FALL 98 - SPRING 99
RATIO ANALYSIS AND NPV/IRR
[1] (15 points)
Emily is considering purchasing 100 shares of Robako, Inc. whose
financial statements are shown below:
| Cash | 25,000 | Accounts Payable | 67,000 |
| Accts. Rec | 43,000 | Income Taxes Payable | 25,000 |
| Inventory | 70,000 | Long-term Debt | 100,000 |
| Property, Plant
and Equipment |
294,000 | Common Stock | 140,000 |
| Retained Earnings | 100,000 | ||
| Total Assets | 432,000 | Liabilities &
Net Worth |
432,000 |
Sales 1,050,000
- Cost Goods Sold 735,000
- Expenses 200,000
Operating Income 115,000
- Interest 15,000
Pre-Tax Income 100,000
- Taxes (40%) 40,000
Net Income 60,000
When valuing a stock, Emily chooses a required discount using this formula:
k' = .40 - .05*(CR) +.4*(DR) - .6*(ROE) - .03*(TIE)
where CR is the current ratio, DR is the debt ratio, ROE is return
on equity and TIE is the times interest earned ratio. Compute all ratios
to two decimals (e.g., 12.3% is .12).
Emily expects Robako's stock to pay cash flows of $8.00 a share for
ever with the next payment in one year's time. The stock is currently selling
for $75 a share.
{a} Calculate the NPV and IRR of Emily's decision to purchase 100
shares. Should she buy the shares?
{b} Explain why the sign of DR is positive and TIE is negative.
RATI0 ANALYSIS AND NPV/IRR
[2] (20 points)
Tricia Robak is contemplating the purchase of 100 shares of the preferred
stock of Falcinelli, Inc. Tricia knows the cash flows of the investment
to be very predictable. She forecasts that these cash flows per share will
be $6.40 a year in perpetuity with the next payment in one year's time.
The stock is currently selling for $45 per share. Tricia has a very unique
method for determining the required discount rate (k) that she uses for
valuing the cash flow stream. She selects her k using this equation:
k = .15-.008*(CR)+.012*(DR)-.007*(TIE)-.4*(ROE)-.009*(TATO)
where: CR = current ratio
DR = debt ratio
TIE = times interest earned ratio
ROE = return on equity
TATO = total asset turnover ratio (based on sales)
Always use 2 decimal places for each ratio (i.e., 56.3% is .56)
Falcinelli's financial statements are shown below:
Balance sheet as of December 31, 1996:
ASSETS LIABILITIES
Cash $155 Accounts payable $258
Receivables 672 Notes payable 168
Inventory 483 Other curr. liab. 234
----- -----
Total curr. Assets $1310 Total curr. liab. $660
Net fixed assets 585 Long-term debt 513
Equity 722
----- -----
TOTAL ASSETS $1895 TOTAL CLAIMS $1895
Income Statement for year ended December 31, 1996
Sales $3215
Cost of Goods Sold 2785
GROSS PROFIT $430
Expenses
Operating expenses 230
Depreciation 60
Interest expense 49
TOTAL EXPENSES 339
-----
PRETAX NET INCOME $91
Taxes (40 %) 36
-----
NET INCOME $55
{a} Calculate the NPV and the IRR of the decision to buy the stock.
{b} Explain the signs in front of the DR and TIE factors in the required
discount equation. In other words, why is one positive and the other negative?
EFFECTIVE RATES
[3] (20 points)
While driving in your car, you hear a newscaster on the radio say
"Last month consumer prices rose by &%$# per cent. At this rate, prices
will rise by 18.16 per cent for the year." You pull your car safely off
the road, whip out your calculator, and compute the number that the static
caused you to miss. How much did prices rise last month?
EFFECTIVE RATES
[4] (25 points)
You win the Pennsylvania state lottery. The jackpot has a present value of $500,000. The state gives you two options as to how you can receive your winnings. Option A is 36 monthly payments of $18,076.20 each. Option B is 12 quarterly payments of $X a quarter that provide you with a return of 18.20% a year, compounded quarterly.
{a} Calculate the total amount received under both options.
{b} Calculate the effective annual rates of both options.
{c} Which option do you choose and why?
TIME VALUE OF MONEY
[5] (30 points)
On September 25, 1997 you deposit $5,000 into an account that pays
8% interest a year. You make 7 more deposits on September 25, 1998 through
September 25, 2004. Your original goal is to be able to withdraw a constant
amount for a trip to Europe each year starting on September 25, 2009. You
plan to do this each year forever.
{a} What is the maximum amount that you would be able to withdraw
annually in perpetuity starting on September 25, 2009? Assume funds continue
to earn 8% interest.
