Ratio Analysis
[1] (25 points)
Sarah Burke is contemplating the purchase of 100 shares of the stock of Falcinelli, Inc. Sarah knows the cash flows of the investment to be very predictable. She forecasts that these cash flows per share will be $5.40 a year for 20 years followed by $6.00 a year in perpetuity with the next $5.40 payment in one year's time. The stock is currently selling for $55 per share. Sarah 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 = .205-.052*(AT)+.015*(DR)-.008*(TIE)-.008*(ARTO)-.29*(GPM)
where AT = acid test ratio
DR = debt ratio
TIE = times interest earned ratio
ARTO = accounts receivable turnover ratio
GPM = gross profit margin
Always use 2 decimal places for each ratio (ie, 56.3% is .56)
Falcinelli's financial statements are shown below:
Balance sheet as of December 31, 1995:
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, 1995
Sales $4415
Cost of Goods Sold 3785
GROSS PROFIT $630
Expenses
Operating expenses 230
Depreciation 160
Interest expense 48
Total expenses 438
-----
PRETAX NET INCOME $192
Taxes (33.3%) 64
-----
NET INCOME $128
{a} Calculate the NPV of the decision to buy the stock.
{b} Calculate the IRR of the decision to buy the stock.
{c} Explain the signs in front of the DR and GPM factors in the required discount equation. In other words, why is one positive and the other negative?
Ratio Analysis
[2] (20 points)
Sarah Burke is contemplating the purchase of 100 shares of the preferred stock of Falcinelli Disco Jeans, Inc. Sarah knows the cash flows of the investment to be very predictable. She forecasts that these cash flows per share will be $6.70 a year in perpetuity with the next payment in one year's time. The stock is currently selling for $48 per share. Sarah 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 = .300+.001*(ACP)-.05*(AT)-1.95*(ROA)-.009*(FATO)-3.1*(NPM)
where ACP = average collection period
AT = acid test ratio
ROA = return on total assets
FATO = fixed asset turnover ratio
NPM = net profit margin
Always use 2 decimal places for each ratio (ie, 56.3% is .56)
Falcinelli's financial statements are shown below:
Balance sheet as of December 31, 1995:
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, 1995
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 of the decision to buy the stock.
{b} Calculate the IRR of the decision to buy the stock.
{c} Explain the signs in front of the ACP and FATO factors in the required discount equation. In other words, why is one positive and the other negative?
Effective Rates
[3] (15 points)
Your kid brother is buying a car and seeks your financial advice. He wants to know which is a better deal: paying back a $2,000 loan with 12 monthly payments of $200 or with 4 quarterly payments of $615. Clearly show your analysis below.
Effective Rates
[4] (20 points)
{a} During the year 1995 the wholesale price index rose by 7.84%. Assume that this rate of increase was uniform each month. If the rate continued into the next year, calculate the rate of inflation (to 4 decimal places) during January of 1996. Clearly show your work.
{b} During the year 1995 the wholesale price index fell by 7.84%. Assume that this rate of decline was uniform each month. If the rate continued into the next year, calculate the rate of deflation (to 4 decimal places) during January of 1996. Clearly show your work.
{c} Explain why you did or did not get the same answer to {a} and {b} with just the opposite sign.
{d} Last week a Lehigh faculty member asked me the following question: If a firm's earnings were $2.5 million in 1995 and $400,000 in 1990, what was the annual compound rate of growth? I told him that any Fin 225 student could do this. Prove me right!
PV/FV Annuities
[5] (30 points)
Starting on February 13, 1996 you make the first of four annual deposits of X dollars per year into an account that pays 5% interest. On February 13, 2000, 2001, 2002 and 2003 you deposit 2X dollars. On February 13, 2004, 2005, 2006 and 2007 you deposit 4X dollars. You plan to withdraw $20 per year for 10 years starting on February 13, 2012 (through 2021) and $40 per year for ever starting on February 13, 2022. Find the minimum value of X that will make your planned withdrawals possible.
