FINANCE 634
Spring 1995 Exam I
1. Consider the following loan conditions:
Amount borrowed = $225,000
Term of Loan = 14 years
Interest Rate = 10.25% stated annual rate
Payment Frequency = Monthly
Answer the following questions:
a. Suppose you pay off the loan immediately following the 136th payment. What is the total
dollar amount of interest you will have paid over the life of the loan? [10]
b. Suppose the largest payment you can afford is $2,000 per month, so you want to arrange
a 5-year balloon loan with a $2,000 payment. What will the amount of the balloon payment be? [5]
c. Returning to the original loan conditions (ignore b), suppose you make an extra payment
of $100 with each required monthly payment. How much money, in actual dollars, would you
save using this payment scenario versus the one described in Part A (make only the required
payment and carry the loan for the full 14 years)? [5]
d. What is the effective annual rate of the loan scenario described in part c? [5]
2. Consider the following annual cash payments:
TIME CASH FLOW
1 0
2 0
3 0
4 0
5 1500
6 1500
7 1500
8 1500
9 ?
10 ?
11 ?
12 ?
13 -1000
14 1200
15 1200
16 1200
17 800
The missing cash flows (?s) are all equal amounts. Using a 9.5% discount rate, the TOTAL
present value of all of the cash flows is $9,500. Find the missing cash flows. [10]
3. You want to construct an investment plan that will allow you to accumlate a large amount of money
for your newborn daughter by the time she reaches retirement age. You will make annual deposits
of $2,500 into an account for the rest of your working life, which is 35 years. You have $5,000 now to use
as a beginning deposit, and the first annual deposit will be made on year from now. You intend to invest
the money in a tax-deferred account that carries a guaranteed 5.0% annual nominal rate with
interest compounded continuously. Your daughter will pay taxes on the amount withdrawn at age 65 (65 years
from now) with an estimated tax rate of 28%. How much cash will she have left from the account at that time? [10]
B. Suppose that instead of investing in a tax-deferred account you decide to invest in a regular taxable account using
the same investment plan described above. This account has a guaranteed 7.0% annual rate with continuous compounding,
but you will pay taxes on the interest earned every year. Is this strategy better or worse than the one described above?
Support your answer with appropriate calculations. [5]
4. You have the choice between two different loan plans to purchase a new car. The
purchase price of the car is $27,500. The two loan plans are described below:
Plan A Plan B
Required down payment $0 $3500
Loan Term 5 years 5 years
Annual Rate 10.4% 4.8%
Cash Rebate $1500 $0
The required down payment is the minimum that is acceptable to the lender. You can pay
more. If you choose to do so, you may use the cash rebate as part or all of the down payment on
Plan A. Regardless of how you finance the car, you plan to keep the car for at three years and
then sell it immediately after the 36th payment is made.
If your personal opportunity rate for cash is 12%, describe the best way to finance the car
and calculate the value of the advantage of the best plan over the next best alternative. [20]
b. What personal opportunity rate would make you indifferent between the best plan and the
next best alternative? [5]
5. You are evaluating a company's common stock based on the following information and assumptions:
The stock is expected to pay no dividend for four years. Then, at the end of the fourth year, the stock is expected
to pay a $1.25 dividend and after that dividends are expected to grow by 6% per year throughout the foreseeable future.
