# The Time Value of Money

The Time Value of Money

5.1 Future value: Chuck Tomkovick is planning to invest \$25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?
5.30 Patrick Seeley has \$2,400 that he is looking to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick’s brother to deliver on his promise?
6.18 Growing perpetuity: You are evaluating a growing perpetuity product from a large financial services firm. The product promises an initial payment of \$20,000 at the end of this year and subsequent payments that will thereafter grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investment products, what is the present value of this growing perpetuity?
6.22 Computing annuity payment: Gary Whitmore is a high school sophomore. He currently has \$7,500 in a money market account paying 5.65 percent annually. He plans to use this and his savings over the next four years to buy a car at the end of his sophomore year in college. He estimates that the car will cost him \$12,000 in four years. How much should he invest in the money market account every year for the next four years if he wants to achieve his target?
Risk and Return
7.3 Expected returns: You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted into medical school is about 10 percent. If you are accepted into medical school, then your starting salary when you graduate will be \$300,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn \$40,000 per year. Without considering the additional educational years or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary?
7.15 Calculating the variance and standard deviation: Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be –25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1, respectively, then what are the expected return and the standard deviation for Kate’s investment?
7.20 Portfolios with more than one asset: Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively.

Probability
Return(A)
Return(B)
Good
0.35
0.30
0.50
OK
0.50
0.10
0.10
Poor
0.15
-0.25

-0.30

7.27 In order to fund her retirement, Glenda requires a portfolio with an expected return of 12 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that will enable Glenda to achieve her investment requirement?

The Fundamentals of Capital Budgeting
10.2 Net present value: Kingston, Inc., is looking to add a new machine at a cost of \$4,133,250. The company expects this equipment will lead to cash flows of \$814,322, \$863,275, \$937,250, \$1,017,112, \$1,212,960, and \$1,225,000 over the next six years. If the appropriate discount rate is 15 percent, what is the NPV of this investment?
10.5 Payback: Quebec, Inc., is purchasing machinery at a cost of \$3,768,966. The company expects, as a result, cash flows of \$979,225, \$1,158,886, and \$1,881,497 over the next three years. What is the payback period?
10.24 Draconian Measures, Inc., is evaluating two independent projects. The company uses a 13.8 percent discount rate for such projects. Cost and cash flows are shown in the table. What are the NPVs of the two projects?

Year
Project 1
Project 2
0 \$(8,425,375) \$(11,368,000)
1 \$3,225,997 \$2,112,589
2 \$1,775,882 \$3,787,552
3 \$1,375,112 \$3,125,650
4 \$1,176,558 \$4,115,899
5 \$1,212,645 \$4,556,424
6 \$1,582,156
7 \$1,365,882

10.28 Jekyll & Hyde Corp. is evaluating two mutually exclusive projects. Their cost of capital is 15 percent. Costs and cash flows are given in the following table. Which project should be accepted? You only have to make the comparison using NPV, don’t bother with IRR.

Year Project 1 Project 2
0 \$(1,250,000) \$(1,250,000)
1 \$250,000 \$350,000
2 \$350,000 \$350,000
3 \$450,000 \$350,000
4 \$500,000 \$350,000
5 \$750,000 \$350,000