Georgia State University Department of Finance

MBA 8622 Fall 2001

MBA 8622: Corporation Finance

Take-Home Problem Set
Instructors:
Lalitha Naveen, N. Daniel, C.Hodges, A. Mettler, R. Morin,
M. Shrikhande,

Directions:
This take-home problem set (THPS) is due at the begin of the regular class in week 13
(Nov 12-16), 2001, and has to be turned in physically (i.e. do not send your answers via
e-mail, an electronically turned in THPS will not be graded).
Though you may use your book, notes, etc., all work on this THPS is to be yours
alone - any discussion of either the questions on the assignment or your answers
with anyone other than the instructor will be considered as cheating and, thus, as a
violation of the GSU honor code.
For the multiple choice questions (Part I), record the letter of the correct multiple choice
answer directly on the answer sheet on the last page (do not show any intermediate steps,
no partial credit will be assigned for multiple choice questions). For the problems with no
answer choices (Part II), record your final numeric answer including relevant calculations
and intermediate steps on separate sheets of paper (partial credit may be assigned for the
problems with no answer choices, if appropriate).
The grade on any assignment turned in after the beginning of class on the relevant date
listed above will be reduced at a daily compounded rate of 10% per day (begin mode). For
grading purposes, each multiple choice question (Part I) has a grading weight of 1 (one),
each question of Part II has a grading weight of 2 (two).

Following:
- Part I: Multiple choice questions (pp. 2-5)
- Part II: Problems and Calculations (pp. 6-8)
- Cover Sheet with answers to Part I (p. 9, to turn in together with the solutions of Part II)
GSU, Department of Finance - Take-Home Problem Set / page 2 - Corporation Finance
Fall 2001 MBA 8622

Part I: Multiple Choice Questions

(Record the letter corresponding with the best answer on the answer sheet)

1. Which of the following statements is most correct?

a) An investment which compounds interest semiannually, and has a nominal rate

of 10 percent, will have an effective rate less than 10 percent.
b) The present value of a three-year $100 annuity due is less than the present value
of a three-year $100 ordinary annuity.
c) The proportion of the payment of a fully amortized loan which goes toward
interest declines over time.
d) Statements a and c are correct.
e) None of the answers above is correct.

2. You are willing to pay $15,625 to purchase a perpetuity which will pay you and your
heirs $1,250 each year, forever. If your required rate of return does not change, how
much would you be willing to pay if this were a 20-year, annual payment,
ordinary annuity instead of a perpetuity (rounded to the next $)?

a) $10,342
b) $11,931
c) $12,273
d) $13,922
e) $17,157

3. The risk-free rate, kRF, is 6 percent and the market risk premium, (k M – kRF), is
5 percent. Assume that required returns are based on the CAPM. Your $1
million portfolio consists of $700,000 invested in a stock that has a beta of 1.2
and $300,000 invested in a stock that has a beta of 0.8. Which of the
following statements is most correct?

a) The portfolio’s required return is less than 11 percent.

b) If the risk-free rate remains unchanged but the market risk premium increases
by 2 percentage points, the required return on your portfolio will increase by
more than 2 percentage points.
c) If the market risk premium remains unchanged but expected inflation
increases by 2 percentage points, the required return on your portfolio will
increase by more than 2 percentage points.
d) If the stock market is efficient, your portfolio’s expected return should equal
the expected return on the market, which is 11 percent.
e) None of the above answers is correct.
GSU, Department of Finance - Take-Home Problem Set / page 3 - Corporation Finance
Fall 2001 MBA 8622

4. Ripken Iron Works faces the following probability distribution:

State of Probability of Stock’s Expected Return

the Economy State Occurring if this State Occurs
Boom 0.25 25%
Normal 0.50 15
Recession 0.25 5
What is the coefficient of variation on the company’s stock?

a) 0.06
b) 0.47
c) 0.54
d) 0.67
e) 0.71

5. If the yield to maturity increased 1 percentage point, which of the following bonds
would have the largest percentage decrease in value?

a) A 10-year zero-coupon bond.

b) A 10-year bond with an 8 percent coupon.
c) A 20-year zero-coupon bond.
d) A 20-year bond with an 8 percent coupon.
e) A 20-year bond with a 12 percent coupon.

