods is:,4.6 Summary and Conclusions (continued),We presented four simplifying formulae:,How do you get to Carnegie Hall?,Practice, practice, practice. Its easy to watch Olympic gymnasts and convince yourself that you are a

24、 leotard purchase away from a triple back flip. Its also easy to watch your finance professor do time value of money problems and convince yourself that you can do them too. There is no substitute for getting out the calculator and flogging the keys until you can do these correctly and quickly.,Corp

25、orate Finance Ross Westerfield Jaffe,Sixth Edition,Chapter Outline,5.1Definition and Example of a Bond 5.2How to Value Bonds 5.3Bond Concepts 5.4The Present Value of Common Stocks 5.5Estimates of Parameters in the Dividend-Discount Model 5.6Growth Opportunities 5.7The Dividend Growth Model and the N

26、PVGO Model (Advanced) 5.8Price Earnings Ratio 5.9Stock Market Reporting 5.10 Summary and Conclusions,Valuation of Bonds and Stock,First Principles: Value of financial securities = PV of expected future cash flows To value bonds and stocks we need to: Estimate future cash flows: Size (how much) and T

27、iming (when) Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security.,5.1Definition and Example of a Bond,A bond is a legally binding agreement between a borrower and a lender: Specifies the principal amount of the loan. Specifies the s

28、ize and timing of the cash flows: In dollar terms (fixed-rate borrowing) As a formula (adjustable-rate borrowing),5.1Definition and Example of a Bond,Consider a U.S. government bond listed as 6 3/8 of December 2009. The Par Value of the bond is $1,000. Coupon payments are made semi-annually (June 30

29、 and December 31 for this particular bond). Since the coupon rate is 6 3/8 the payment is $31.875. On January 1, 2002 the size and timing of cash flows are:,5.2How to Value Bonds,Identify the size and timing of cash flows. Discount at the correct discount rate. If you know the price of a bond and th

30、e size and timing of cash flows, the yield to maturity is the discount rate.,Pure Discount Bonds,Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date - todays date Face value (F) Discount rate (r),Present value of a pure discount bond at time 0:,Pure Discount Bond

31、s: Example,Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.,Level-Coupon Bonds,Information needed to value level-coupon bonds: Coupon payment dates and time to maturity (T) Coupon payment (C) per period and Face value (F) Discount rate,Value of a Level-coupon bon

32、d = PV of coupon payment annuity + PV of face value,Level-Coupon Bonds: Example,Find the present value (as of January 1, 2002), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. On January 1, 2002 the size and timing of cash flows are:,

33、5.3Bond Concepts,Bond prices and market interest rates move in opposite directions. 2.When coupon rate = YTM, price = par value. When coupon rate YTM, price par value (premium bond) When coupon rate YTM, price par value (discount bond) A bond with longer maturity has higher relative (%) price change

34、 than one with shorter maturity when interest rate (YTM) changes. All other features are identical. 4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.,YTM and Bond Value,800,1000,1100,1200,1300,$1400,0,0.01,0.02,0.0

35、3,0.04,0.05,0.06,0.07,0.08,0.09,0.1,Discount Rate,Bond Value,When the YTM coupon, the bond trades at a premium.,When the YTM = coupon, the bond trades at par.,When the YTM coupon, the bond trades at a discount.,Maturity and Bond Price Volatility,Consider two otherwise identical bonds. The long-matur

36、ity bond will have much more volatility with respect to changes in the discount rate,Coupon Rate and Bond Price Volatility,Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate,5.4The Present Value of Common Stocks,Div

37、idends versus Capital Gains Dividend-Discount Model Valuation of Different Types of Stocks Zero Growth Constant Growth Differential Growth,Case 1: Zero Growth,Assume that dividends will remain at the same level forever,Since future cash flows are constant, the value of a zero growth stock is the pre

38、sent value of a perpetuity:,Case 2: Constant Growth,Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:,Assume that dividends will grow at a constant rate, g, forever. i.e.,.,.,.,Case 3: Differential Growth,Assum

39、e that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to: Estimate future dividends in the foreseeable future. Estimate the future stock price when the stock becomes a Constant Growth St

40、ock (case 2). Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.,Case 3: Differential Growth,Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter,.,.,.,.,.,.,Case 3: Differential Growth,Dividends

41、 will grow at rate g1 for N years and grow at rate g2 thereafter,0 1 2,NN+1,Case 3: Differential Growth,We can value this as the sum of: an N-year annuity growing at rate g1,plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1,Case 3: Differential Growth,To value a Di

42、fferential Growth Stock, we can use,Or we can cash flow it out.,A Differential Growth Example,A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth?,With the Formula,A Differential Growth Example

43、(continued),0 1 234,0 1 2 3,The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.,5.5 Estimates of Parameters in the Dividend-Discount Model,The value of a firm depends upon its growth rate, g, and its discount rate, r. Where does g come from? Where does r co

44、me from?,Formula for Firms Growth Rate,g = Retention ratio Return on retained earnings,Where does r come from?,The discount rate can be broken into two parts. The dividend yield The growth rate (in dividends) In practice, there is a great deal of estimation error involved in estimating r.,Case,5.6Gr

45、owth Opportunities,Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100-percent of its earnings as dividends and the net present value of the growth opportunities.,5.7The Dividend Grow

46、th Model and the NPVGO Model (Advanced),We have two ways to value a stock: The dividend discount model. The price of a share of stock can be calculated as the sum of its price as a cash cow plus the per-share value of its growth opportunities.,The Dividend Growth Model and the NPVGO Model,Consider a

47、 firm that has EPS of $5 at the end of the first year, a dividend-payout ratio of 30%, a discount rate of 16-percent, and a return on retained earnings of 20-percent. The dividend at year one will be $5 .30 = $1.50 per share. The retention ratio is .70 ( = 1 -.30) implying a growth rate in dividends

48、 of 14% = .70 20% From the dividend growth model, the price of a share is:,The NPVGO Model,First, we must calculate the value of the firm as a cash cow.,Second, we must calculate the value of the growth opportunities.,Finally,Dividend Discount Model Revisit,Dividend-Discount Model,COMEQUITY=PV(DIVID

49、ENDS),Other Capital Claims,Other Useful Models,Free Cash Flow Model,Other Capital Claims,ComEquity=PV(FCF+NONOP-DEBT-OCAP,ComEquity=PV(FCF+NONOP-DEBT-OCAP,ComEquity=PV(FCF+NONOP-DEBT-OCAP,Other Useful Models,Free Cash Flow Model,Other Capital Claims,Other Useful Models,Adjusted Present Value Model,C

50、omEquity=PV(FCF at Unlevered cost of equity + VALUE of Leverage +NONOP-DEBT-OCAP,Other Capital Claims,Other Usful Model,Residual Model,ComEquity=BV(CORE) + PV( RI from CORE +NONOP-DEBT-OCAP,Other Capital Claims,5.8Price Earnings Ratio,Many analysts frequently relate earnings per share to price. The

51、price earnings ratio is a.k.a the multiple Calculated as current stock price divided by annual EPS The Wall Street Journal uses last 4 quarters earnings Firms whose shares are “in fashion” sell at high multiples. Growth stocks for example. Firms whose shares are out of favor sell at low multiples. Value stocks for example.,Other Price Ratio Analysis,Many analysts frequently relate earnings per share to variables other than price, e.g.: Price/Cash Flow Ratio cash flow = net income + depreciation = cash flow from operations or operating cash flow Price/Sales current stock price divid