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Unformatted text preview: Session 4 Homework Solutions THIS DOCUMENT IS STRICTLY FOR THE USE OF CURRENT STUDENTS IN MGMT 640 COURSE. IT 5.1 Future value: Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that return of 8 percent each year. What will be the value of the investment in 10 years? Solution: PV= i= N= Find FV= 25,000 8% 10 FV10 = PV ×(1 + i ) = $53,973.12 $53,973.12 This will be the amount in the fund at the end of 10 years if the fund e MGMT 640 COURSE. IT MAY NOT BE REPRODUCED OR DISTRIBUTED TO OTHERS, INCLUDING ANY FUTURE STUDE in a mutual fund that will provide a t in 10 years? FV10 = PV ×(1 + i ) n = $25,000 ×(1.08)10 = $53,973.12 d of 10 years if the fund earns a return of 8%, compounded annually. DING ANY FUTURE STUDENTS OF THE COURSE. 5.30 Patrick Seeley has $2,400 that he is looking to invest. His brother approached him w investment opportunity that could double his money in four years. What interest rate would investment have to yield in order for Patrick’s brother to deliver on his promise? Solution: FV4 = PV × (1 + i ) 4
PV= N= FV= Find i= $2,400 4 $4,800 18.92% $4,800 = $2,400(1 + i ) 4 $4,800 (1 + i ) 4 = = 1.4800 $2,400 i = ( 2.000) 4 − 1 = 0.1892 = 18.92%
1 This type of problem -- doubling the money -- can also be solved taking any values arbitrarily a PV= N= FV= Find i= $1 4 $2 18.92% er approached him with an at interest rate would the promise? V × (1 + i ) 4 2,400(1 + i ) 4 $4,800 = 1.4800 $2,400 2.000) 4 − 1 = 0.1892 8.92%
g any values arbitrarily as shown below:
1 6.18Growing perpetuity: You are evaluating a growing perpetuity product from a large financia product promises an initial payment of $20,000 at the end of this year and subsequent paym grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investment p present value of this growing perpetuity? Solution: Cash flow at t = 1 = CF1 Annual growth rate = g Discount rate = i
Find PV= 20,000 3.40% 9% $357,142.86 Note: In this type of problems, it is important to recognize if the initial payment is as of today (t= In this problem the initial payment is at the end of this year. Therefore, there is no need to multi As you will learn more on this later, this model is also called the constant growth model or Gord t from a large financial services firm. The and subsequent payments that will thereafter rate for investment products, what is the ayment is as of today (t=0) or at the end of the year (t=1). there is no need to multiply the amount of $20,000 with (1.034). nt growth model or Gordon model that is widely used in valuing common stocks. 6.22 Computing annuity payment: Gary Whitmore is a high school sophomore. He currentl in a money market account paying 5.65 percent annually. He plans to use this and his sav next four years to buy a car at the end of his sophomore year in college. He estimates that cost him $12,000 in four years. How much should he invest in the money market account e the next four years if he wants to achieve his target? Solution: Amount needed at the end of four years $12,000 First, find the FV of the amount in the money market. PV= 7500 i= 5.65% N= 4 Find FV= $9,344.14 By the end of fourn years, $7,500 in the account today will accumulate to this a The shortfall is $2,655.86 (12,000 - 9,344.14) and Gary will have to make annu by the end of four years -- so that the full need of $12,000 is met. Next, find the PMT amount that Gary needs to save each year in order to have $2,655.86 in four yea FV= i= N= Find PMT= $2,655.86 5.65% 4 $610.27 (1 + i ) n FVA = PMT × i FVA PMT = = 1 − (1 + i ) n i = $610.27 − 1 $2,655.86 $2,655.86 = 4 (1.0565) − 1 4.351949 0.0565 Alternatively, the problem could be solved in one step. FV $12,000.00 PV ($7,500.00) i 5.65% n 4 PMT ($610.27) homore. He currently has $7,500 use this and his savings over the e. He estimates that the car will ey market account every year for will accumulate to this amount. will have to make annual contributions to have this amount 00 is met. e $2,655.86 in four years. .86 $2,655.86 = 4 ) − 1 4.351949 65 ...
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- Summer '09