[1] (30 points) EFFECTIVE RATES  Solution
{a} First National Bank offers its customers a savings account that pays an APR of 8%, compounded monthly. Last National Bank wants to be competitive by offering the same EAR as FNB but it pays its interest on the same type of savings account daily. What APR should LNB offer in order to pay the same EAR as FNB? (5 decimal place accuracy, please)
{b} You borrow $40,000 for 3 years by agreeing to make 6 equal semiannual payments of $8,521,80. What EAR are you paying? (4 decimal place accuracy, please)
{c} You hear on the news “Last month the Consumer Price Index fell 2%.” If this rate continues every month for a year, will the absolute value of the annual rate of deflation rate be more than 24%, equal to 24% or less than 24%? Explain your choice and then compute the annual rate of deflation? (4 decimal place accuracy, please)
 

[2] (25 points) EFFECTIVE RATES  Solution
{a} You need to borrow $85,000 for 2 years. Al’s Bank offers you two borrowing plans: Plan A is an APR of 28%, compounded quarterly and Plan B is monthly payments of $4,700. For both loans compute the APR, EAR and total payments over the 2-year life of the loan. Which loan do you select and why? (6 decimal places, please, e.g.,12.3456% or .123456)
{b} While driving home one day you hear on you cheap radio the news anchor say “Last month prices rose by ^?*@ percent. This is an annual rate of inflation of 12%.” You pull safely off the road, whip out your calculator and compute the value of last month’s price rise that the static caused you to miss. (4 decimal places, please, e.g.,12.34% or .1234)
 

[3] (35 points) TIME VALUE OF MONEY  Solution
On September 28, 2004 you make the first of 6 annual bank deposits of $1,000. The deposits continue through September 28, 2009. You can earn 8% interest and you expect that rate to continue indefinitely. You intend to clean out the account by making 15 equal annual withdrawals starting on September 28, 2015 and continuing through 2029.
On September 28, 2017 (just after making your third planned withdrawal) you take a closer look at your bank statement. The bank shows a balance that is a lot smaller than you expected. You discover that on September 28, 2008 they had reduced the interest rate to 5% and kept it there and didn’t bother to notify you.
{a} What account balance is the bank reporting immediately after you made the third withdrawal?
{b} If you still want to make 12 more of the originally planned withdrawals starting in 2018 and continuing through 2029 without adding anything more to the investment, you obviously need to start earning a higher return. Calculate the minimum return you must earn starting on September 28, 2017 if you still want to make the remaining 12 original withdrawals.
 

[4] (40 points) TIME VALUE OF MONEY  Solution
Assume that today is February 22, 2005. Today you make the first of 6 annual deposits into an account that you expect to pay 9% annual interest in perpetuity. The deposits have to be of sufficient size to enable you to withdraw $1,000 a year for 30 years starting on February 22, 2017. Assume that you make the 6 planned deposits and also make the first 4 planned $1,000 withdrawals (the last one is 2020). In checking your balance right after making the fourth withdrawal, you are shocked that it is much larger than you expected. The bank tells you they raised the interest rate to 12.5% on February 22, 2008 and never bothered to notify you. Assume that the rate stays at 12.5%.
{a} What is the amount of each of your 6 deposits?
{b} What is the shocking balance on February 22, 2020?
Assume parts {c} and {d} are independent of each other.
{c} Starting with February 22, 2021, how much could you withdraw annually in perpetuity?
{d} How low could the interest rate drop (starting on February 22, 2020) if you still wanted to make the 26 remaining planned withdrawals of $1,000 each.
 