6. A 10-year bond has a 10 percent annual coupon and a yield to maturity of 12

percent. The bond can be called in 5 years at a call price of $1,050 and the bond’s
face value is $1,000. Which of the following statements is most correct?

a) The bond’s current yield is greater than 10 percent.

b) The bond’s yield to call is less than 12 percent
c) The bond is selling at a price below par
d) Both answers a and c are correct
e) None of the above answers is correct

7. You have $2,000 invested in a bank account that pays a 4 percent nominal annual
interest with daily compounding. How much money will you have in the account in
132 days from today? (Assume there are 365 days in each year.)

a) $2,029.14
b) $2,028.93
c) $2,040.00
d) $2,023.44
e) 2,023.99
GSU, Department of Finance - Take-Home Problem Set / page 4 - Corporation Finance
Fall 2001 MBA 8622

8. Which of the following is most correct?

a) The present value of a 5-year annuity due will exceed the present value of a
5-year ordinary annuity. (Assume that both annuities pay $100 per period and
there is no chance of default.)
b) If a loan has a nominal rate of 10 percent, then the effective rate can never be
less than 10 percent.
c) If there is annual compounding, then the effective, periodic, and nominal rates
of interest are all the same.
d) Answers a and c are correct.
e) All of the answers above are correct.

9. If it were evaluated with an interest rate of 0 percent, a 10-year regular annuity would
have a present value of $3,755.50. If the future (compounded) value of this annuity,
evaluated at Year 10, is $5,440.22, what effective annual interest rate must the
analyst be using to find the future value?

a) 7%
b) 8%
c) 9%
d) 10%
e) 11%

10. Assume you are to receive a 20-year annuity with annual payments of $50. The first
payment will be received at the end of Year 1, and the last payment will be received
at the end of Year 20. You will invest each payment in an account that pays 10
percent. What will be the value in your account at the end of Year 30?

a) $6,354.81
b) $7,427.83
c) $7,922.33
d) $8,591.00
e) $6,752.46
GSU, Department of Finance - Take-Home Problem Set / page 5 - Corporation Finance
Fall 2001 MBA 8622

11. You recently purchased a 20-year investment which pays you $60 at t=1, $80 at t=2,
$100 at t=3, $120 at t=4, and some fixed cash flow, X, at the end of each of the
remaining 16 years. The investment cost you $1,387.47. Alternative investments of
equal risk have a required return of 6 percent. What is the annual cash flow
received at the end of each of the final 16 years, that is, what is X?

a) $120
b) $125
c) $130
d) $135
e) $140

12. Which of the following statements is most correct?

a) All else equal, an increase in interest rates will have a greater effect on the
prices of long-term bonds than it will on the prices of short-term bonds
b) All else equal, an increase in interest rates will have a greater effect on
higher-coupon bonds than it will have on lower-coupon bonds
c) An increase in interest rates will have a greater effect on a zero coupon bond
with 10 years maturity than it will have on a 9-year bond with a 10 percent
annual coupon.
d) All of the statements above are correct
e) Answers a and c are correct

13. Jeremy Wintergarden has just purchased a BMW and borrowed $48,980 towards the
purchase. The amount is to be repaid over a period of 5 years in payments of
$1,000 each month. What is the Annual Percentage Rate (APR) of the loan?

a) 0.69%
b) 4.08%
c) 5.13%
d) 8.29%
e) 8.61%
GSU, Department of Finance - Take-Home Problem Set / page 6 - Corporation Finance
Fall 2001 MBA 8622

14. Foster Industries has a project which has the following cash flows:
Year 0 -300.00
Year 1 100.00
Year 2 125.43
Year 3 90.12
Year 4 ?

