【正文】 would be less than the $10,000 the investment promised, and we would be worse off in FV terms : $9,500 () = $9,975 $10,000 410 The Multiperiod Case ? The general 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. 411 Future Value ? Suppose a stock currently pays a dividend of $, which is expected to grow at 40% per year for the next five years. ? What will the dividend be in five years? FV = C0 (1 + r)T $ = $ ()5 412 Future Value and Compounding ? Notice that the dividend in year five, $, is considerably higher than the sum of the original dividend plus five increases of 40percent on the original $ dividend: $ $ + 5 [$ .40] = $ This is due to pounding. 413 Future Value and Compounding 0 1 2 3 4 5 $3)($ ?$)($ ?$2)($ ?$5)($ ?$4)($ ?$414 Present Value and Discounting ? How 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%? 0 1 2 3 4 5 $20,000 PV 5)(0 0 0,20$ 4 3,9$ ?415 Finding the Number of Periods If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000? TrCFV )1(0 ??? T)(000,5$000,10$ ??2021,5$ 000,10$)( ??T)2ln () ( ?Ty e a r s 9 5 6 9 3 ) n ( )2l n ( ???T416 Assume 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 today. What rate of interest must you earn on your investment to cover the cost of your child’s education? What Rate Is Enough? TrCFV )1(0 ??? 12)1(0 0 0,5$0 0 0,50$ r???100 0 0,5$ 0 0 0,50$)1( 12 ??? r12110)1( ?? r2 1 1 1 1 121 ?????rAbout %. 417 Calculator Keys ? Texas Instruments BAII Plus ? FV = future value ? PV = present value ? I/Y = periodic interest rate ? P/Y must equal 1 for the I/Y to be the periodic rate ? Interest is entered as a percent, not a decimal ? N = number of periods ? Remember to clear the registers (CLR TVM) after each problem ? Other calculators are similar in format 418 Multiple Cash Flows ? Consider an investment 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? ? If the issuer offers this investment for $1,500, should you purchase it? 419 Mult