PV/FV Annuities
[6] (30 points)
Your son is going to go to start college on October 10, 2005. The annual tuition today is $25,000. You expect to pay a constant annual tuition on October 10, 2005, 06, 07 and 08. The rate of inflation applied to tuition between now and 2005 is 3% a year. For simplicity, you should assume that tuition will remain constant for the four years at the 2005 rate.
You PLAN to make six equal annual deposits starting today and running through October 10, 2000 that will be sufficient to pay the expected tuition.
After having made the first four deposits as planned, you learn that tuition will actually be $40,000 a year for the four years. Two more of the original planned deposits will not be enough to pay the four years of tuition. Instead of the last two planned deposits, you decide to deposit $X on October 1999 and $2X on October 2000.
Find the minimum amount of X necessary to pay the four $40,000 tuition bills. Assume a rate of return of 8% a year.
Capital Budgeting
[7] (25 points)
Matty's Widgets is thinking of purchasing a piece of equipment. The new equipment would be expected to increase sales by $200,000 a year and increase operating expenses by $50,000 a year. It would cost $900,000 and be depreciated using straight-line to a zero salvage value over a depreciable life of 6 years. The equipment would require additional net working capital of $40,000. Matty's marginal tax rate is 30% and its required rate of return is 12%.
Calculate the expected net-present-value if there is a 30% chance that the new equipment could last only 4 years and be scrapped for $100,000 and a 70% chance that it could last 9 years with a zero scrap value.
Capital Budgeting
[8] (30 points)
Bunky's Burgers, Inc. is contemplating replacing some existing equipment with some new hardware. The existing equipment, carried on the books at $800,000, is being depreciated using the straight-line method to a zero salvage value over its remaining life of 8 years. Bunky's could scrap the equipment today for $1,000,000.
The new machinery would also be depreciated using the straight-line method to salvage value of $400,000 over its expected life of 8 years. The new equipment would be expected to increase annual sales by $1,000,000. The new machinery would require additional new-working-capital of $120,000. Bunky's has a required return of 7% and a marginal tax rate of 40%.
Find the maximum amount that the firm would be willing to pay for the new equipment if replacement is to be worthwhile.
Capital Budgeting
[9] (30 points)
Keeley Novelties, Inc., makers of the famous "Mugaphone" is contemplating the purchase of a new high capacity machine for cutting and shaping its cardboard product. The new machine has a purchase price of $240,000 and would be depreciated using the straight-line method over an expected life of seven years to a salvage value of $30,000. The machine would enable Keeley to increase its annual sales by $100,000 but would also increase operating expenses by $45,000 per year. Additional net-working-capital of $14,000 would be required. The firm's marginal tax rate is 35 per cent and its required rate of return is 18 per cent. Keeley is currently using a machine that is three years old that was purchased for $100,000. This machine is being depreciated using the straight-line method over an original life of 10 years to a salvage value of $10,000. If Keeley can realize $82,000 from the sale of this existing equipment, should the firm make the replacement? Use either the NPV or IRR approach.
Risk-adjusted discount rates
[10] (40 points)
Bunky's Burgers is contemplating the purchase of
a nuclear french fryer and needs your advice. The fryer would cost $800,000
and be depreciated over an 8 year life to a zero salvage value using the
straight-line method. If the fryer is purchased, Bunky's estimates the
following probability distribution of revenues over pre-tax expenses for
each year:
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Bunky's uses the risk-adjusted discount rate approach
when making a capital budgeting decision and selects its required return
based upon the coefficient of variation of cash flows from the following
table:
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Bunky's has a marginal tax rate of 30% and the fryer would require an additional $30,000 in net working capital. Bunky's is unsure as to how long the fryer will actually last.