[5] (35 points) CAPITAL BUDGETING  Solution
EmmyLiz, Inc. is contemplating replacing a piece of equipment with a new model but is unsure of how much it can spend on the new machine.
The old machine was purchased 2 years ago for $8,000. It is being depreciated using straight-line over its 10-year original life to a salvage value of 0. If it were sold today, the firm would receive $4,000 for it.
The new equipment would be depreciated over an 8-year expected life to a salvage value equal to 20% of its purchase price. The new machine would save the company $3,200 a year in lower operating expenses. There would be no change in expected sales. The new equipment would require additional net working capital of $1,960. The firm’s marginal tax rate is 40% and its required hurdle rate is 12%.
Find the maximum price the firm would be willing to pay for new machine in order to want to make the replacement.
 

[6] (35 points) CAPITAL BUDGETING  Solution
GEM Industries is considering replacing a piece of equipment with a newer, more efficient model. The existing equipment was purchased 2 years ago for $480 and is being depreciated using straight-line to a salvage value of $40 over an originally expected life of 10 years. The proposed new equipment has a purchase price of $880 and would be depreciated using straight-line to a salvage value of $80 over an expected life of 8 years. The new machine would require additional net working capital of $25. The firm has a marginal tax rate of 30% and a required rate of return of 16%.
GEM estimates that the new equipment would increase annual sales by $300 and increase annual operating expenses by $120. GEM is unsure of how much it can sell the existing equipment for but knows that this is a critical factor in its decision to replace the equipment. Calculate minimum amount that the firm would need to receive in order for the replacement to clear the 16% hurdle.

[7] (45 points) CAPITAL BUDGETING UNDER RISK  Solution
Emmo Enterprises is contemplating the purchase of a new piece of equipment. It has a purchase price of $1000, will be depreciated over a 10 year expected life to a zero salvage value using the straight-line method.
Additional net working capital of $80 would be required.
The firm forecasts the following for each year:

Probability	DS - DC
.30	800
.40	1,000
.30	1,500

The firm has a marginal tax rate of 40%. The risk-free rate of interest is 5%.
If the firm utilizes the certainty equivalents method as part of its capital budgeting process, it selects the certainty equivalent coefficient for all operating cash flows from the table below. You may assume they use a certainty equivalents coefficient of 1.0 for all non-operating cash flows.

Coefficient of Variation of Cash Flows	0 - .15	.16 - .35	.36 - .80	.8+
a	.8	.6	.5	.4

If the firm utilizes the Capital Asset Pricing Model or the “Beta Model” as part of its capital budgeting process, you may assume they use a market risk premium of 5% and a project beta of 1.6.
Compute the expected NPV of the purchase if there is a 50% chance it will actually last only 7 years with a scrap value of $150 and a 50% chance that it will actually last 14 years with a zero scrap value. You should assume
{a} that the firm is well-diversified and then repeat assuming
{b} that the firm is NOT well-diversified.
 

[8] (40 points) CAPITAL BUDGETING UNDER RISK  Solution
GEM Industries is considering the purchase of a new piece of equipment. It would cost $150 and be depreciated over a life of 5 years to a zero salvage value using the straight-line method. If the purchase is made, GEM estimates the following probability distribution of revenues over operating expenses for each year:

GEM 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:

has a marginal tax rate of 40% and the new investment would require additional net working capital of $50. 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 5%, the investment’s beta is 2 and the market’s risk-premium over and above the risk-free rate is 6%.
{a} Calculate the risk-adjusted NPV of the investment if there is a 50% chance the equipment will actually last only 4 years and be scrapped for $45 and a 50% chance it will actually last 12 years at which time its scrap value will be zero.
{b} Suppose that instead of using the certainty equivalents approach, GEM 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 GEM should use the Beta Model; i.e., must GEM be diversified or just in one or two lines of business? Explain systematic risk (include an example) and explain unsystematic risk (include an example)? Which does beta account for and what happens to the other one?
 

[9] (25 points) BOND YIELDS Solution
{a} What are subordinated debentures?
{b} Why would a firm want to add a call feature to a new issue of subordinated debentures? Are there any drawbacks from the firm’s point of view to adding the call feature?
{c} Why would a firm want to add a conversion feature to a new issue of subordinated debentures? Are there any drawbacks from the firm’s point of view to adding the conversion feature?
{d} Draw and label a yield curve of whatever shape you want BEFORE answering this part and your answer must be consistent with the curve you draw. Why would a firm want to make the maturity of a new issue of subordinated debentures very long-term? Are there any drawbacks from the firm’s point of view to making them very long-term?
 

