CHAPTER 3 THE TIME VALUE OF MONEY

P3-41. Determine the length of time required to double the value of an investment, given the following rates of return.

a. 4 percent

b. 10 percent

c. 30 percent

d. 100 percent

P3-42. Consider the following three investments of equal risk. Which offers the greatest rate of return?

Investment

End of Year	A	B	C
0	-$10,000	-$20,000	-$25,000
1	0	9,500	20,000
2	0	9,500	30,000
3	24,600	9,500	-12,600

r = 40%

P3-43. You are given the series of cash flows shown in the following table.

Cash Flows

Year	A	B	C
1	$500	$1,500	$2,500
2	560	1,550	2,600
3	640	1,610	2,650
4	720	1,680	2,650
5	800	1,760	2,800
6		1,850	2,850
7		1,950	2,900
8			2,060
9			2,170
10			2,280

a. Calculate the compound annual growth rate associated with each cash flow stream.

b. If year-1 values represent initial deposits in a savings account paying annual interest, what is the annual rate of interest earned on each account?

c. Compare and discuss the growth rate and interest rate found in parts a and b, respectively.

P3-44. Determine which of the following three investments offers you the highest rate of return on your $1,000 investment over the next five years.

Investment 1: $2,000 lump sum to be received in five years

Investment 2: $300 at the end of each of the next five years

Investment 3: $250 at the beginning of each of the next five years

a. Which investment offers the highest return?

b. Which offers the highest return if the payouts are doubled (i.e., $4,000, $600, and $500)?

c. What causes the big change in the returns on the annuities?

P3-45. Find the rates of return required to do the following:

a. Double an investment in 4 years

b. Double an investment in 10 years

c. Triple an investment in 4 years

d. Triple an investment in 10 years

P3-46. The viatical industry offers a rather grim example of present value concepts. A firm in this business, called a viator, purchases the rights to the benefits from a life insurance contract from a terminally ill client. The viator may then sell claims on the insurance payout to other investors. The industry began in the early 1990s as a way to help AIDS patients capture some of the proceeds from their life insurance policies for living expenses.

Suppose a patient has a life expectancy of 18 months and a life insurance policy with a death benefit of $100,000. A viator pays $80,000 for the right to the benefit, and then sells that claim to another investor for $80,500.

a. From the point of view of the patient, this contract is like taking out a loan. What is the compound annual interest rate on the loan if the patient lives exactly 18 months? What if the patient lives 36 months?

b. From the point of view of the investor, this transaction is like lending money. What is the compound annual interest rate earned on the loan if the patient lives 18 months? What if the patient lives just 12 months?

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Answer to MiniCase

Present Value

Casino.com Corporation is building a $25 million office building in Las Vegas and is financing the construction at an 80 percent loan-to-value ratio, where the loan is in the amount of $20,000,000. This loan has a ten-year maturity, calls for monthly payments, and is contracted at an interest rate of 8 percent.

Assignment

Using the above information, answer the following questions.

1. What is the monthly payment?

2. How much of the first payment is interest?

3. How much of the first payment is principal?

4. How much will Casino.com Corporation owe on this loan after making monthly payments for three years (the amount owed immediately after the thirty-sixth payment)?

5. Should this loan be refinanced after three years with a new seven-year 7 percent loan, if the cost to refinance is $250,000? To make this decision, calculate the new loan payments and then the present value of the difference in the loan payments.

6. Returning to the original ten-year 8 percent loan, how much is the loan payment if these payments are scheduled for quarterly rather than monthly payments?

7. For this loan with quarterly payments, how much will Casino.com Corporation owe on this loan after making quarterly payments for three years (the amount owed immediately after the twelfth payment)?

8. What is the annual percentage rate on the original ten-year 8 percent loan?

9. What is the effective annual rate (EAR) on the original ten-year 8 percent loan?