公司理財(cái)原版英文課件4

1、discounted cash flow valuationchapter 4copyright 2010 by the mcgraw-hill companies, inc. all rights reserved.mcgraw-hill/irwin4-1key concepts and skillsobe able to compute the future value and/or present value of a single cash flow or series of cash flowsobe able to compute the return on an investme

2、ntobe able to use a financial calculator and/or spreadsheet to solve time value problemsounderstand perpetuities and annuities4-2chapter outline4.1 valuation: the one-period case4.2 the multiperiod case4.3 compounding periods4.4 simplifications4.5 loan amortization4.6 what is a firm worth?4-34.1 the

3、 one-period caseoif you were to invest $10,000 at 5-percent 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)qthe total amount due a

4、t the end of the investment is call the future value (fv). 4-4future valueoin the one-period case, the formula for fv can be written as:fv = c0(1 + r)where c0 is cash flow today (time zero), and r is the appropriate interest rate.4-5present valueoif you were to be promised $10,000 due in one year wh

5、en interest rates are 5-percent, your investment would be worth $9,523.81 in todays dollars. 05. 1000,10$81.523, 9$the amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the present value (pv).note that $10,000 = $9,523.81(1.

6、05).4-6present valueoin the one-period case, the formula for pv can be written as:rcpv11where c1 is cash flow at date 1, and r is the appropriate interest rate.4-7net present valueothe net present value (npv) of an investment is the present value of the expected cash flows, less the cost of the inve

7、stment.osuppose 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?4-8net present value81.23$81.523, 9$500, 9$05. 1000,10$500, 9$npvnpvnpvthe present value of the cash inflow is greaterthan the cost. in other words, the net

8、 presentvalue is positive, so the investment should be purchased.4-9net present valuein the one-period case, the formula for npv can be written as:npv = cost + pvif we had not undertaken the positive npv project considered on the last slide, and instead invested our $9,500 elsewhere at 5 percent, ou

9、r fv would be less than the $10,000 the investment promised, and we would be worse off in fv terms :$9,500(1.05) = $9,975 $1.10 + 5$1.10.40 = $3.30this is due to compounding.4-13future value and compounding01234510. 1$3)40. 1 (10. 1$02. 3$)40. 1 (10. 1$54. 1$2)40. 1 (10. 1$16.2$5)40. 1 (10. 1$92. 5$

10、4)40. 1 (10. 1$23. 4$4-14present value and discountingohow much would an investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%?012345$20,000pv5)15. 1 (000,20$53.943, 9$4-154.5 finding the number of periodsif we deposit $5,000 today in an account pay

11、ing 10%, how long does it take to grow to $10,000?trcfv)1 (0t)10. 1 (000, 5$000,10$2000, 5$000,10$)10. 1 (t)2ln()10. 1ln(tyears 27. 70953. 06931. 0)10. 1ln()2ln(t4-16assume the total cost of a college education will be $50,000 when your child enters college in 12 years. you have $5,000 to invest tod

12、ay. what rate of interest must you earn on your investment to cover the cost of your childs education? what rate is enough?trcfv)1 (012)1 (000, 5$000,50$r10000, 5$000,50$)1 (12r12110)1 (r2115.12115. 1110121rabout 21.15%.4-17calculator keysotexas instruments ba-ii plusnfv = future valuenpv = present

13、valueni/y = periodic interest rateop/y must equal 1 for the i/y to be the periodic rateointerest is entered as a percent, not a decimalnn = number of periodsnremember to clear the registers (clr tvm) after each problemnother calculators are similar in format4-18multiple cash flowsoconsider an invest

14、ment that pays $200 one year from now, with cash flows increasing by $200 per year through year 4. if the interest rate is 12%, what is the present value of this stream of cash flows?oif the issuer offers this investment for $1,500, should you purchase it?4-19multiple cash flows01234200400600800178.

15、57318.88427.07508.411,432.93present value cost do not purchase4-20valuing “l(fā)umpy” cash flowsfirst, set your calculator to 1 payment per year.then, use the cash flow menu:cf2cf1f2f1cf0120011,432.930400inpv12cf4cf3f4f3160018004-214.3 compounding periodscompounding an investment m times a year for t ye

16、ars provides for future value of wealth:tmmrcfv104-22compounding periodsq for example, if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow to93.70$)06. 1 (50$212.150$632fv4-23effective annual rates of interesta reasonable question to ask in the above example is “

17、what is the effective annual rate of interest on that investment?”the effective annual rate (ear) of interest is the annual rate that would give us the same end-of-investment wealth after 3 years:93.70$)06. 1 (50$)212.1 (50$632fv93.70$)1 (50$3ear4-24effective annual rates of interestso, investing at

