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# Price of a six-year \$1000 face-value bond

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1 Calculate the NPV and the IRR for the following project and state whether or not you would accept the new project.

Required rate of return = 9%
Current prime rate = 11%
Initial outflow = \$75,000
Inflows = \$25,000 for years 1-3
= (\$10,000) for year 4
= \$30,000 for year 5
= \$10,000 for year 6

2 Calculate the payback period for the following investment: A machine costs \$100,000 with installation costs of \$15,000.
Cash inflows are expected to be 26,000 per year for the next seven years.

3. Given the following information, calculate the net present value:
Initial outlay is \$50,000; required rate of return is 10%; current prime rate is 12%; and cash inflows for the next 4 years are \$60,000, \$30,000, \$40,000, and \$50,000.

4 Calculate the IRR for the following investment project: Initial investment is \$75,000; inflows are \$20,000 for the next five years; Required rate of return is 15%. (Round your answer to the nearest whole percentage).

5 Calculate the price of a six-year \$1000 face-value bond with a 7% annual coupon rate and a yield-to-maturity of 6% with semi-annual coupon payments.

6 All but which of the following would affect dividend policy?

a. a firm's need for funds
b. prospectus restrictions
c. stockholders' expectations
contractual restrictions

#### Solution Preview

1 Calculate the NPV and the IRR for the following project and state whether or not you would accept the new project.

Required rate of return = 9%
Current prime rate = 11%
Initial outflow = \$75,000
Inflows = \$25,000 for years 1-3
= (\$10,000) for year 4
...

#### Solution Summary

This provides the steps to calculate the price of a six-year \$1000 face-value bond

\$2.19

## Finance: Capital Structure and Ratios

1. Last year Wei Guan Inc. had \$350 million of sales, and it had \$270 million of fixed assets that were used at 65% of capacity. In millions, by how much could Wei Guan's sales increase before it is required to increase its fixed assets? 188.5 million

2. Europa Corporation is financing an ongoing construction project. The firm will need \$5,000,000 of new capital during each of the next 3 years. The firm has a choice of issuing new debt or equity each year as the funds are needed, or issue only debt now and equity later. Its target capital structure is 40% debt and 60% equity, and it wants to be at that structure in 3 years, when the project has been completed. Debt flotation costs for a single debt issue would be 1.6% of the gross debt proceeds. Yearly flotation costs for 3 separate issues of debt would be 3.0% of the gross amount. Ignoring time value effects, how much would the firm save by raising all of the debt now, in a single issue, rather than in 3 separate issues?

3. Warren Corporation's stock sells for \$42 per share. The company wants to sell some 20-year, annual interest, \$1,000 par value bonds. Each bond would have 75 warrants attached to it, each exercisable into one share of stock at an exercise price of \$47. The firm's straight bonds yield 10%. Each warrant is expected to have a market value of \$2.00 given that the stock sells for \$42. What coupon interest rate must the company set on the bonds in order to sell the bonds-with-warrants at par?

4. Nebraska Pharmaceuticals Company (NPC) is considering a project that has an up-front cost at t = 0 of \$1,500. (All dollars in this problem are in thousands). The project's subsequent cash flows are critically dependent on whether a competitor's product is approved by the Food and Drug Administration. If the FDA rejects the competitive product, NPC's product will have high sales and cash flows, but if the competitive product is approved, that will negatively impact NPC. There is a 75% chance that the competitive product will be rejected, in which case NPC's expected cash flows will be \$500 at the end of each of the next seven years (t = 1 to 7). There is a 25% chance that the competitor's product will be approved, in which case the expected cash flows will be only \$25 at the end of each of the next seven years (t = 1 to 7). NPC will know for sure one year from today whether the competitor's product has been approved.

NPC is considering whether to make the investment today or to wait a year to find out about the FDA's decision. If it waits a year, the project's up-front cost at t = 1 will remain at \$1,500, the subsequent cash flows will remain at \$500 per year if the competitor's product is rejected and \$25 per year if the alternative product is approved. However, if NPC decides to wait, the subsequent cash flows will be received only for six years (t = 2 ... 7).

Assuming that all cash flows are discounted at 10%, if NPC chooses to wait a year before proceeding, how much will this increase or decrease the project's expected NPV in today's dollars (i.e., at t = 0), relative to the NPV if it proceeds today?

5. Komishito has 100,000 bonds and 5,000,000 shares outstanding. The bonds have a 9% annual coupon (paid semi-annually), \$1,000 face value, \$1,100 market value and 10 year maturity. The beta on the stock is 1.20 and its price per share is \$50. The risk-less return is 6%, the expected market return is 14% and the corporate tax rate is 40%.
a. What is the after-tax cost of debt financing?
b. What is the after-tax cost of equity financing?
c. What is the WACC?

6. Stockholders are surprised to learn that the firm has invested \$43 million in a project that has an expected payoff of \$8 million per year for six years. The project's cost of capital is 12%.
a. What is the project's NPV?
b. There are 3 million shares outstanding. What should be the direct impact of this investment on the per-share value of the common stock?

7. The Canton Sundae Corporation is considering the replacement of an existing machine. The new machine would provide better sundaes, but it costs \$120,000. The X-tender requires \$20,000 in setup costs that are expensed immediately and \$20,000 in additional working capital. The X-tender's useful life is 10 years, after which it can be sold for a salvage value of \$40,000. Canton uses straight-line depreciation, and the machine will be depreciated to a book value of \$0 on a six-year basis Canton has a tax rate of 45% and a 16% cost of capital on projects like this one. The X-tender is expected to increase revenues minus expenses by \$35,000 per year. What is the NPV of buying the X-tender?

N = 10 || i = 16% || Tax rate = 45% || SV year 10 = 40,000
P = - 120,000 - 20,000 - 20,000 = - 160,000
Depreciation = (120,000-40,000)/6 = 13,333.33
Yearly flow Years 1 to 6:
A1-6 = 35,000 - (35,000-13,333.33)*45% = 25,250
Yearly flow Years 7 to 10:
A1-6 = 35,000 - (35,000)*45% = 19,250
NPV = - 160,000 + 25,250*(P/A,i=16%,N=6) + 19,250*(P/A,i=16%,N=4) + 40,000*(P/F,i=16%,N=10)
NPV = - 160,000 + 25,250*(3.6847) + 19,250*(2.7982) + 40,000*(0.2267)
NPV = -4,027.98

8. Suppose a firm is unleveraged and has an unleveraged required return, r = 15%. The firm borrows 30% of the value of the firm at r(d) = 8%. Because of the financial leverage, r(e) becomes 18%. What is the firm's WACC:
a. Assuming the firm is operating in a perfect capital market (including no taxes)?
b. Assuming there are only corporate taxes at a rate of 35% in an otherwise perfect capital market?

9. A common stockholder owns 30% of a firm's 1 million outstanding shares. The firm plans to sell 200,000 new shares.
a. By how much is the stockholder's percentage ownership diluted if the firms sells all the shares to new investors?
b. How should the stockholder maintain her 30% ownership interest?

10. Neighborhood Savings Bank is considering leasing \$100,000 worth of computer equipment. A 4 year lease would require payments in advance of \$22,000 per year. The bank does not currently pay income taxes and does not expect to have to pay income taxes in the foreseeable future. If the bank purchased the computer equipment, it would depreciate the equipment on a straight-line basis down to an estimated salvage value of \$20,000 at the end of the 4th year. The bank's cost of secured debt is 14%, and its cost of capital is 20%. Calculate the net advantage to leasing. \$24,056.72.

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