[10] (30 points) BOND YIELDS Solution
You are spending your summer working as an intern for Crazy Al’s Investment Bank and one of your clients seeks your advice on several independent potential bond issues.
{a} The client is considering issuing either subordinated debentures or mortgage bonds. Explain the concept of a risk premium between the two issues. Explain how and why this risk premium is likely to change as the outlook for the economy begins to worsen.
{b} The client is considering whether to add a convertible feature to a potential new issue of long-term bonds. Explain the concept of a premium as it applies to convertible versus non-convertible bonds. Explain how and why this premium is likely to change as the outlook for the company’s future profits begins to worsen.
{c} The client wants to know the advantages and disadvantages of issuing long-term and of issuing short-term bonds. Assume an inverted, downward sloping yield curve. Draw and label your yield curve.
 

[11] (30 points) BOND VALUATION  Solution
The Acme Company has some outstanding $1,000 par value subordinate debentures that mature in 20 years. The annual coupon rate is 9% payable semi-annually. The bonds are convertible into Acme stock at a conversion price of $25 a share and are callable at $1045. You buy a bond for $920.
{a} Calculate the yield to maturity that you are earning.
Parts {b} and {c} are independent of each other.
{b} You hold the bond for 6 years and then convert it to Acme stock. At the time of conversion the expected dividend (D1) is $4.34, the stock market requires a return of 20% on Acme stock and the earnings and dividends are expected to grow at 6% a year for the indefinite future. Calculate the IRR you earn over the 6 year period.
{c} You hold the bond for 6 years and then the firm calls it. Find the annual IRR you earn over the 6 year period.
{d} Continuing with part {c}, suppose the firm finances the call with an equal number of new 14 year bonds issued at par. The annual yield to maturity is 6%, compounded semi-annually. Compute the NPV per bond of the decision to refinance the bonds.
 

[12] (20 points) BOND VALUATION  Solution
You buy a $1,000 par value debenture of the Eli Manufacturing Company for $631.89. The bond pays an annual coupon rate of 8% and matures in 25 years.
{a} Calculate the yield to maturity on the bond (express your answer as an effective annual rate).
{b} Six years after purchasing the bond, you sell it in the open market. The yield to maturity on the bonds has fallen to 10% a year, compounded semiannually. Calculate the selling price and the annual rate of return you earned over the 6 year period (express your answer as an effective annual rate).
 

[12.5] (10 points) PREFERRED STOCK  Solution
Today you buy 100 shares of Bunky’s Burgers callable, convertible preferred stock. The stock is currently priced to yield 12% a year. The preferred stock pays an annual dividend of $6.50 a share and is convertible into Bunky’s common stock at a ratio of 5 shares of common stick for each share of preferred. The preferred stock is callable at a price of $55 a share.
{a} Calculate the price per share that you paid.
{b} Assume you hold the stock for 3 years and then learn that the stock is being called by Bunky’s at $55. Bunky’s common stock at the time of the call is selling for $13.50 a share. Calculate the rate of return you earn over the 3 years if you follow the better course of strategy.
 

[13] (35 points) EQUITY VALUATION - "SUPERGROWTH" Solution
Today, November 23, 2004, you buy a $1,000 par value bond for $940. The annual coupon rate is 8%, payable semiannually and the bond matures in 15 years. The bond is convertible into the firm’s stock at a conversion price of $100 a share. At the time of purchase you forecast that the firm’s dividends will grow at 25% per year for 10 years. Thereafter, dividends will grow at a rate of 5% for the indefinite future. Yesterday the firm paid a dividend of $3.00 a share. Stockholders require a 16% rate of return on the stock.
{a} If all the forecasts are correct and you hold the bond for 7 years and convert, calculate the rate of return you earn over the 7-year holding period.
{b} Now suppose that you hold the bond until maturity and then convert. Calculate the rate of return you earn over the 15-year holding period.

