FIN 5080 Homework Assignment

3. How
many years would it take $500 to double if you invested it in a bank
that pays 4.25% per year?

4. You
want to buy a new sports car 5 years from now, and you plan to save $5,800 per
year, beginning immediately. You
will make 5 deposits in an account that pays 4.75% interest. Under these assumptions, how much will you
have 5 years from today?

5. What’s the present value of a 4-year
ordinary annuity of $3,595 per year plus an additional $1,500 at the end of
Year 4 if the interest rate is 9%?

6. What’s
the future value of $2,500 after 10 years if the appropriate nominal interest
rate is 8.75%, compounded quarterly?

7. An
investment promises the following cash flow stream: $3,500 at Time 0; $2,750 at the end of Year 1
(or at t = 1); $3,450 at the end of Year 2; and $5,400 at the end of Year
3. At a discount rate of 6.0%, what is
the present value of the cash flow stream?

8. Suppose
you are buying your first house for $500,000, and are making a $100,000 down
payment. You have arranged to finance
the remaining amount with a 15-year, monthly payment, amortized mortgage at a 3.10%
nominal interest rate. What will your
equal monthly payments be?

9. You
plan to borrow $125,000 at a 9.5% annual interest rate. The terms require you to amortize the loan
with 10 equal end-of-year payments. How
much interest would you be paying in Year 3?

10. You
just deposited $4,000 in a bank account that pays a 6.25% nominal interest
rate, compounded quarterly. If you also
add another $9,000 to the account one year (12 months) from now and another
$7,500 to the account two years from now, how much will be in the account three
years (12 quarters) from now?

11. Your sister turned 35 today, and she is planning
to save $12,000 per year for retirement, with the first deposit to be made one
year from today. She will invest in a
mutual fund that will provide a return of 7.0% per year. She plans to retire 30 years from today, when
she turns 65, and she expects to live for 25 years after retirement, to age
90. Under these assumptions, how much
can she spend in each year after she retires? Her first withdrawal will be made
at the beginning of her first retirement year.

12. You anticipate that you will need $3,750,000 when you retire 40
years from now. You plan to make 40
deposits, beginning today, in a bank account that will pay 7% interest,
compounded annually. You expect to
receive annual raises of 2%, so you will increase the amount you deposit each
year by 2%. (That is, your 2nd deposit
will be 2% greater than your first, the 3rd will be 2% greater than the 2nd,
etc.) How much must your 1st deposit be
if you are to meet your goal?

13. Which of the following factors
could explain why Dellva Energy had a negative net cash flow last year, even
though the cash on its balance sheet increased?

a.

The
company sold a new issue of bonds.

b.

The
company made a large investment in new plant and equipment.

c.

The
company paid a large dividend.

d.

The company
had high amortization expenses.

e.

The
company repurchased 20% of its common stock.

14. Medium
Size Retailers, Inc. (MSR) has EBIT of
$225,000, interest expense of $35,000, dividend income of $30,000, short term
capital gains of $15,000, and long term capital losses of $20,000. What is MSR’s income tax liability?

15. Frederickson
Office Supplies recently reported $17,500 of sales, $7,750 of operating costs
other than depreciation, and $1,775 of depreciation. The company had no amortization charges and
no non-operating income. It had $20,000
of bonds outstanding that carry a 9.5% interest rate, and its
federal-plus-state income tax rate was 40%.
How much was the firm’s taxable income, or earnings before taxes (EBT)?

16. Over
the years, Janjigian Corporation’s stockholders have provided $45,950 of
capital, partly when they purchased new issues of stock and partly when they
allowed management to retain some of the firm’s earnings. The firm now has 2,250 shares of common stock
outstanding, and it sells at a price of $26.50 per share. How much value has Janjigian’s management
added to stockholder wealth over the years, i.e., what is Janjigian’s MVA?

17. Zumbahlen Inc. has the following balance
sheet. How much total net operating
capital does the firm have?

Cash

$ 25.00

Accounts payable

$ 50.00

Short-term
investments

60.00

Accruals

50.00

Accounts
receivable

40.00

Notes payable

30.00

Inventory

60.00

Current liabilities

$130.00

Current assets

$185.00

Long-term debt

130.00

Gross
fixed assets

$225.00

Common stock

30.00

Accumulated
deprec.

