Lab 6 Problems
1.
The Connecticut Computer Company has the following selected financial results.
10% Debt
Debt (TL)
Equity
Total Assets
$ 10,000
90,000
$100,000
Shares @ $5
18,000
EBIT
Interest ( 15%)
EBT
Tax (40%)
EAT
$18,000
1,500
$16,500
6,600
$ 9,900
40% Debt
75% Debt
ROE
EPS
The company is considering a capital restructuring to increase leverage from its present level of
10% of capital (total assets).
a. Calculate Connecticut’s ROE and EPS under its current capital structure.
b. Restate the financial statement line items shown, the number of shares outstanding, ROE, and
EPS if Connecticut borrows money and uses it to retire stock until its capital structure is 40%
debt assuming EBIT remains unchanged and the stock continues to sell at its book value.
(Develop the second column of the chart shown.)
c. Recalculate same figures assuming Connecticut continues to restructure until its capital
structure is 75% debt. (Develop the third column of the chart.)
d. How is increasing leverage affecting financial performance? What overall effect might the
changes have on the market price of Connecticut’s stock? Why? (Words only. Hint: consider
the move from 10% to 40% and that from 40% to 75% separately.)
Answers are provided here for question 1 part d and questions 2 and 3. The point of this selection
of questions is to illustrate financial risk:
d. Increasing leverage is improving financial performance as measured by ROE and EPS. As
debt increases, earnings, equity, and the number of shares outstanding all decrease. However,
since equity decreases fastest the ratios ROE (EAT/Equity) and EPS (EAT/Shares) get larger.
The increase in debt from 10% to 40% of capital is likely to increase stock price, because
investors will react favorably to the improvement in ratios. In this leverage range debt is not
excessively high, so the positive effect of the improving ratios will probably overcome the
negative effect of increasing risk.
The move from 40% to 75% debt, on the other hand, is likely to be perceived by
investors as making the company uncomfortably risky. At higher leverage levels the negative
effect on investors of increased risk usually overwhelms the positive effect of improving
performance ratios, and the net result is a decline in stock price.
2.
Reconsider the Connecticut Computer Company of problem 1 assuming the firm has
experienced some difficulties, and its EBIT has fallen to $8,000.
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a. Reconstruct the three-column chart developed in problem 1 assuming Connecticut’s
EBIT remains at $8,000.
b. Interpret the result in terms of stock price and the advisability of restructuring capital
under these conditions.
c. Could these results have been predicted more easily? Use the ROCE or BEP concept
to come to the same conclusion.
Answer provided here:
10% Debt
40% Debt
75% Debt
Debt
Equity
Total Capital
$ 10,000
90,000
$100,000
$ 40,000
60,000
$100,000
$ 75,000
25,000
$100,000
Shares @ $5
18,000
12,000
5,000
EBIT
Interest ( 15%)
EBT
Tax (40%)
EAT
$8,000
1,500
$6,500
2,600
$ 3,900
$8,000
6,000
$2,000
800
$1,200
$ 8,000
11,250
($ 3,250)
($ 3,250)
ROE
EPS
4.3%
$.22
2.0%
$.10
(13.0%)
($.65)
b. Stock price would almost certainly decline as a result of restructuring. Increased debt is
causing a deterioration of financial performance measured by ROE and EPS as well as increasing
risk. Both of these have negative effects on investors’ attitudes. Under these conditions (a low
EBIT) it would virtually never be advisable to exchange equity for debt.
c. Leverage is not advisable if the return on capital employed, ROCE, is less than the after tax
cost of debt. Currently Connecticut’s ROCE is
ROCE = EBIT(1  T) / (Debt + Equity)
= $8,000(1  .4) / $100,000
= $4,800 / $100,000
= 4.8%
Its after tax cost of debt is
15%(1 – T) = 15%(1  .4) = 9%
Hence at an EBIT of $8,000, Connecticut’s ROCE is less than its after tax cost of debt and we
would not expect adding leverage to do the firm any good.
3.
Assume Connecticut Computer Company of the last two problems is earning an EBIT of
$15,000. Once again, calculate the chart showing the implication of adding more leverage.
Verbally rationalize the result.