[14] (30 points) EQUITY VALUATION - "SUPERGROWTH" Solution
Today you buy 100 shares of Bunky’s Burgers callable, convertible preferred stock. The stock is currently priced to yield 12% a year. The preferred stock pays an annual dividend of $6.50 a share and is convertible into Bunky’s common stock at a ratio of 5 shares of common stick for each share of preferred.
Yesterday the firm paid a dividend of $0.56 on its common stock. Earnings and common dividends are expected to grow at rate of 25% a year for the next 5 years before stabilizing at a growth rate of 4% for the indefinite future. Common stockholders require a return of 16%.
{a} Calculate the price per share that you paid for the preferred stock..
{b} If you hold the preferred stock for 3 years and then convert it into Bunky’s common stock at the prevailing price, calculate the rate of return you earn over the 3 years.
 

[15] (65 points) COST OF CAPITAL Solution
Emmo.com is planning its investment and financing decisions for the forthcoming fiscal year and needs some of your expert advice. Emmo.com has a marginal tax rate of 40%. Four years ago the firm paid a dividend per share of $3.168 and yesterday (D0) it paid a dividend of $4.00. This rate of growth is expected to continue for the indefinite future. The common stock is currently selling for $24 a share. The firm has $80,000,000 from retained earnings available for investment this year. The firm will raise funds using the following proportions which it considers to be optimal: debt 60%, preferred stock 20% and common equity 20%. If those percentages are maintained, new securities can be raised under the following conditions:

BONDS: Up to $150,000,000 in new 20 year, $1,000 par value bonds with a coupon rate of 10% (payable annually) can be sold to yield the investor 9%. Investment bankers charge a fee of $31.29 per bond. Beyond $150,000,000 the coupon rate rises to 12% (payable annually) and the yield to the investor becomes 11%. On these bonds the investment bankers charge a fee of $59.63 per bond.

PREFERRED STOCK: Up tp $50,000,000 in $50 par value stock can be sold at par with flotation costs of $5.00 a share. The dividend rate is 18%. Beyond $50,000,000 the stock can still be sold at par but the dividend rate rises to 20%. Flotation costs are still $5.00 a share.

COMMON STOCK: All new common stock can be sold with flotation costs and underpricing of $5.00 a share.

Emmo.com has the following slate of potential investment projects:

Project	Outlay	IRR
F	100,000,000	12.5%
J	100,000,000	19.0%
M	150,000,000	14.0%
Z	100,000,000	15.0%

{a} Calculate the marginal cost of capital for each of the segments of its cost of capital schedule. Clearly display your cost of capital on a graph.
{b} Plot Emmo.com’s IRR schedule on the same graph. Which projects are accepted?
{c} Calculate the average cost of capital for the capital budget advocated in part {b}.
{d} Calculate the NPV for project M. Assume a life of 6 years and uniform annual cash flows.
{e} Explain the implicit benefits of using equity as a source of funds.
{f} Explain why the after-tax cost of debt is so much less than the cost of equity.
 

[16] (70 points) COST OF CAPITAL Solution
Bunky’s Burgers has the following capital structure that it believes is optimal and will be maintained:

Debt	$600,000,000
Preferred Stock	100,000,000
Common Equity	300,000,000
TOTAL 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 $12,000,000 and its common stock has a dividend yield of 10%. Earnings and dividends are expected to grow indefinitely at a 10% rate.
New securities can be sold under the following conditions:
: 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.
ERRED STOCK: Up to $7,000,000 in new $100 par value preferred stock with a dividend rate of 10% can be sold to net the firm $66.67. Beyond $7,000,000 the dividend rate must be 12% and the firm nets $70.59.
ON STOCK: Up to $9,000,000 in new common stock can be sold with under pricing and flotation costs equal to 20% of the common stock’s current price. Beyond $9,000,000 the under pricing and flotation costs total 33.33% of the stock’s price.
The following three investment projects have been proposed (outlay in $millions):

Project	Outlay	IRR
A	10	13.0%
B	20	15.0%
C	25	12.2%
D	20	12.8%

{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 C. Assume uniform cash flows and a life of 4 years.
{e} If financing with common equity is so expensive compared to financing with debt, why does the firm still obtain 30% of its funds from common equity?

