Business Investment Rules

Capital Budgeting Rules Part 1 (Overview) , Capital Budgeting Rules Part 2 (NPV versus IRR), and Capital Budgeting Rules Part 3 (Minor Methods).

Below are audio solutions to problems of the type you will see from this chapter.

a. Audio Solution to: Determine the net present value for a project that costs $104,000 and would yield after-tax cash flows of $16,000 the first year, $18,000 the second year, $21,000 the third year, $23,000 the fourth year, $27,000 the fifth year, and $33,000 the sixth year. Your firm's cost of capital is 12.00%.

b. Audio Solution to: Determine the net present value for a project that costs $253,494.00 and is expected to yield after-tax cash flows of $29,000 per year for the first ten years, $37,000 per year for the next ten years, and $50,000 per year for the following ten years. Your firm's cost of capital is 12.00%.

c. Audio Solution to: Determine the internal rate of return for a project that costs $78,000 and would yield after-tax cash flows of $12,000 the first year, $14,000 the second year, $17,000 the third year, $19,000 the fourth year, $23,000 the fifth year, and $29,000 the sixth year.

d. Audio Solution to: Determine the internal rate of return for a project that costs $180,532.00 and is expected to yield after-tax cash flows of $25,000 per year for the first five years, $33,000 per year for the next five years, and $46,000 per year for the following five years.

e. Audio Solution to: Your company has an opportunity to invest in a project that is expected to result in after-tax cash flows of $18,000 the first year, $20,000 the second year, $23,000 the third year, -$8,000 the fourth year, $30,000 the fifth year, $36,000 the sixth year, $39,000 the seventh year, and -$6,000 the eighth year. The project would cost the firm $142,000. If the firm's cost of capital is 12%, what is the modified internal rate of return for the project?

f. Audio Solution to: Your company has an opportunity to invest in a project that is expected to result in after-tax cash flows of $8,000 the first year, $10,000 the second year, $13,000 the third year, -$8,000 the fourth year, $20,000 the fifth year, and $26,000 the sixth year. The project would cost the firm $59,000. If the firm's cost of capital is 13%, what is the modified internal rate of return for the project?

g. Audio Solution to: Determine the payback period (in years) for a project that costs $120,000 and would yield after-tax cash flows of $20,000 the first year, $22,000 the second year, $25,000 the third year, $27,000 the fourth year, $31,000 the fifth year, and $37,000 the sixth year.

Capital Budgeting Cash Flows

A useful handout on recognizing relevant cash flows., the Initial Cash Flows, Operating Cash Flows the Terminal Cash Flows and Inflation's Impact on Capital Budgeting and Project Risk Analysis (Video).

Here are audio solutions related to the estimation of cash flows.

Use the following information to answer questions a-e. You have been asked by the president of your company to evaluate the proposed acquisition of new equipment. The equipment’s basic price is $177,000, and shipping costs will be $3,500. It will cost another $26,600 to modify it for special use by your firm, and an additional $12,400 to install the equipment. The equipment falls in the MACRS 3-year class, and it will be sold after three years for $22,000. The equipment is expected to generate revenues of $173,000 per year with annual operating costs of $81,000. The firm’s tax rate is 30.0%.  Here is the MACRS depreciation schedule, Year 1=33%, Year 2=45%, Year 3=15%, Year 4= 7%.

a.What is the net investment (initial outlay) for the project?

b.What is the operating cash flow for year 1?

c.What is the operating cash flow for year 2?

d.What is the operating cash flow for year 3?

e.What is the value of the terminal year non-operating cash flows at the end of Year 3? (What is the after-tax cash flow associated with the sale of the equipment?)

Use the following information to answer questions f-j. You have been asked by the president of your company to evaluate the proposed acquisition of new equipment. The equipment’s basic price is $195,000, and shipping costs will be $3,900. It will cost another $23,400 to modify it for special use by your firm, and an additional $9,800 to install the equipment. The equipment falls in the MACRS 3-year class, and it will be sold after three years for $30,200. The equipment is expected to generate revenues of $179,000 per year with annual operating costs of $90,000. The firm’s tax rate is 25.0%.Here is the MACRS depreciation schedule, Year 1=33%, Year 2=45%, Year 3=15%, Year 4= 7%.

f. What is the net investment (initial outlay) for the project?

g. What is the operating cash flow for year 1?

h. What is the operating cash flow for year 2?

i. What is the operating cash flow for year 3?

j. What is the value of the terminal year non-operating cash flows at the end of Year 3? (What is the after-tax cash flow associated with the sale of the equipment?)