60.00

Retained earnings

60.00

Net fixed
assets

$165.00

Total common equity

$ 90.00

Total assets

$350.00

Total liab. & equity

$350.00

18. HHH
Inc. reported $17,500 of sales and $6,575 of operating costs (including
depreciation). The company had $18,750
of investor-supplied operating capital, the weighted average cost of that
capital (the WACC) was 11.75%, and the federal-plus-state income tax rate was 35%. What was HHH’s Economic Value Added (EVA),
i.e., how much value did management add to stockholders’ wealth during the
year?

19. Wells Water Systems recently reported $12,550
of sales, $4,250 of operating costs other than depreciation, and $1,400 of
depreciation. The company had no
amortization charges, it had $3,250 of outstanding bonds that carry a 6.75%
interest rate, and its federal-plus-state income tax rate was 25%. In order to sustain its operations and thus
generate sales and cash flows in the future, the firm was required to spend $1,050
to buy new fixed assets and to invest $475 in net operating working
capital. How much free cash flow did
Wells generate?

20. Amram Company’s current ratio is 1.9. Considered alone, which of the following
actions would reduce the company’s current ratio?

a.

Borrow
using short-term notes payable and use the proceeds to reduce accruals.

b.

Borrow
using short-term notes payable and use the proceeds to reduce long-term debt.

c.

Use cash
to reduce accruals.

d.

Use cash
to reduce short-term notes payable.

e.

Use cash
to reduce accounts payable.

21. Northwest Lumber had a net profit margin of 5.25%, a total
assets turnover of 2.95, and an equity multiplier of 1.65. What was the firm’s ROE?

22. An
investor is considering starting a new business. The company would require $575,000 of assets,
and it would be financed entirely with common stock. The investor will go forward only if she
thinks the firm can provide a 24.0% return on the invested capital, which means
that the firm must have an ROE of 24.0%.
How much net income must be expected to warrant starting the business?

23. Helmuth
Inc.’s latest net income was $1,450,000, and it had 225,000 shares
outstanding. The company wants to pay
out 45% of its income as dividends. What
dividend per share should it declare?

24. Heaton
Corp. sells on terms that allow customers 45 days to pay for merchandise. Its sales last year were $725,000, and its
year-end receivables were $110,000. If
its DSO is less than the 45-day credit period, then customers are paying on
time. Otherwise, they are paying
late. By how much are customers paying
early or late? Base your answer on this
equation: DSO – Credit period = days early or late, and use a 365-day year when
calculating the DSO. A positive answer
indicates late payments, while a negative answer indicates early payments.

25. Last
year Mason Inc. had a total assets turnover of 2.75 and an equity multiplier of
1.95. Its sales were $225,000 and its
net income was $9,549. The CFO believes
that the company could have operated more efficiently, lowered its costs, and
increased its net income by $5,400 without changing its sales, assets, or
capital structure. Had it cut costs and
increased its net income in this amount, by how much would the ROE have
changed?

26. Muscarella
Inc. has the following balance sheet and income statement data:

Cash

$ 14,000

Accounts payable

$ 42,000

Receivables

60,000

Other current liabilities

28,000

Inventories

225,000

Total CL

$ 70,000

Total CA

$299,000

Long-term debt

75,000

Net fixed assets

121,000

Common equity

275,000

Total
assets

$420,000

Total
liab. and equity

$420,000

Sales

$250,000

Net income

$ 15,000

The new
CFO thinks that inventories are excessive and could be lowered sufficiently
to cause the current ratio to equal the industry average, 2.65, without
affecting either sales or net income.
Assuming that inventories are sold off and not replaced to get the
current ratio to the target level, and that the funds generated are used to
buy back common stock at book value, by how much would the ROE change?

27. Stock X has a beta of 0.5 and Stock Y has a
beta of 1.5. Which of the following
statements must be true, according to the CAPM?

a.

If you
invest $50,000 in Stock X and $50,000 in Stock Y, your 2-stock portfolio will
have a beta significantly lower than 1.0, provided the returns on the two
stocks are not perfectly correlated.

b.

Stock Y’s
return during the coming year will be higher than Stock X’s return.

c.

If
expected inflation increases but the market risk premium is unchanged, the
required returns on the two stocks will increase by the same amount.

d.

Stock Y’s
return has a higher standard deviation than Stock X.

e.

If the
market risk premium declines, but the risk-free rate is unchanged, Stock X
will have a larger decline in its required return than will Stock Y.