SOLUTION:
Debt
Equity
10% Debt
40% Debt
75% Debt
$ 10,000
90,000
$ 40,000
60,000
$ 75,000
25,000
2
Total Capital
$100,000
$100,000
$100,000
Shares @ $5
18,000
12,000
5,000
EBIT
Interest ( 15%)
EBT
Tax (40%)
EAT
$15,000
1,500
$13,500
5,400
$ 8,100
$15,000
6,000
$9,000
3,600
$ 5,400
$15,000
11,250
$ 3,750
1,500
$ 2,250
9.0%
$.45
9.0%
$.45
9.0%
$.45
ROE
EPS
Leverage has no effect on financial performance, but it still adds risk hence the effect on
stock price would probably be negative.
At an EBIT of $15,000 the ROCE and the after tax cost of debt are both 9%. Trading
equity for debt or vice versa makes no difference on performance, because the firm is earning on
capital exactly what it pays for the use of additional debt funds. I.e., there’s no “leverage.” The
risk effect, however, is still there because as the firm adds more debt it must pay more interest
making its profit margin narrower. This will probably drive the stock’s price down in the absence
of a counteracting favorable change in ratios.
Time Value of Money Problems
Several of the choices in the list of multiple choices assume that the problem is being worked by
using tables rather than a calculator and the rounding that results from using tables leads to
slightly different answers than the financial calculator. The keys to some of the problems are also
a cut and paste from keys provided by the textbook (using tables). However, in AGEC 424 you
are expected to use a financial calculator and you are expected to list your calculator inputs and
outputs, which constitutes “showing your work.” So, some of your answers will be a little
different than the choices and sometimes the keys, and if you hand in homework with the notation
of the tabled factors it is very likely that you are copying from old keys
Timelines and listing calculator inputs and outputs will be emphasized in lab.
Multiple Choice Problems.
1. How much must be invested today to have $1,000 in two years if the interest rate is 5%?
a. $909.09
c. $907.00
b. $900.00
d. $950.00
2. Find the present value of $100 to be received at the end of two years if the discount rate is
12% compounded monthly.
a. $66.50
d. $91.80
b. $78.76
e. $79.75
c. $68.80
3. What is the rate of return on an investment if you lend $1,000 and are repaid $1,254.70 two
years later?
a. 12%
d. 18%
b. 25%
e. 4%
c. 6%
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4. Determine how much $1,000 deposited in a savings account paying 8% compounded
annually will be worth after 5 years.
a. $5,526
c. $1,400
b. $784
d. $1,469
5. At an effective interest rate of 12%, a single sum invested today will double itself in how
many years?
a. 8 years.
c. 6 years.
b. 12 years.
d. Insufficient data to determine answer.
6. Your bank balance is exactly $10,000. Three years ago you deposited $7,938 and have not
touched the account since. What annually compounded rate of interest has the bank been
paying?
a. 8.65%
c. 8.00%
b. 26.00%
d. 6.87%
7. Which of the following interest rates will come closest to doubling invested money in five
years?
a. 13%
c. 15%
b. 14%
d. 16%
8. $3,947 deposited four years ago has grown to $5,000. What semiannually compounded rate
of interest has the bank been paying?
a. 5.26%
c. 3.00%
b. 6.00%
d. 6.67%
9. Using an annual interest rate of 9%, how long will it take a deposit of $1,000 to grow to
$3,000, assuming no additional deposits are made?
a. 8.04 years
d. 12.75 years
b. 10.00 years
e. 13.50 years
c. 11.11 years
10. If you invest the $10,000 you receive at graduation (age 22) in a mutual fund which averages
a 12% annual return, how much will you have at retirement in 40 years?
a. $909,090
d. $510,285
b. $930,510
c. $783,879
11. Assume that you have just won “$5,000,000” in the lottery and will receive $250,000 per
year for the next 20 years. How much is your prize worth today if the interest rate is 8%?
a. $1,072,731
c. $2,185,219
b. $2,454,525
d. $1,165,250
12. Ralph has decided to put $2,400 a year (at the end of each year) into an IRA over his 40 year
working life and then retire. What will Ralph have at retirement if the account earns 10
percent compounded annually?
