FALL 1988
S. G. BUELL SECTION_____________________
[1] (30 points)
On September 29, 1988 Maria Giovannelli makes the first of what she anticipates being six equal annual deposits into an account that pays 8 percent interest. The final deposit would be on September 29, 1993. Maria is saving her money so that she may attend grad school at Mel's Institute of Technology starting in 2000. She anticipates making four equal annual tuition payments of $15,000 starting on September 29, 2000 and continuing through September 29, 2003.
After she makes her fourth deposit on September
29, 1991, Maria changes her plans. She decides to not make the last two
deposits and to not try to cram her graduate education into four years.
Instead she will take just a couple of courses each year but she expects
to attend MIT for ever. How much will Maria have to spend each year on
tuition and books if she takes her first courses starting on September
29, 2000?
[2] (20 points)
You are analyzing an investment that pays 10 percent interest every six months (nominally 20 percent a year, compounded semiannually). What is the present value of the infinite stream of $100 PER YEAR with the first payment in one year's time?
{a} What is the annual effective rate of interest?
{b} What is the present value of the infinite
stream?
[3] (25 points)
Bunky's Burgers is contemplating two mutually exclusive capital projects X and Y. Some of Bunky's present equipment which would be replaced regardless of whether X or Y is selected has a market value of $40,000, is being depreciated using the straight line method to a salvage value of $5000, has a remaining life of three years and is being carried on the books at $53,000.
Proposals X and Y would each cost $160,000 and have a depreciable life of 3 years and an expected salvage value of $10,000. Over the next three years X would increase sales over operating expenses by $80,000, $50,000 and $25,000 while Y would increase them by $25,000, $80,000 and $70,000. The firm has a marginal tax rate of 40 percent.
At approximately what discount rate would the
firm be indifferent to the two projects? What is the NPV of either project
at this rate? A higher rate would favor which project? Explain why.
[1] (20 points)
Within the past few days newspapers reported the following: (a) "Last month wholesale prices rose 1.5%."
(b) "The consumer price index rose 9%. during the past six months."
(c) "The GNP deflator is expected to rise by 4.5% over the next quarter."
(d) "The producer price index is forecasted to rise by a total of 40% over the next two years."
Convert all four statements to their respective
annual inflation rates.
[2] (30 points)
Bunky's Burgers, Inc. is thinking of replacing
an aging piece of equipment with a newer model. The existing machinery
was purchased 4 years ago for $400,000 and is being depreciated using the
straight line method to a salvage value of $40,000 over a life of 10 years.
If the machine were sold today, Bunky's would receive an unknown amount.
The new equipment has a purchase price of $700,000 and would be depreciated
over an expected life of 6 years to a salvage value of $100,000. Bunky's
estimates that the new machine will lower before-tax expenses by $100,000
per year for the first two years and by $150,000 for the next four years.
If the firm's marginal tax rate is 40% and it's required return is 12%,
what is the minimum amount that Bunky's must receive today from the sale
of the existing equipment in order to justify its replacement?
[3] (30 points)
On February 16, 1989 Maria Giovannelli makes the first of what she EXPECTS to be five equal annual deposits into an account that pays 10% annual interest. The deposits must be of sufficient size to enable Maria to withdraw $500 per year forever starting on February 16, 1997. She fully EXPECTS the 10% rate to continue forever.
After making the originally PLANNED deposits on February 16, 1990 and 1991, Maria falls on hard times and is unable to make the final two deposits. However, on February 16, 1994 Maria, still EXPECTING the 10% rate to continue forever, makes the first of what she EXPECTS to be two equal deposits designed to enable her to still make the originally PLANNED $500 withdrawals in perpetuity starting in 1997.
On the way to the bank to make the second deposit
on February 16, 1995, Maria is told that starting that day the interest
rate will drop to 8% and never change. If she still wants to maintain her
original withdrawal schedule ($500 starting in 1997), Maria knows she will
have to go back home and get more money. How much more?
Hint: You will most likely want to draw at
least two time lines.