If your opportunity cost is 10.5% for investments of this risk level, what is the maximum price that you would be willing to pay for
a share of this stock? [5]
6. You deposit $5000 now and $500 at the end of each calendar quarter for 10 years (40 $500
deposits) in an account that has a stated annual rate of 9.25% with interest compounded
monthly. How much will be in the account immediately following the final deposit? (Assume that
every month has 30 days and every quarter has 3 months and 90 days.) [5]
7. You deposit $5000 now and make equal monthly deposits for 15 years (180 monthly
deposits) in an account that has a stated annual rate of 10.25% with interest compounded
quarterly. If the account has a total of $45,000 in it immediately following the final deposit,
what was the dollar amount of your monthly payment? (Assume that every month has 30 days
and every quarter has 3 months and 90 days.) [5]
8. You deposit $5000 now and make equal monthly deposits of $125 for 20 years (240
monthly deposits) in an account that has interest compounded daily. If the account has a total of
$130,000 in it immediately following the final deposit, what was the stated (nominal) annual
interest rate on the account? (Assume that every month has 30 days and every quarter has 3
months and 90 days.) [5]
9. Suppose a corporate bond is listed with a closing price of 109-3/8 and a Current Yield of 8.4 in
today's Wall Street Journal. The bond has 15 years remaining until maturity, a $1,000 face value,
semiannual coupon payments, and the next coupon payment is due in exactly 6 months. Suppose
you purchased the bond today and held it for 5 years. Immediately after receiving an interest
payment (your 10th interest payment) you sell the bond to another investor for exactly $85 more
than you paid for it. What was your holding period return on an annual basis for the five years of
the investment? [10]
b. By how many basis points (hundredths of a percent) did the yield to maturity change
between the time you bought the bond and the time you sold it? [5]
Multiple Choice:
1. In class, it was pointed out that corporations came into being to do all of the following except:
A. diversify risk
B. pool investor's funds
C. perpetuate the enterprise
D. separate ownership from management
E. None of the above is an exception
2. The current state of the capital markets differs from that of a few years ago in which of the following manners?
A. It is more conservative.
B. Competition for capital is more intense.
C. Shareholders have a stronger influence on managers.
D. Two of the above.
E. All of the above.
3. Which of the following statements is (are) true?
A. Synergy in corporate mergers occurs with a reasonable frequency.
B. Companies that diversify their business activities in order to reduce risk are more attractive to investors
than companies that are less diversified.
C. The efficient allocation of capital is the primary objective of the capital market.
D. More than one of the above.
E. None of the above.
4. Which of the following statements is (are) true?
A. One way in which the agency problem is addressed in companies is through the inclusion of negative covenants
in bond indentures.
B. In the Conceptual Framework of Accounting, the primary tenet is the concept of conservatism.
C. The rules of accounting ensure that the values reported for assets on the balance sheet reflect the
true value of the assets of the company.
D. More than one of the above.
E. None of the above.
5. Which of the following statements is (are) true?
A. A balance sheet represents a "stock" concept and an income statement represents a "flow" concept.
B. A company could possibly have negative operating cash flow and positive free cash flow in a given period.
C. A company could possibly have negative operating cash flow and positive total cash flow in a given period.
D. Two of the above.
E. All of the above.
6. Which of the following statements is (are) true?
A. The major factor that influences the day-to-day change in the price of corporate bonds is fluctuations in the default
risk of the bonds.
B. A bond that is rate BBB is known as a speculative grade or junk bond.
C. A "hump" in the yield curve is taken as a reasonably strong indicator of a long period of strong economic growth.
D. More than one of the above.
E. None of the above.
7. Which of the following statements is (are) true?
A. The main difference between financial intermediaries and financial middlemen is that middlemen create new secuties out of existing ones.
B. The rates on long-term Treasury bonds are always higher than the rates on short-term Treasury bonds or notes.
C. For a given change in the general level of interest rates, the value of a 20-year bond will fluctuate more than the value of a 3-year
bond, other things equal.
D. More than one of the above.
E. None of the above.
8. According to the constant dividend growth model of common stock valuation,
A. an increase in the current dividend will increase any stock's price.
B. It is not possible for a company to have an expected growth rate that is higher than investors' required return.
C. The price of common stock is most closely affected by the company's dividend policy.
D. More than one of the above.
E. None of the above.
ANSWERS
Question 1:
A. $189,222.38
B. $218,910.09
C. $18,407.46
D. $10.75%
Question 2:
$3,462.06
Question 3:
A. $774,338.67
B. $1,224,687.71
Question 4:
A. The low interest rate loan is the best. The high interest rate loan with the rebate not applied to the
down payment is next best. The value of the advantage of the best over the next best plan is $886.59.
B. 20.92%
Question 5:
$20.58
Question 6:
$45,026.03
Question 7:
$52.71
Question 8:
9.88%
Question 9:
A. 9.646%
B. 139
Multiple Choice:
1. E
2. D
3. C
4. A
5. C
6. E
7. E
8. E
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