{a} Calculate the expected IRR of the purchase if there is a 70% chance the fryer will actually last 6 years (with a salvage value of $40,000) and a 30% chance it will actually last 12 years (with a salvage value of $0. Should Bunky's buy the nuclear french fryer?
{b} Suppose that instead of using the risk-adjusted discount rate approach, Bunky's was a well-diversified firm that used the "Beta Model" for selecting its hurdle rate. Assume the risk-free rate is 4%, the fryer's beta is 1.9 and the market's risk premium over and above the risk-free rate is 5.5%. Should Bunky's buy the nuclear french fryer?
Risk and Uncertainty - Certainty Equivalents
[11] (25 points)
You forecast the following annual cash flows for
a potential project:
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{a} Using the IRR method, should the firm accept the investment if it uses a risk adjusted discount rate based on the Beta Model (aka CAPM)?
{b} Using the IRR method, should the firm accept the investment if it uses the certainty equivalents method to account for risk?
{c} Using the IRR method, should the firm accept the investment if it uses a risk adjusted discount rate based upon the coefficient of variation of cash flows?
Bond Valuation
[12] (30 points)
On March 28, 1990 you purchased a subordinated debenture of McDonald's. The bond which matures on March 28, 2015 has an annual coupon rate of 8%, payable semi-annually, and a face value of $1000. The bond is priced to produce an annual yield to maturity of 12%, compounded semi-annually. On March 28, 1996 you sell the bond for its market value. The market yield to maturity is 6% a year compounded semi-annually on 19 year bonds and 6.5% on 25 year bonds. Initially assume that the bond is neither callable nor convertible.
{a} Compute the (effective) rate of return you earned between 1990 and today.
{b} Compute the (effective) rate of return you would have earned between 1990 and today if the bond were called today at $1070.
{c} Compute the (effective) rate of return you would have earned between 1990 and today if you converted the bond. The conversion price is $50 a share and the stock is currently selling for $55 a share.
Bond Valuation
[13] (25 points)
Bunky's Burgers issues some new $1,000 par value subordinated debentures with an annual coupon rate of 12% payable semiannually. The bonds mature in 30 years. The bond does not contain a call feature. The market interest rate is 13%, compounded semiannually. You buy a bond. 10 years later the market interest rate on 20 year bonds is 10%, compounded semiannually, and on 30 year bonds is 12%, compounded semiannually. You sell your bond.
{a} Compute the annual rate of return you earned over the 10 year period.
{b} Change the assumptions of the problem and now suppose the bond is callable at 1065. It is also convertible into Bunky's common stock at a price of $100 per share. At the end of the 10 year holding period, Bunky's common stock is selling for $125 a share. The firm calls the bond. Compute the annual rate of return you earned over the 10 year period.
Yield Differentials
[14] (32 points)
{a} A firm is about to sell a new issue of 20 year callable debentures and another issue of 20 year noncallable debentures. The level of interest rates has been steadily rising so now rates are thought to be near their historical highs. Comment on the relative size of the difference between the yields on the two issues.
{b} Interest rates are near their historical lows. Forecasters are predicting they are going to rise soon. Describe 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? Of issuing long-term securities?
{c} Explain what happens to the yield differential between a firm's mortgage bonds and its subordinated debentures as the outlook for the economy begins to worsen? How would you expect investors in both types of the firm's bonds to react as they gradually have less confidence in the economy?
{d} Explain what happens to the yield differential between a firm's outstanding straight (nonconvertible) bonds and its outstanding convertible bonds if positive 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 accepted.
Miscellaneous
[15] (25 points)
As a summer intern working in the finance department of a major corporation you accompany the VP of Finance to the annual stockholders meeting. Your job is supposed to be working the projector as the VP makes her presentation. Five minutes before the meeting is to begin, she is overcome with food poisoning and you must take her place on the podium. How would you answer the following stockholders' questions?