{b} Suppose that when the time comes to make the withdrawals, you
get greedy and make three withdrawals of twice the amount you calculated
in {a} on September 25, 2009, 10 and 11. Also on September 25, 2011, it
dawns on you that you’re not going to live forever so you decide to take
all of your remaining money out in only 20 equal withdrawals starting on
September 25, 2012. What is this constant amount?
TIME VALUE OF MONEY
[6] (30 points)
Dale Falcinelli make nine $1,000 deposits on February 12, 1998, 99,
00, 01, 02, 04, 05, 06 and 07 (skips 2003) into an account paying 12% interest.
The account will continue to 12% until February 12, 2010 at which time
Mr. Falcinelli must switch the money to another investment that pays an
unknown rate of interest.
He wants to be able to withdraw $2,000 per year starting on February
12, 2011.
{a} What is the minimum interest rate the second investment must earn if he is to withdraw the $2,000 each year for ever?
{b} Suppose that instead of the infinite stream of $2,000 withdrawals, Mr. Falcinelli decides to withdraw $2,000 a year starting on February 12, 2011 but for only 20 years. Now what is the minimum rate of interest the second investment must earn?
{c} Suppose that the second investment can earn only 2% a year. How
many full $2,000 withdrawals can be made starting on February 12, 2011
and what will be left in the account after the last full $2,000 withdrawal?
CAPITAL BUDGETING
[7] (30 points)
Bunky's Burgers, Inc. is thinking of replacing a piece of equipment
with a new, larger model. The existing machinery was purchased three years
ago for $80,000. It is being depreciated using the straight-line method
to a salvage value of $8,000 over its original expected life of eight years.
The new equipment would lower before-tax expenses each year but would not
affect sales revenues. It costs $150,000, has a zero salvage value and
would be depreciated over its expected life of five years using the straight-line
method. The firm would require additional net-working-capital of $10,000
if the new machine is purchased. If the firm were to scrap the existing
machine today, it would realize $15,000 from the sale. The firm's required
rate of return is 12% and its marginal tax rate is 40%. What is the minimum
annual reduction in before-tax expenses necessary for the replacement to
become worthwhile?
CAPITAL BUDGETING
[8] (30 points)
MattMan Industries is considering replacing a piece of equipment
with a new, more efficient model. The existing equipment cost $60,000 when
new; it is 2 years old and is being depreciated toward a $4,000 salvage
value over its original expected 7 year life using straight-line depreciation.
MattMan would receive $20,000 today if it sold the equipment. The new equipment
would cost $50,000 and be depreciated over a 5 year life to a $5,000 salvage
value using straight-line. Replacing the equipment would have no effect
on sales but would probably reduce operating expenses. Because of a new
design, the new equipment would require $2,000 LESS net working capital
(reduction in spare parts inventory).
The firm as a 15% required return and a 40% marginal tax rate.
What is the minimum reduction in annual operating expenses necessary
for the replacement to be worthwhile?
CAPITAL BUDGETING UNDER UNCERTAINTY
[9] (50 points)
Mattman Industries is considering the purchase of a new piece of
equipment. It would cost $150,000 and be depreciated over a life of 5 years
to a zero salvage value using the straight-line method. If the purchase
is made, Mattman estimates the following probability distribution of revenues
over operating expenses for each year:
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Mattman uses the certainty equivalents method when making
a capital budgeting decision and selects the appropriate certainty equivalent
coefficients based upon the coefficient of variation of cash flows from
this table:
| s/DCF |
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Mattman has a marginal tax rate of 40% and the new investment
would require additional net working capital of $30,000. You may assume
that any non-operating terminal year cash flows are known with certainty,
i. e., their certainty equivalent coefficients are equal to 1.0.
The risk-free rate is 4%, the investment’s beta is 2 and
the market’s risk-premium over and above the risk-free rate is 7%.
{a} Calculate the risk-adjusted NPV of the investment
if there is a 50% chance the equipment will actually last only 3 years
and be scrapped for $40,000 and a 50% chance it will actually last 10 years
at which time its scrap value will be zero.
{b} Suppose that instead of using the certainty equivalents
approach, Mattman uses the "Beta Model" for selecting its hurdle rate.
Calculate the NPV if the information in {a} still holds.
{c} Explain the circumstances under which Mattman should
use the Beta Model; i.e., must Mattman be diversified or just in one or
two lines of business? What is systematic risk and what is unsystematic
risk? Which does beta account for and what happens to the other one?
CAPITAL BUDGETING UNDER UNCERTAINTY
[10] (45 points)
Bunky's Burgers, Inc. is considering the purchase of equipment
which has a purchase price of $630,000. The machinery will be depreciated
using the straight-line method over a life of six years to a salvage
value of $30,000. If the purchase is made, additional net working capital
of $50,000 will be needed. The firm has made the following forecasts of
the change in sales over operating costs:
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The firm has a cost of capital of 14% and a marginal tax
rate of 40%. The risk-free rate of interest is 6%. The firm has a beta
coefficient of 1.6 and the market’s risk premium over and above the risk-free
rate is 5%.