[4] (20 points)
"The rate of return on stockholders' equity ROE is really the product of a lot of other ratios." Comment on this statement by discussing how each of the following ratios is related to ROE. In other words, how does a change in each of these ratios affect ROE?
{a} Average Collection Period
{b} Debt to Total Assets
{c} Acid Test
[1] (30 points)
Bunky's Burgers, Inc. has some outstanding subordinated debentures that mature in 2003. The $1000 par value bonds were issued in 1983 with a coupon rate of 13%, payable semi-annually. The bonds are convertible into Bunky's common stock at a price of $25 per share. Also the bonds have a call feature that would enable the firm to redeem them at a price of $1080. In 1983 the yield to maturity on comparable 20 year bonds was 14%, compounded semi-annually. The firm is contemplating refinancing the bonds by issuing new 15 year bonds at par. The current yield to maturity on 15 year bonds is 10% and on 20 year bonds, 14%, compounded semi-annually. The firm's common stock is currently being traded for $23 per share.
{a} Calculate the NPV of the firm's decision to refinance its debt if it calls the bonds. Ignore any flotation costs.
{b} Calculate (approximately) the rate of return earned by an investor who bought the bond in 1983 and followed the better course of action when the bond was called. Did the investor welcome the call? Explain.
{c} Do part {b} over assuming the stock is
selling for $28 a share.
[2] (30 points)
The following data pertains to US Treasury
securities. All bonds have a $1,000 face value and all interest is paid
semi-annually.
Maturity Date Annual Coupon Price
Apr 27, 1989 12% 995.31
Oct 27, 1990 13% 1053.19
Oct 27, 2003 8% 1000.00
Infinity 14% 2000.00
Plot the resulting yield curve and label the appropriate axes. What does the shape of the curve suggest about investors' expectations with regard to the future course of interest rates?
Suppose that you believe the general consensus
was incorrect and that rates would move opposite to the market's expectations.
Which maturity should you invest in and why? Suppose you were a corporate
treasurer who believed the market's excpectations were correct. What are
the advantages and disadvantages of issuing long and of issuing short?
[3] (30 points)
Bunky's Burgers is contemplating the purchase of a new bun warmer and needs your financial expertise. The existing equipment which would be replaced has a book value of $25,000 and is being depreciated over its remaining 5 year life to a zero salvage value. The new warmer would cost $80,000 and would have a depreciable life of 5 years. Its expected salvage value at the end of the fifth year is 0. The existing equipment could be sold today for $5,000. The new bun warmer would lower before tax costs by $20,000 a year. Bunky's believes there is a 40% chance the new equipment will last 8 years and a 60% chance that it will last 12 years. The firm has a marginal tax rate of 40% and, despite its name is a well diversified company. Its beta coefficient is 2. Currently the risk-free rate of interest is 4% and the market's excess return over the risk free rate is only 2%.
Find the expected risk-adjusted NPV of the
replacement decision.
[4] (20 points)
On October 27 King George Industries announces
a rights offering for stockholders as of November 12. There are currently
20,000,000 shares of King George outstanding. The firm wishes to raise
$20,000,000 through the rights offering. On November 20 you buy 1000 rights
for $1000 while the stock is trading for $10.00 a share. Five days later
when the stock is selling for $15.00, you sell the rights. What is your
percentage rate of return? Explain the concept of leverage as it pertains
to this problem.
[1] (25 points)
Explain fully how and why the following yield
differentials will change when the stated conditions occur:
{a} The yield differential between a firm's
first mortgage bonds and its subordinated debentures when the forecasted
outlook for the economy begins to brighten.
{b} The yield differential between a firm's
long-term subordinated debentures and its short-term subordinated debentures
when the overall level of interest rates begins to rise.
{c} The yield differential between a firm's
about to be issued callable and noncallable debentures when the overall
level of interest rates begins to rise.
{d} The yield differential between a firm's
convertible and nonconvertible 20 year bonds if the outlook for the firm's
industry over the next decade is downgraded from rosy to crummy.