What cash flow will the project have to generate in the fourth year in order for the
project to have a 15% rate of return?

a) $ 15.55
b) $ 58.95
c) $100.25
d) $103.10
e) $150.75

15. Your portfolio consists of $100,000 invested in a stock which has a beta = 0.8,
$150,000 invested in a stock which has a beta = 1.2, and $50,000 invested in a
stock which has a beta = 1.8. The risk-free rate is 7 percent. Last year this portfolio
had a required rate of return of 13 percent. This year nothing has changed except
for the fact that the market risk premium has increased by 2 percent (two percentage
points). What is the portfolio's current required rate of return?

a) 5.14%
b) 7.14%
c) 11.45%
d) 15.33%
e) 16.25%

16. Assume an all equity firm has been growing at a 20 percent annual rate and is
expected to continue to do so for 3 more years. At that time, growth is expected to
slow to a constant 5 percent rate. The firm maintains a 40 percent payout ratio, and
this year's retained earnings net of dividends were $1.5 million. The firm's beta is
1.5, the risk-free rate is 4 percent, and the market risk premium is 6 percent. If the
market is in equilibrium, what is the market value of the firm's common equity (1
million shares outstanding)?

a) 17.4 million
b) $19.1 million
c) $21.9 million
d) $28.7 million
e) $ 47.8 million
GSU, Department of Finance - Take-Home Problem Set / page 7 - Corporation Finance
Fall 2001 MBA 8622

Part II: Problems & Calculations

Record your final numeric answer including relevant calculations and intermediate steps
(partial credit may be assigned, if appropriate)

17. A 20-year ordinary annuity has a present value of $1,000,000 (monthly

compounded). What is the amount of each annuity payment under the following
assumptions:

a) Interest rate = 3% p.a.

b) Interest rate = 6% p.a.
c) Interest rate = 12% p.a.

18. Henry invests a lump sum of $10,000 in an account that guarantees 5%

(compounded annually) and Abby invests $10,000 in account guaranteeing 8%
(compounded semiannually).

a) How long will it take the value of Abby’s investment to be twice as much as
Henry's (rounded to the next whole number of years)?
b) How long will it take the value of Abby's investment to be three times as
much as Henry's (rounded to the next whole number of years)?
c) How long will it take the value of Abby's investment to be four times as much
as Henry's (rounded to the next whole number of years)?

(The problem can be solved either mathematically [using logarithms], with excel
[using goal seek], or by trial-and-error)

19. The future value of a 20-year annuity due in Euro (the newly created European
currency) is Euro 2,000,000. Which is the underlying annual interest rate (2
decimal places) under the following assumptions:

a) The annuity pays an annual amount of Euro 50,000

b) The annuity pays an annual amount of Euro 75,000
c) The annuity pays an annual amount of Euro 100,000
GSU, Department of Finance - Take-Home Problem Set / page 8 - Corporation Finance
Fall 2001 MBA 8622

20. Assume that you won the PowerBall Lottery. You are offered two alternatives. You
can either receive $200 million now or $12 million per year for the next 30 years, with
the first payment being received one year from now. Which alternative would you
choose if your opportunity cost is

a) 5% p
b) 10% p.a.
c) At what opportunity cost are you indifferent between the two alternatives (2
decimal places)?

21. You invest today $100,000 in a bank account that pays a certain constant nominal
annual interest rate of i%, annually compounded. You know that, based on this
interest rate, the future value exactly 10 years from today will be $859,442.55.
What would the future value be if interest was compounded …… instead of
annually (everything else remains constant)?

a) semiannually
b) quarterly
c) monthly

22. Ted and Gina Bartondo recently obtained a 15-year (180-month), $200,000
mortgage with a 5.75 percent nominal annual interest rate and monthly payments.
What will be the remaining balance on the mortgage

a) after four years (i.e. after 48 payments)?

b) after eight years (i.e. after 96 payments)?
c) after twelve years (i.e. after 144 payments)?