18、 12.36% compounded annually is the same as investing at 12% compounded semi-annually.93.70$)1 (50$3earfv50$93.70$)1 (3 ear1236.150$93.70$31ear4-25effective annual rates of interestofind the effective annual rate (ear) of an 18% apr loan that is compounded monthly.owhat we have is a loan with a month

19、ly interest rate rate of 1%.othis is equivalent to a loan with an annual interest rate of 19.56%.1956. 1)015. 1 (1218.111212mmr4-26ear on a financial calculatorkeys:description:2nd iconvopens interest rate conversion menu eff= cpt19.56texas instruments baii plus nom= 18 entersets 18 apr. c/y= 12 ent

20、ersets 12 payments per year4-27continuous compoundingothe general formula for the future value of an investment compounded continuously over many periods can be written as:fv = c0ertwhere c0 is cash flow at date 0,r is the stated annual interest rate, t is the number of years, ande is a transcendent

21、al number approximately equal to 2.718. ex is a key on your calculator.4-284.4 simplificationsoperpetuityna constant stream of cash flows that lasts foreverogrowing perpetuityna stream of cash flows that grows at a constant rate foreveroannuityna stream of constant cash flows that lasts for a fixed

22、number of periodsogrowing annuityna stream of cash flows that grows at a constant rate for a fixed number of periods4-29perpetuitya constant stream of cash flows that lasts forever01c2c3c32)1 ()1 ()1 (rcrcrcpvrcpv 4-30perpetuity: examplewhat is the value of a british consol that promises to pay 15 e

23、very year for ever? the interest rate is 10-percent.011521531515010.15pv4-31growing perpetuitya growing stream of cash flows that lasts forever01c2c(1+g)3c (1+g)2322)1 ()1 ()1 ()1 ()1 (rgcrgcrcpvgrcpv4-32growing perpetuity: examplethe expected dividend next year is $1.30, and dividends are expected

24、to grow at 5% forever. if the discount rate is 10%, what is the value of this promised dividend stream?01$1.302$1.30(1.05)3$1.30 (1.05)200.26$05.10.30. 1$pv4-33annuitya constant stream of cash flows with a fixed maturity01c2c3ctrcrcrcrcpv)1 ()1 ()1 ()1 (32trrcpv)1 (11tc4-34annuity: exampleif you can

25、 afford a $400 monthly car payment, how much car can you afford if interest rates are 7% on 36-month loans?01$4002$4003$40059.954,12$)1207.1 (1112/07.400$36pv36$4004-35 what is the present value of a four-year annuity of $100 per year that makes its first payment two years from today if the discount

26、 rate is 9%? 22.297$09. 197.327$0pv0 1 2 3 4 5$100 $100 $100 $100$323.97$297.2297.323$)09. 1 (100$)09. 1 (100$)09. 1 (100$)09. 1 (100$)09. 1 (100$4321411ttpv2-354-36growing annuitya growing stream of cash flows with a fixed maturity01cttrgcrgcrcpv)1 ()1 ()1 ()1 ()1 (12trggrcpv)1 (112c(1+g)3c (1+g)2t

27、 c(1+g)t-14-37growing annuity: examplea defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3% each year. what is the present value at retirement if the discount rate is 10%?01$20,00057.121,265$10. 103. 1103.10.000,20$40pv2$20,000(1.03)40 $2

28、0,000(1.03)394-38growing annuity: exampleyou are evaluating an income generating property. net rent is received at the end of each year. the first years rent is expected to be $8,500, and rent is expected to increase 7% each year. what is the present value of the estimated income stream over the fir

29、st 5 years if the discount rate is 12%?0 1 2 3 4 5500, 8$)07. 1 (500, 8$2)07. 1 (500, 8$095, 9$65.731, 9$3)07. 1 (500, 8$87.412,10$4)07. 1 (500, 8$77.141,11$34,706.264-394.5 loan amortizationopure discount loans are the simplest form of loan. the borrower receives money today and repays a single lum

30、p sum (principal and interest) at a future time.ointerest-only loans require an interest payment each period, with full principal due at maturity.oamortized loans require repayment of principal over time, in addition to required interest.4-40pure discount loansotreasury bills are excellent examples

31、of pure discount loans. the principal amount is repaid at some future date, without any periodic interest payments.oif a t-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?npv = 10,000 / 1.07 = 9,345.794-41interest-o

32、nly loanoconsider a 5-year, interest-only loan with a 7% interest rate. the principal amount is $10,000. interest is paid annually.nwhat would the stream of cash flows be?oyears 1 4: interest payments of .07(10,000) = 700oyear 5: interest + principal = 10,700othis cash flow stream is similar to the cash flows on corporate bonds, and