[2] (30 points)
The Eli Manufacturing Company, Inc. is contemplating purchasing a new widgetron that would cost $1,500,000 and be depreciated over a life of 10 years to a zero salvage value. The firm forecasts that for each of the first six years there is a 40% probability that the new machine would lower its annual before-tax expenses by $200,000, 40% probability that the decrease would be $300,000 and 20% that it would be $400,000. For years seven and beyond, the forecast is 40% ($0), 40% ($300,000) and 20% ($600,000). The firm has a marginal tax rate of 40%. The widgetron has a forecasted beta of 1.2, the risk-free rate of interest is 6% and the market's excess return is 5%.
If there is a 60% chance the widgetron will
actually last only 7 years (it could be scrapped at that time for $100,000)
and a 40% chance it will last 10 years, calculate the net-present-value
of the decision to purchase if
{a} The firm uses the certainty equivalents
method and selects its coefficients from the following table:
Coeff. of variation CF period t |0-.3|.31-.5|.51-.9|.91+ |
-------------------------------------|----|------|------|-----|
Certainty equivalent coeff. period t | .8 |
.7 | .6 | .5 |
{b} The firm has a well-diversified portfolio
and selects its risk-adjusted discount rate based on systematic risk using
the "beta" model.
[3] (25 points)
Ten years ago Bunky's Burgers, Inc. issued
some 25 year $1000 par value callable subordinated debentures with a coupon
of 15%, paid semi-annually. The securities are callable at $1075. The bonds
were initially sold to yield 16%, compounded semi-annually. Today the yield
on comparable 15 year bonds is 12% and on 25 year bonds, 15%.
{a} If Bunky's exercises its call option and
refinances with an equal number of new 15 year subordinated debentures
(issued at par), what is the NPV of the decision to refinance?
{b} What rate of return did the investor earn
over the past 10 years?
{c} Suppose that in addition to being callable,
the bonds were convertible into Bunky's common stock at a price per share
of $125. How would your answer to {b} change (or would it?) if the current
price of Bunky's stock is $145 per share?
[4] (20 points)
The Vice-President of Finance of the Garfield
Company is taken ill on his way to the meeting of the board of directors
and you, a summer intern, have to take his place and answer board members'
questions:
{a} "What is operating leverage and how does
it influence our production process?"
{b} "Why is the yield curve currently downward
sloping and how does knowing that influence our financial decision?"
{c} "Why are our convertible debentures selling
to yield so much less than our nonconvertible debentures since the bonds
are identical in every other respect? There must be some catch. What is
it?"
{d} "I need some personal advice; I heard there is opportunity for a quick profit by dealing in stock rights. It has something to do with leverage? Explain this to me."
[1] (30 points)
You purchase a 20 year $1000 bond of the Apple Core Corp. for $984.66. The bond carries an annual coupon of 12%, paid semi-annually and is convertible into Apple Core's common stock at a conversion price of $25 per share. At the time of purchase, Apple Core's earnings and dividends are forecasted to grow at 25% for the next 8 years before declining to a 6% rate for the indefinite future. The market uses a 16% discount rate when valuing Apple Core's stock. Yesterday the firm paid a dividend of $0.91.
If you convert the bond 4 years from now and
immediately sell the shares, what rate of return did you earn over your
holding period of 4 years? Assume that the original earnings forecast was
(and still is) accurate.
[2] (50 points)
Bunky's Burgers, Inc. is planning its 1989 capital budgeting and financing decisions and needs your expert assistance. The firm has a marginal tax rate of 40%, its common stock is currently selling for $100 a share, its earnings and dividends are expected to grow at 9% for the indefinite future, the stock's dividend yield (based on D1) is 9% and the firm has $9 million dollars available from internal sources for investment this year.
The firm's capital structure shown below is
thought to be optimal and will be maintained:
Debt (7%) $60,000,000
Preferred stock 10,000,000
Common stock $10,000,000
Retained earnings 20,000,000
Common equity 30,000,000
------------
TOTAL CLAIMS $100,000,000
New securities can be sold under the following conditions:
BONDS: Up to $9,000,000 in new bonds can be sold to the public at par with flotation costs of $91.29. The bonds have a face value of $1000, mature in 20 years and carry a coupon of 8%, paid annually. Beyond $9,000,000 the coupon rate will be 10% and the bonds can be sold for $1091.29 with flotation costs of $91.29.