23. At the begin of 1996 John Huberman bought a vacation home in Hinterzarten
(Germany), nicely located in the Black Forest, at 5000 feet above sea level. The
purchase price was DM 250,000 (250,000 Deutschmark). John borrowed 80% of the
purchase price with a 20-year, quarterly payable mortgage at a fixed nominal rate of
8% p.a. Since he wanted to pay off the mortgage sooner than scheduled, he has
paid an additional DM 1,000 (onethousand Deutschmark) above the required amount
on each of the payments he has made from the first payment. Starting in January
2002, the DM will be replaced by the Euro (fixed exchange rate: 1.95583
Deutschmark = 1 Euro). Therefore John’s mortgage balance will be converted to
Euros right after his payment (in DM) on Jan 1 st, and all his future mortgage
payments (as well as the additional DM 1,000) will be paid in Euros from then on. At
the end of 2002 John will just have made his 28th payment of the mortgage. What
will then (i.e. just after the 28th payment) be the remaining balance on your
mortgage, expressed in Euros?
(It is highly recommended - but not mandatory - to set up a spreadsheet for this
problem)
GSU, Department of Finance - Take-Home Problem Set / page 9 - Corporation Finance
Fall 2001 MBA 8622

24. Gordon Sentry faces two investment opportunities: Stock AAA (expected return =
7%, risk = 10%) and Stock BBB (expected return 18%, risk 30%). He decides to
invest 60% of his funds in Stock AAA and 40% in Stock BBB. Calculate risk and
expected return of his portfolio under the following assumption (1 decimal place):

a) Correlation (AAA, BBB) = +0.7

b) Correlation (AAA, BBB) = 0
c) Correlation (AAA, BBB) = -0.4

25. Same situation as in problem 24) above. Additional information:

- The correlation between Stock AAA and Stock BBB is +0.7.
- Gordon Sentry has the opportunity to invest in Stock AAA, Stock BBB, and
riskless assets
He decides to invest 30% of his funds in riskless assets, 50% in Stock AAA and 20%
in Stock BBB. Calculate risk and expected return of his new portfolio under the
following assumption (1 decimal place):

a) Expected risk-free return = 3%

b) Expected risk-free return = 5%
c) Expected risk-free return = 7%

26. The present value (t=0) of the following cash flow stream is $40,000, when
discounted at the discount rates shown below. Calculate the value of the missing
(i.e., t=3) cash flow (2 decimal places).

Year 1 2 3 4 5 6
Cash Flow $6,000 $8,000 ??? $4,000 $7,000 12,000

a) Discount rate = 10% p.a., semiannual compounding

b) Discount rate = 6%, quarterly compounding
c) Discount rate = 0%, monthly compounding
GSU, Department of Finance - Take-Home Problem Set / page 10 - Corporation Finance
Fall 2001 MBA 8622

27. It is now January 1, 2001. Trellos Inc. Inc. is expected to to experience a 40% annual
growth rate for the next 3 years (years 1-3) and a 25% annual growth rate for the two
following years (years 4 and 5). By the end of 5 years, Trellos Inc.’s growth rate will
slow to 10% percent per year indefinitely. Stockholder require a return of 14% on
Trellos Inc.’s stock. The most recent annual dividend (D0 ), which was just paid
yesterday, was $8.00 per share.

a) Calculate the value of the stock today, based on the assumptions above.

b) Calculate the value of the stock today under the following assumptions:
Growth rate next three years = 20%, growth rate years 4 and 5 = 15%, growth
rate after year 5 = 5%, required return on the stock = 18%

28. A Coratis Industries bond has a 10 percent coupon rate and a $1,000 face value.
Interest is paid semiannually, and the bond has 15 years to maturity. If investors
require a .......% nominal yield, what is the bond’s value and what is the effective
annual yield on the bond

a) 12%
b) 10%
c) 8%
GSU, Department of Finance - Take-Home Problem Set / page 11 - Corporation Finance
Fall 2001 MBA 8622

MBA 8622: Corporation Finance

Fall 2001
Take-Home Problem Set
Answer Sheet
Instructors:
Lalitha Naveen, N. Daniel, C.Hodges, A. Mettler, R. Morin, M. Shrikhande,

Name: …………………………………………………….

Total: …… / 40

Grade: …………. of 100

Part I: Multiple Choice

1) 2) 3) 4)
5) 6) 7) 8)
9) 10) 11) 12)
13) 14) 15) 16)