There is a 40 percent chance the equipment will actually
last only 4 years and be scrapped for $50,000 (assume this value is known
with certainty) and a 60 percent chance if will last 10 years and have
a zero scrap value.
{a} Assume that Bunky's uses the certainty equivalents approach when making its capital budgeting decision and chooses the certainty equivalents coefficients from the table below. Compute the expected net-present-value.
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{b} Now assume that Bunky’s uses the "beta model" when
making its capital budgeting decision. Compute the expected net-present-value.
LEVERAGE
[11] (20 points)
{a} What is operating leverage and why does it occur?
Explain why the degree of operating leverage decreases as the level of
output increases.
{b} What is financial leverage and why does it occur?
Is financial leverage a good thing or a bad thing?
BOND VALUATION
[12] (30 points)
You buy a $1,000 par value debenture of Emily's, Inc.
that carries a 14% annual coupon, payable semiannually. The bond matures
in 30 years. The bond is priced to produce a yield to maturity of 15% a
year, compounded semiannually.
{a} Eight years after purchasing the bond, you sell it
in the open market. The yield to maturity on 22 year bonds has fallen to
10% a year, compounded semiannually while the yield to maturity on 30 year
bonds has dropped to 8% a year, compounded semiannually. What annual rate
of return did you earn over the 8 year period?
{b} Supposed the bond had been callable at $1,070 and
had also been convertible into Emily's stock at a conversion price of $40
a share. Emily's common stock was trading at 42 and 3/8 when the bond was
called. What annual rate of return did you earn over the 8 year period
if you took the better course of strategy?
{c} Why would the firm want to include a call provision
with a bond issue?
BOND VALUATION
[13] (30 points)
Each question is independent of the other three.
{a} Explain what happens to the yield differential between
a firm's mortgage bonds and its debentures as the outlook for the economy
begins to brighten? How would you expect investors in both types of the
firm's bonds to react as they gradually have more confidence in the economy?
{b} A firm is about to sell a new issue of 20 year
callable subordinated debentures and another new issue of 20 year
noncallable subordinated debentures. The level of interest rates has been
steadily falling so now rates are thought to be near their historical lows.
Comment on the relative size of the differential between the yields on
the two issues. Explain your reasoning.
{c} Interest rates are near their historical highs. Forecasters
are predicting they are going to drop soon. Draw the probable shape of
the yield curve. What advice would you give to a firm regarding the maturity
they should choose for their impending bond issue? What are the pros and
cons of issuing short-term securities at this time? Of issuing long-term
securities?
{d} Explain what happens to the yield differential between
a firm's outstanding straight (nonconvertible) bonds and its outstanding
convertible bonds if negative publicity regarding the company begins to
surface. For example, consider a pharmaceutical company whose applications
for FDA approval of several of their new drugs appear likely to be rejected.
Use supply and demand in your analysis.
BOND VALUATION
[14] (25 points)
Bunky's Burgers, Inc. has some outstanding subordinated debentures that mature in 2012. The $1000 par value bonds were issued in 1992 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 1992 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. Flotation costs are $30 per bond.
{b} Calculate the rate of return earned by an investor
who bought the bond in 1992 and followed the better course of action when
the bond was called. Did the investor welcome the call? Explain.
COMMON STOCK VALUATION - "SUPER" GROWTH
[15] (30 points)
On November 24, 1997, Emmy Liz's paid a dividend of $4.00 on its common stock. Analysts forecast the following dividend stream for the company:
1998 $5.00 1999 $5.00 2000 $0 2001 $4.00 2002 $5.00
2003 $5.50 2004 $6.00
Starting in 2005 Emmy Liz’s’ dividends are expected to
grow at 8% a year indefinitely.
{a} If you buy the stock on November 25, 1999 and the
forecasts still hold, what price did you pay if the market's required rate
of return is 17%?
{b} Suppose you sell the stock on November 25, 2010 and
the original forecasts still hold. What did you receive for the stock?
{c} What rate of return did you earn over the 11 years?
Think before proceeding on this one!!
COMMON STOCK VALUATION -- "SUPER" GROWTH
[16] (35 points)
Today you purchase a convertible bond of Bunky's Burgers
at par. The bond matures in 20 years, has a coupon rate of 10%, payable
semiannually, and is convertible into Bunky's common stock at a conversion
price of $80 a share.