a. $394,786
b. $ 23,470
c. $1,062,223
d. $810,917
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13. If you were to borrow $10,000 over five years at 12% compounded monthly, what would be
your monthly payment?
a. $122.44
c. $168.38
b. $222.44
d. $187.28
14. Five years after an accident, you received $100,000 to pay the medical expenses incurred at
the time of the accident. What is the present value (at the time of the accident) of the
payment? Assume interest rates are 9%.
a. $153,900
c. $65,000
b. $68,100
d. $70,800
15. You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190.
What was the annual rate of return on your investment?
a. 12%
c. 10%
b. 11%
d. 9%
16. Designs Now is opening a showcase office to display and sell its computer designed poster
art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year,
$240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present
value of the cash flows?
a. $429,720
c. $456,000
b. $457,620
d. $424,820
17. What is the most you should pay to receive the following cash flows if you require a return of
12 percent?
Year 1
$5,000
a. $58,580
Year 2
$8,000
b. $104,135
Year 3
$12,000
c. $68,105
Year 4-10
$15,000
d. none of the above
18. You have borrowed $130,000 to buy a new motor home. Your loan is to be repaid over 15
years at 8% compounded monthly. Calculate the principal paid to the bank in month 2 of the
loan.
a. $242.67
c. $413.61
b. $378.19
d. $581.25
19. First Bank offers you a car loan at an annual interest rate of 10% compounded monthly. What
effective annual interest rate is the bank charging you?
a. 10.38%
c. 10.45%
b. 10.42%
d. 10.47%
20. Your monthly statement from your bank credit card shows that the monthly rate of interest is
1.5%. What is the effective annual rate of interest you are being charged on your credit card?
a. 18.00%
c. 19.56%
b. 18.64%
d. 29.74%
21. Jim Luster wants to have saved enough money by the time he is 65 to invest it and earn a
$60,000 annual income for the rest of his life. He wants to be able to leave that same amount
to his heirs, no matter how long he lives. If he can earn 8% on invested money, how much
does he need to have accumulated by the time he is 65?
a. $480,000
d. $900,000
b. $600,000
e. Cannot be determined based on the information given.
c. $750,000
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22. You want to purchase a beach house for $220,000 funding as much of the cost as possible
with a home mortgage loan. Banks are currently offering standard thirty year mortgages at
8% (monthly compounding). Unfortunately, you can only afford payments of $1,500 per
month. How much cash will you need for a down payment in order to buy the home? (Round
to the nearest dollar)
a. $11,142
b. $13,778
c. $15,575
d. $17,457
23. A perpetuity has a cash flow of $20 and a discount rate of 10%. What is the value of the
perpetuity?
a. $22
b. $500
c. $200
d. none of the above
24. You want to purchase a boat that costs $40,000. You want to finance as much of the purchase
as possible with a 5-year bank loan at 12% compounded monthly, but can only afford loan
payments of $750 per month. How much will you need as a down payment to buy the boat?
(Round to the nearest dollar)
a. $3,523
b. $4,637
c. $5,147
d. $6,284
Perpetual Annuities:
1. Find the PV of a perpetual (ordinary) annuity of $200 per year. Draw a time line. Assume a
5% discount rate.
2. Same as #1 except the first payment is today (an annuity due).
3. Same as #1 except the first payment is 10 years from today. This is a two step problem.
Problems from the Book:
33.
Merritt Manufacturing needs to accumulate $20 million to retire a bond issue that
matures in 13 years. The firm’s manufacturing division can contribute $100,000 per quarter to an
account that will pay 8%, compounded quarterly. How much will the remaining divisions have to
contribute every month to a second account that pays 6% compounded monthly in order to reach
the $20 million goal?
34.
Carol Pasca just had her fifth birthday. As a birthday present, her uncle promised to
contribute $300 per month to her education fund until she turns 18 and starts college. Carol’s
parents estimate college will cost $2,500 per month for four years, but don’t think they’ll be able
to save anything toward it for five years. How much will Carol’s parents need to contribute to the
fund each month starting on her tenth birthday to pay for her college education? Assume the fund
earns 6% compounded monthly.
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