PREFERRED STOCK: Up to $3,000,000 in new $100 par value stock with a dividend of 15% can be sold to the public for $125 with the firm netting $115.38. Beyond $3,000,000 the price of $125 still holds but the net proceeds fall to $107.14.
COMMON STOCK: Up to $6,000,000 in new common stock can be sold at a cost of 20%. Beyond $6,000,000 the cost to the firm rises to 24%.
Bunky's is considering the following projects:
PROJECT OUTLAY LIFE IRR
A $10,000,000 6 16.0%
D 10,000,000 5 10.0%
M 10,000,000 6 14.3%
P 10,000,000 4 15.3%
W 10,000,000 8 11.3%
Z11 20,000,000 6 11.6%
-----------
$70,000,000
{a} Calculate the flotation costs and underpricing associated with the first $6,000,000 in new common stock.
{b} Accurately plot Bunky's marginal cost of capital schedule for $0 to $70,000,000.
{c} On the same graph plot Bunky's Internal Rate of Return schedule. Which projects should the firm accept? Calculate the average cost of capital for the total capital budget you are advocating.
{d} Suppose that the firm is able to obtain $9,000,000 (instead of $6,000,000) in new common stock at a cost of 20%. Clearly fix your graph. Does this affect your conclusion to {c}? You need not recalculate the average cost of capital if your conclusion has changed.
{e} Calculate the NPV of project A.
[3] (20 points)
{a} Clifford Construction can raise up to $14,000,000
at 15%. Beyond $14,000,000 the cost rises to 18%. The firm is considering
three projects: A which has an outlay of $10,000,000 and an IRR of 16.5%,
B which has an outlay of $10,000,000 and an IRR of 18% and C which has
an outlay of $8,000,000 and an IRR of 15.2%. Display the cost of capital
and investment schedules on a graph. Which projects should the firm accept?
You must back up your answer with the appropriate calculations.
{b} In problem [2] why is the cost of retained
earnings not equal to zero; i.e., why should the firm not consider retained
earnings to be free?
[2] (30 points)
Today you buy 100 shares of McAfee Roundball Ltd.'s convertible preferred stock for $105 per share. The preferred stock has a par value of $100, a dividend rate of 10% and is convertible into 5.5 shares of McAfee's common stock. At the time of purchase the company's earnings and common dividends are expected to grow at 30% for the next two years and then 20% for an additional three years before stabilizing at 5% for the indefinite future. The firm has a marginal tax rate of 40% and investors in common stock require a return of 15%. The firm just paid a dividend on its common stock of $1.00 per share.
{a} Assuming the forecasts hold and that you convert to the common stock after three years, what rate of return did you earn over the period?
{b} Suppose you had waited until the end of the sixth year to convert. What rate of return did you earn over the six years? Why is this answer higher or lower than {a}?
SOME SELECTED ANSWERS
1. D=$4,267.74, T=$2,847.55/yr
2. PV = $476.19
3. Outlay=114,800 DCF=61,600
k=21.7% NPV=-16,086
4. (a) 19.56%, (c) 19.25%,
(d) 18.32%
5. DCF(1&2)=85,600,
DCF(4-6)=115,600
MV=237,708
6. Original=$615.31 Final=$1,987.18
8. P(83)=$933.34 NPV=$150.59
r=16.10%/yr comp s.a.
9. i(1)=13%/yr i(2)=10%/yr
10. DCF=16,400
NPV(8)=19,527 NPV(12)=41,002
11. S=$5.00 N=5
rights
13. DCF=$228,000
s=44.90 D204,000 s(7)
134.70
14.
p=983.83 NPV=$131.47 (b)16.59% comp s.a.
16. P(4) $42.50
17. breaks at D=15, P=30, Eq=30
& 50 0-15 MCC=9.94%
19. Plan A:0-40 k=12.40%
40-100 k=13.80%
20. Conversion value=$151.29
r=21.47% P(6)=$32.19