28. Rick
Kish has a $120,000 stock portfolio. $50,000
is invested in a stock with a beta of 1.25 and the remainder is invested in
a stock with a beta of 2.85. These are
the only two investments in his portfolio.
What is his portfolio’s beta?

29. ABC
Company’s stock has a beta of 1.95, the risk-free rate is2.75%, and the
market risk premium is7.50%.
What is ABC’s required rate of return using CAPM?

30. Ripken Iron Works believes the following
probability distribution exists for its stock. What is the standard deviation of return on
the company’s stock?

State of
the Economy

Probability of State Occurring

Stock’s Expected Return

Boom

0.25

35%

Normal

0.50

13%

Recession

0.25

-13%

31. Joel Foster is the portfolio manager of the Go
Anywhere Fund, a $3 million hedge fund that contains the following stocks. The
required rate of return on the market is 9.00% and the risk-free rate is 2.00%.
What rate of return should investors expect (and require) on this fund?

Stock

Amount

Beta

A

$1,075,000

1.20

B

675,000

1.50

C

750,000

3.35

D

500,000

1.10

$3,000,000

32. Hazel
Morrison, a mutual fund manager, has a $60 million portfolio with a beta of
1.00. The risk-free rate is 3.25%, and the market risk premium is 6.00%. Hazel
expects to receive an additional $40 million, which she plans to invest in
additional stocks. After investing the additional funds, she wants the fund’s
required and expected return to be 16.00%. What must the average beta of the
new stocks be to achieve the target required rate of return?

33. Campbell’s father holds just one stock,
East Coast Bank (ECB), which he thinks is a very low-risk security. Campbell
agrees that the stock is relatively safe, but he wants to demonstrate that
his father’s risk would be even lower if he were more diversified. Campbell
obtained the following returns data shown for West Coast Bank (WCB). Both have had less variability than most
other stocks over the past 5 years.
Measured by the standard deviation of returns, by how much would his
father’s historical risk have been reduced if he had held a portfolio
consisting of 60% ECB and the remainder in WCB?

Year

ECB

WCB

2010

20.00%

25.00%

2011

-10.00%

15.00%

2012

35.00%

-5.00%

2013

-5.00%

-10.00%

2014

15.00%

35.00%

34. Which of the
following statements is CORRECT?

a. If a coupon bond is selling at par, its
current yield equals its yield to maturity.
b. If a coupon bond is selling at a
discount, its price will continue to decline until it reaches its par value at
maturity.
c. If interest rates increase, the price
of a 10-year coupon bond will decline by a greater percentage than the price of
a 10-year zero coupon bond.
d. If a bond’s yield to maturity exceeds
its annual coupon, then the bond will trade at a premium.
e. If a coupon bond is selling at a
premium, its current yield equals its yield to maturity.

35. Garvin Enterprises’ bonds currently sell
for $1,150. They have a 6-year maturity,
an annual coupon of $90, and a par value of $1,000. What is their current yield?

36. Sadik Inc.’s bonds currently sell for
$1,275 and have a par value of $1,000.
They pay a $115 annual coupon and have a 15-year maturity, but they can
be called in 4 years at $1,115. What is
their yield to call (YTC)?

37. Moerdyk Corporation’s bonds have a 10-year
maturity, a 5.25% coupon rate with interest paid semiannually, and a par value
of $1,000. The nominal required rate of
return on these bonds is 6.50%. What is
the bond’s intrinsic value?

38. Niendorf Corporation’s 5-year bonds yield
8.75%, and 5-year T-bonds yield 4.50%.
The real risk-free rate is r* = 2.45%, the inflation premium for 5-year
bonds is IP = 1.65%, the default risk premium for Niendorf’s bonds is DRP = 2.85%
versus zero for T-bonds, and the maturity risk premium for all bonds is found with
the formula MRP = (t – 1) x 0.1%, where t = number of years to maturity. What is the liquidity premium (LP) on
Niendorf’s bonds?

39. A 30-year, $1,000 par value bond has a 7.50%
coupon rate with interest paid semiannually. The bond currently sells for $825. What is the capital gains yield on these
bonds?

40. O’Brien Ltd.’s outstanding bonds have a
$1,000 par value, and they mature in 20 years.
Their nominal yield to maturity is 8.25%, they pay interest
semiannually, and they sell at a price of $875.
What is the bond’s nominal (annual) coupon interest rate?