[1] (a) FNB: EAR = 8.300%; LNB APR = 7.974%; (b) i = .0750002; EAR = 15.56%; (c) EAR = 21.53% deflation

[2] {a} Plan A: EAR = 29.9600%, R=$29,172.41; total payments = $116,689.62; Plan B: i per period = 2.399533%, APR = 28.7944%, total payments = $112,800; {b} Last months' inflation = .9489% (.95%/month)

[3] W = $1259.29; balance 2017 = 6,608.57; (b) i = 15.7667%

[4] {a} D = $814.25; {b} Balance at 2020 = $16,108.10; {c} perpetual withdrawal = $2,013.51; {d} i = 3.93%

[5] BV = 6400; DD = .1P-800; outlay= P-3000; DCF=1600+.04P; NPV=0; P=16,300.94

[6] Outlay = 787.4-.7MV; DCF=142.80/yr; MV = $210.44

[7] outlay = 1080; DCF_1-10=694; DCF₁₁₊=654; cv=168.53/694=.24; {a} NPV₇ = $2112.56; NPV₁₄ = $3,273.33; {b} NPV₇ = $1,535.54; NPV₁₄ = $3,029.95

>[8] outlay = 200; DCF_1-5=56.4; DCF₅₊=44.4; cv=22.96/56.4=.407; a=.6; {a} NPV₄ = -6.78; NPV₁₂ = $95.13; {b} NPV₄ = 2.21; NPV₁₂ = 67.48

[11] {a} yield = 9.93%/year compounded s.a.; {b} r = 13.71% per year; {c} r = 11.42% per year; {d} NPV = $236.46

[12] (a) i=6.50%/period or EAR=13.42%; (b) P₆= 831.32, r = 7.994%, EAR = 16.63%

[12.5] P = 54.17; conversion value = 67.50, r = 18.84%

[13] P₇ = 220.79; P₁₀ = 266.70; IRR₇ = 18.64%; P₁₅ = 340.38; IRR₁₅ = 14.04%

[14] P_pfd=54.17; P_{3, common stock}=13.46; r₃=18.73%

[15]Break points: Debt $250,000,000; Pf'd Stock $250,000,000; Equity $400,000,000; Component costs: Debt 5.60% and 7.04%; Pf'd Stock 20% and 22.22%; Equity RE 23.67% and Common Stock 28.32%; Weighted marginal costs: (0 - 250) MC₁ = 12.09%; (250 - 400) MC₂ = 13.40% and (400+) MC₃ = 14.33%; Accept projects J-Z-M and raise a total of $350,000,000 at an average cost of 12.46%; NPV_M = 4,357,563; k_M = 12.96% and CF_M = $38,573,624/year

[16] Break points: Debt $20,000,000; Pf'd Stock $70,000,000; Equity $40,000,000 and $70,000,000; Component costs: Debt 6.50% and 7.20% (7.15%); Pf'd Stock 15% and 17%; Equity RE 20% and Common Stock 22.0% and 25.0%; Weighted marginal costs: (0 - 20) MC₁ = 11.4%; (20 - 40) MC₂ = 11.8%,(40-70) MC₃ = 12.6% and (70+) MC₄ = 13.5%; Accept projects B-A-D and raise a total of $50,000,000 at an average cost of 11.8%; NPV_C = -311,820 (-260,297); k_C = 12.78% (12.71%) and CF_M = $8,265,557/year