Yesterday Bunky's paid a dividend of $3.00 a share on
the common stock. Investors require an annual return on 16% on the common
stock. Analysts forecast that earnings and dividends will continue to grow
at an annual rate of 30% for another 5 years. They predict that after the
5 years, the growth rate will drop to a constant normal rate for the indefinite
future.
You hold the bond for only two years and then convert
at the prevailing market price. You earn an annual rate of 16.04%, compounded
semiannually. If all of the analysts' forecasts hold, what normal growth
rate were they predicting?
COST OF CAPITAL
[17] (70 points)
Mattman Industries is planning its 1998 capital budget
and needs your advice. The firm believes that the capital relations shown
below are optimal and will be maintained.
Debt $600,000,000
Preferred Stock 240,000,000
Common Equity 360,000,000
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TOTAL CLAIMS $1,200,000,000
The firm has a marginal tax rate of 40% and has $9,000,000
of retained earnings available for investment this year. On November 24,
1994 Mattman paid a dividend of $6.01 on its common stock. Yesterday it
paid a dividend of $8.00. The stock is currently selling for $88 a share.
Assume that this growth rate continues indefinitely. The firm can raise
funds under these conditions:
BONDS: Up to $8,000,000 in new perpetual bonds carrying a 10% coupon (paid annually) can be sold to yield the investor 11%; however, flotation costs total 10% of the price paid.
For $8,000,000 to $20,000,000, the flotation costs rise to 20% of the price paid. The investor still makes 11%.
Beyond $20,000,000, the investor makes 13% and the flotation
costs are 20% of the price paid.
PREFERRED STOCK: Up to $8,000,000 in $50 par preferred stock with a dividend rate of 14% can be sold at $60 a share with flotation costs of $6.15.
Beyond $8,000,000 the flotation costs rise to $13.33 a
share.
COMMON STOCK: Up to $3,000,000 in new common stock can be sold to net the firm $73.33.
Beyond $3,000,000 the net proceeds total $58.67.
The firm is considering four potential projects with the
following forecasted cash flows:
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{a} Compute Mattman’s marginal cost of capital for each
segment of the marginal cost schedule.
{b} Clearly demonstrate using a CLEARLY LABELED
graph which projects are acceptable and compute the average cost of capital
for the capital budget you are advocating.
{c} Why does the firm net only $73.33 per share when the
common stock is currently selling for $88 a share?
{d} Why is Mattman accepting a project whose IRR is less
than the rate of return that shareholders require?
{e} Using a graph of the ‘traditional’ approach to
the optimal capital structure question shown in the last lecture, explain
the implicit benefit of using equity as a source of funds. In other words,
if the cost of equity is so much greater than the cost of debt, why does
the firm use so much of it?
COST OF CAPITAL
[18] (65 points)
Emmo Enterprises is planning its forthcoming capital budget and needs your advice. The firm's capital structure relations shown below are believed to be optimal and will be maintained.
Debt $100,000,000
Preferred Stock 20,000,000
Common Stock $30,000,000
Retained Earnings 50,000,000
Common Equity 80,000,000
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TOTAL CLAIMS $200,000,000
The firm's common stock is currently trading for $100
per share and yesterday it paid a dividend of $8.00. Earnings and dividends
are expected to grow at 8% for the indefinite future. Emmo's marginal tax
rate is 40%. The firm has $12,000,000 available from retained earnings
for investment this year. New securities can be sold under the following
conditions:
DEBT: Up to $10,000,000 of new perpetual bonds carrying an 8% coupon (paid annually) can be sold for $1000. Flotation costs total $40.00.
Beyond $10,000,000 new perpetual bonds carrying an 10%
coupon (paid annually) are sold at par with flotation costs totalling $40.00.
PREFERRED STOCK: Any size issue of $50 par value
preferred stock carrying a 14% dividend rate can be sold for $65.00 with
the firm netting $58.33.
COMMON STOCK: Up to $8,000,000 new stock can be
sold with underpricing and flotation costs of $20.00. Beyond $8,000,000
the underpricing and costs rise to $28.00.
The following is a list of potential investments that the firm is considering:
PROJECT OUTLAY IRR%
A $20,000,000 11.3
B 10,000,000 14.0
C 10,000,000 12.1
D 20,000,000 15.0
E 5,000,000 10.7
{a} Calculate the marginal cost of capital for each segment
of the marginal cost schedule.
{b} Clearly demonstrate using a CLEARLY LABELED
graph which projects are acceptable and compute the average cost of capital
for the capital budget you are advocating.
{c} Compute the NPV of project C assuming a life of 8
years and uniform annual cash flows.
{d} Why is Emmo accepting project D with an IRR less than
the rate of return required by stockholders?
{e} Why does Emmo think that raising only half of its capital from bonds is "optimal" if its cost of debt is so much less than its cost of equity?
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