k.The Target Copy Company is contemplating the replacement of its old printing machine with a new model costing $67,000. The old machine, which originally cost $31,000, has 9 years of expected life remaining and a current book value of $13,000 versus a current market value of $19,000. Target's corporate tax rate is 32 percent. If Target sells the old machine at market value, what is the initial after-tax outlay for the new printing machine? Since this is a cash outlay, be sure to use the - sign when writing your answer. Do not use the $ symbol or , in your answer. Show your answer to the nearest dollar.

l. Your company plans to produce a product for two more years and then to shut down production. You are considering replacing an old machine used in production with a new machine. The Old machine originally cost $818 and was bought Three (3) years ago (i.e. it has depreciated for three years). It could be sold today for $367 or sold in two years for $121. The New machine would cost $703 and could be sold in two years for $231. The new machine is more efficient than the old machine and would reduce waste, and therefore the cost of materials, by $300 per year. Due to the lower waste, we could also have a one-time reduction in inventory of 21. The firm's tax rate is 43%. Both machines are in the 4 year MACRS class, with depreciation amounts of 15%, 45%, 33% and 7%. What are the Operating Cash Flows in the first year (Year 1) with the new machine?

Financial and Real Options

A useful handout on Options and Real Options.

Here are links to video discussions of the topics in this chapter:

a. Option Basics.

b. Solving for the value of a call option using the one-period Binomial problem. The current price of a stock is $22.  In one year, the price will be either $27 or $17.  The annual risk-free rate is 6 percent.  What is the price of a call option on the stock that has an exercise price of $22 and that expires in one year, rounded to the nearest dollar? [Hint: use daily compounding.

c. Valuing an Abandonment Option as a difference in NPVs. •You are considering a project that costs $1050. If the product is a success (probability of success = 0.5), cash flows will be $200 per year in perpetuity. If it is a failure, the cash flows will be $0 per year in perpetuity. Assume a discount rate of 10%. Round all answers to the nearest dollar. •1. What is the expected NPV of the project? 2. At the end of the first year, you will learn more about the economic viability of the project. If the project is a failure, the firm will sell off its assets for a scrap value of $500. What is the NPV of the project given the additional information? 3. What is the value to the company of the abandonment option?

Here are audio solutions to problems that are covered in this chapter;

a.Suppose you believe that Du Pont's stock price is going to decline from its current level of $84.39 sometime during the next 5 months. For $396.18 you could buy a 5-month put option giving you the right to sell 100 shares at a price of $82 per share. If you bought a 100-share contract for $396.18and Du Pont's stock price actually changed to $86.79, your net profit (or loss) after exercising the option would be ______? Show your answer to the nearest .01. Do not use $ or , signs in your answer. Use a - sign if you lose money on the contract.

b.Suppose you believe that Du Pont's stock price is going to decline from its current level of $84.46 sometime during the next 5 months. For $517.89 you could buy a 5-month put option giving you the right to sell 100 shares at a price of $85 per share. If you bought a 100-share contract for $517.89and Du Pont's stock price actually changed to $75.30, your net profit (or loss) after exercising the option would be ______? Show your answer to the nearest .01. Do not use $ or , signs in your answer. Use a - sign if you lose money on the contract.

c.Suppose you believe that Bennett Environmental's stock price is going to increase from its current level of $31.09 sometime during the next 7 months. For $535.00 you could buy a 7-month call option giving you the right to buy 100 shares at a price of $28 per share. If you bought a 100-share contract for $535.00and Bennett's stock price actually changed to $32.62, your net profit (or loss) after exercising the option would be ______? Show your answer to the nearest .01. Do not use $ or , signs in your answer. Use a - sign if you lose money on the contract.

d. The current price of a stock is $62.60 and the annual effective risk-free rate is 3.8 percent. A call option with an exercise price of $55 and one year until expiration has a current value of $13.23. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Show your answer to the nearest .01. Do not use $ or , in your answer. Because of the limitations of WEBCT random numbers, some of the options may be trading below their intrinsic value. Hint, to find the present value of the bond, you do not need to make the e x adjustment, simple discount at the risk free rate.

e. The current price of a stock is $54.98 and the annual risk-free rate is 4.3 percent. A put option with an exercise price of $55 and one year until expiration has a current value of $3.61. What is the value of a call option written on the stock with the same exercise price and expiration date as the put option? Show your answer to the nearest .01. Do not use $ or , in your answer. Because of the limitations of WEBCT random numbers, some of the options may be trading below their intrinsic value. Note, the given interest rate is an effective rate, so for calculation purposes, you need only discount the using the risk free rate, no e x adjustment is needed.