{a} "The yield curve is downward sloping at the moment. What maturity bonds are you planning to issue next month? Please explain your reasoning"
{b} "Even though the company is involved in only one industry, why can't we use the 'Beta Model' for accounting for risk? I've heard it's really good."
{c} "I've heard that the company has a very high degree of operating leverage. Is that good or should we be concerned? By the way, what the heck is operating leverage anyway?"
Stock Valuation - "Super Growth"
[16] (30 points)
Mattman Enterprises paid a dividend yesterday of $3.00. The firm expects that its earnings and dividends will grow at a +20% rate for the next 3 years and then decline at a 20% rate for an additional 3 years before stabilizing at a +6% for the indefinite future.
{a} If stockholders require a return of 15%, calculate the market value of the stock at the end of year 3 (i.e., three years from today).
{b} If everything continues as forecasted above, what will be the market value of the stock at the end of year 10?
{c} What annual rate of return would an investor earn over the 7 year period if she bought the stock for the price you found in {a} at the end of year 3 and sold it for the price you found in {b} at the end of year 10?
{d} Suppose the price at the end of year 10 was actually $60.00. Assume the investor bought the stock at the end of year 3 for the price you found in {a}. What rate of return did she earn over the 7 years if all growth rate forecasts are still valid? You should be able to not only set this part up but also be able to solve it with your calculator.
Stock Valuation - "Super Growth"
[17] (40 points)
Bunky's Burgers always pays its annual dividend on April 24. In 1989 the firm paid a dividend of $5.00 a share and in 1994 it paid only $3.00 a share. The market believes that this uniform rate of decline will continue through and including April of 2001 when the public's preoccupation with "eating healthy" will end and the firm's earnings and dividends will begin to grow at a positive annual rate of 6% a year for the indefinite future. Investors require a return of 18%.
{a} Find the predicted value of the stock on April 25, 1998.
{b} Find the predicted value of the stock on April 25, 2008.
{c} Find the (internal) rate of return earned by an investor who bought the stock on April 25, 1998 at the value you found in {a} and who sold it on April 25, 2008 for the value you found in {b}. EXPLAIN HOW YOU WERE ABLE TO ANSWER THIS PART CORRECTLY WITHOUT DOING ANY CALCULATIONS!!
{d} Find the net-present-value of buying the stock on April 25, 1998 for the value you found in {a} and selling it on April 25, 2000 to a "sucker" for $15 a share more than you paid for it. Assume a required return of 18% and that dividends are paid as forecasted.
Cost of Capital
[18] (70 points)
Bunky's Burgers is planning its 1996 financing and investment decisions and needs your help. The firm's capital structure relations shown below are believed to be optimal and will be maintained.
DEBT $160,000,000
PREFERRED STOCK 80,000,000
RETAINED EARNINGS $70,000,000
CAPITAL SURPLUS 90,000,000
COMMON EQUITY 160,000,000
============
TOTAL CLAIMS $400,000,000
The firm has a marginal tax rate of 40%. In 1989 Bunky's paid a dividend of $3.253. By 1993 the dividend had grown at a constant annual rate to $3.661. Assume that this growth rate continues for the indefinite future. The firm's common stock is currently selling for $20 a share. Assume that the 1996 dividend is D1. The firm has $8,000,000 available from retained earnings for investment during the coming year. New securities can be sold under the following conditions:
DEBT: Up to $6,000,000 in new perpetual bonds carrying a 12% coupon, paid annually, can be sold for $1,000 with flotation costs of $40 per bond. From $6,000,000 to $16,000,000 the coupon rises to 14% and the flotation costs are $50. Beyond $16,000,000 the coupon must be 15% and flotation costs are $60.
PREFERRED STOCK: Up to $8,000,000 in new $50 par value preferred stock carrying a 16% dividend rate can be sold at par with flotation costs total $4.00 per share. Beyond $8,000,000, the dividend rises to 18%, the shares are still sold at par and the flotation costs total $5.00.
