# Net present value

NPV versus IRR. Here are the cash flows for two mutually exclusive projects:

Project C0 C1 C2 C3

A -$20,000 +$8,000 +$8,000 +$8,000

B -$20,000 0 0 +$25,000

a. At what interest rates would you prefer project A to B?

b. What is the IRR of each project?

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#### Solution Preview

a. At what interest rates would you prefer poject A to B?

Let Payment = 8000

FV = -25000

PV = 0

Number of periods = 3

compute Rate = 4.11%

Then if Rate < 4.11%, the PV of ...

#### Solution Summary

Net present value and other investment criteria are emphasized.

Capital Budgeting Decisions: Net Present Value, IRR

South American Mining

Suppose that a mining operation has spent $8 million developing an ore deposit in South America. Current expectations are that the deposit will require 2 years of development and will result in a realizable cash flow of $10 million at that time. The company engineer has discovered a new way of extracting the ore in only 1 year, but the procedure would necessitate an immediate outlay of $1 million.

Required:

a. Compute the IRR for the new outlay. (Note: There are two solutions! One is 787%. Find the other one.)

b. Based on your answer to (a), use the IRR criterion to determine if the company should make the outlay. Assume the market interest rate is 15% on 1- and 2-year bonds.

Toledo Stadium

The city of Toledo has received a proposal to build a new multipurpose outdoor sports stadium. The expected life of the stadium is 20 years. It will be financed by a 20-year bond paying 8% interest annually. The stadium's primary tenant will be the city's Triple-A baseball team, the Red Hots. The plan's backers anticipate that the site also will be used for rock concerts and college and high school sports. The city does not pay any taxes. The city's cost of capital is 8%. The costs and estimated revenues are presented below.

Required:

a. Should the city build the stadium? (Assume payments are made at the end of the year.)

b. The Red Hots have threatened to move out of Toledo if they do not get a new stadium. The city comptroller estimates that the move will cost the city $350,000 per year for 10 years in lost taxes, parking, and other fees. Should the city build the stadium now? State your reasoning.

PQR Coal Company

The PQR Coal Company has several conventional and strip mining operations. Recently, new legislation has made strip mining, which produces coal of high sulfur content, unprofitable, so those operations will be discontinued. Unfortunately, PQR purchased $1 million of earthmoving equipment for the strip mines 2 years ago and this equipment is not particularly well-suited to conventional mining.

Ms. Big, the president, suggests that since the equipment can be sold for $500,000, it should be scrapped. In her words, "I learned a long time ago that when you make mistakes it's best to admit them and take your lumps. By ignoring sunk costs you aren't tempted to throw good money after bad. The original value of the equipment is gone."

A new employee, Mr. Embeay, has suggested that the equipment should be adapted to the conventional operations. He argues, "We are about to spend $800,000 on some new conventional equipment. However, for a smaller expenditure of $250,000 we can adapt the old equipment to perform the same task. Of course, it will cost about $20,000 per year more to operate over the assumed 10-year lives of each alternative. But at an interest rate of 10%, the inclusion of the present value of $20,000 per year for 10 years and the initial $250,000 is still less than $800,000 for new equipment. While it's true that we should ignore sunk costs, at least this way we can cut our losses somewhat."

Who's correct? Why? What should PQR do? Why?

Electric Generator

A firm that purchases electric power from the local utility is considering the alternative of generating its own electricity. The current cost of obtaining the firm's electricity from its local utility is $42,000 per year. The cost of a steam generator (installed) is $140,000, and annual maintenance and fuel expenses are estimated at $22,000. The generator is expected to last for 10 years, at which time it will be worthless. The cost of capital is 10%, and the firm pays no taxes.

Required:

a. Should the firm install the electric generator? Why or why not?

b. The engineers have calculated that with an additional investment of $40,000, the excess steam from the generator can be used to heat the firm's buildings. The current cost of heating the buildings with purchased steam is $21,000 per year. If the generator is to be used for heat as well as electricity, additional fuel and maintenance costs of $10,000 per year will be incurred. Should the firm invest in the generator and the heating system? Show all calculations.