COMMON STOCK: Up to $8,000,000 of new common stock can be sold with a $2.00 flotation cost. Beyond $8,000,000 the flotation costs rise to $4.00 a share.
The firm is considering five potential projects shown below.
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{b} On the same graph, plot Bunky's internal-rate-of-return schedule. Which projects should the firm accept?
{c} Compute the average cost of capital for the capital budget you are recommending in {b}.
{d} Assuming that you found that the cost of debt for this firm was considerablly less than its cost of equity, how can the firm think that using only 40% debt is "optimal"? Why shouldn't Bunky's use 80 or 90% debt? Explain your reasoning.
{e} If project H has a life of 5 years and uniform cash flows, calculate its NPV.
Cost of Capital
[19] (60 points)
Oshkosh B'Gosh has the following capital structure which is believes is optimal and will be maintained:
Debt $600,000,000
Preferred Stock 100,000,000
Common Equity 300,000,000
_____________
CLAIMS $1,000,000,000
The firm is planning its capital budget for the coming year and needs your expertise. The firm's marginal tax rate is 35%, it has retained earnings available for investment of $9,000,000 and its common stock is trading for $60 a share. In 1988 its dividend on common stock was $3.2636 per share; by 1996 it had risen to $5.6075 (D0). Assume that this growth rate is expected to continue for the indefinite future.
New securities can be sold under the following conditions:
DEBT: Up to $12,000,000 in new 30 year debentures with an 8% coupon (payable annually) can be sold for $852.48 with flotation costs of $41.02. Beyond $12,000,000 the flotation costs rise to $113.29 per bond.
PREFERRED STOCK: Up to $2,000,000 in new $100 par value preferred stock with a dividend rate of 8% can be sold to net the firm $66.67. Beyond $2,000,000 the dividend rate must be 10% and the firm nets $71.43.
COMMON STOCK: Up to $6,000,000 in new common stock can be sold with underpricing and flotation costs of $10 per share. Beyond $6,000,000 the total is $17.143.
The following six investment projects have been proposed (outlay in $millions):
PROJECT OUTLAY IRR
F 5 13.5
H 5 11.0
A 10 10.5
K 10 9.5
B 15 15.0
P 15 13.0
{a} Compute the cost of capital for all segments of the cost of capital schedule. ACCURATELY display your results on a graph.
{b} On the same graph, draw the firm's IRR schedule. Which projects should the firm accept?
{c} Compute the average cost of capital for the amount of the capital budget you found in {b}.
{d} Compute the NPV of project H. Assume uniform cash flows and a life of 4 years.
{e} Suppose that before undertaking any investment
the firm "finds" an additional $3,000,000 in retained earnings. How does
this change your answers (or does it?) to {b} and {d}?
PARTIAL ANSWERS TO SELECTED PROBLEMS
3. 41.30% vs. 40.27%
4. (a) .64%/month
(b) -.69%/month
6. Tuition = $33,579.91
D=$11,149.85 X=$12,590.15
7. n=4 Outlay = 940,000
NPV = -382,715 n=9 DCF
(7-9) 90,000 NPV = -213,773
9. DCF
= $43,100 Outlay = $175,150 NPV = -$199.71
10. DCF
= 226,000 cv. 52.38/226 = .23 IRR(6) = 18.19% IRR(12)
= 25.08%
11. DCF
= 9,000 c.v. = 2.68/9 a=.8
k'=12% (b) IRR = 6.40%
12. P(90) = $684.76
P(96) = $1224.92 EAR = 20.16% (c) Conversion Value =
$1,100 EAR = 18.54%
13. P(0) = 924.84 P(10)
= $1,171.59 IRR = 7.13%/period
16. P(6) = 31.26 P(3)
26.67 P(10) = $39.47
18. Breaks at $15,000,000,
$20,000,000 and $40,000,000 MC(1) = 15.68%,
MC(2) = 16.21% MC(3) = 17.10% MC(4) = 19.03%