## Describe how the IRR is calculated, and describe the information this measure provides about a sequence of cash flows. What is the IRR criterion decision rule?

1. Payback Period and Net Present Value [LO1, 2] If a project with conventional cash flows has a payback period less than the project’s life, can you definitively state the algebraic sign of the NPV? Why or why not? If you know that the discounted payback period is less than the project’s life, what can you say about the NPV? Explain.

Internal Rate of Return [LO5] Concerning IRR:

1. Describe how the IRR is calculated, and describe the information this measure provides about a sequence of cash flows. What is the IRR criterion decision rule?
2. What is the relationship between IRR and NPV? Are there any situations in which you might prefer one method over the other? Explain.
3. Despite its shortcomings in some situations, why do most financial managers use IRR along with NPV when evaluating projects? Can you think of a situation in which IRR might be a more appropriate measure to use than NPV? Explain.
4. Net Present Value [LO1] It is sometimes stated that “the net present value approach assumes reinvestment of the intermediate cash flows at the required return.” Is this claim correct? To answer, suppose you calculate the NPV of a project in the usual way. Next, suppose you do the following:
5. Calculate the future value (as of the end of the project) of all the cash flows other than the initial outlay assuming they are reinvested at the required return, producing a single future value figure for the project.
6. Calculate the NPV of the project using the single future value calculated in the previous step and the initial outlay. It is easy to verify that you will get the same NPV as in your original calculation only if you use the required return as the reinvestment rate in the previous step.

1. Comparing Investment Criteria Consider the following two mutually exclusive projects:

Year         Cash Flow (A)     Cash Flow (B)

If you apply the payback criterion, which investment will you choose? Why?

1. If you apply the discounted payback criterion, which investment will you choose? Why?
2. If you apply the NPV criterion, which investment will you choose? Why?
3. If you apply the IRR criterion, which investment will you choose? Why?
4. If you apply the profitability index criterion, which investment will you choose? Why?

1. Equivalent Annual Cost [LO4]
2. When is EAC analysis appropriate for comparing two or more projects?
3. Why is this method used?

3 .Are there any implicit assumptions required by this method that you find troubling? Explain.

1. Cash Flow and Depreciation [LO1] “When evaluating projects, we’re concerned with only the relevant incremental after tax cash flows. Therefore, because depreciation is a noncash expense, we should ignore its effects when evaluating projects.” Critically evaluate this statement.

QUESTION AND PROBLEMS

1. Relevant Cash Flows [LO1] Parker & Stone, Inc., is looking at setting up a new manufacturing plant in South Park to produce garden tools. The company bought some land six years ago for \$5 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent these facilities from a competitor instead. If the land were sold today, the company would net \$5.3 million. The company wants to build its new manufacturing plant on this land; the plant will cost \$12.5 million to build, and the site requires \$770,000 worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project? Why?

1. Relevant Cash Flows [LO1] Winnebagel Corp. currently sells 30,000 motor homes per year at \$68,000 each and 12,000 luxury motor coaches per year at \$105,000 each. The company wants to introduce a new portable camper to fill out its product line; it hopes to sell 25,000 of these campers per year at \$14,000 each. An independent consultant has determined that if Winnebagel introduces the new campers, it should boost the sales of its existing motor homes by 2,400 units per year and reduce the sales of its motor coaches by 1,100 units per year. What is the amount to use as the annual sales figure when evaluating this project? Why?
2. Calculating OCF [LO1] Consider the following income statement:

Fill in the missing numbers and then calculate the OCF. What is the depreciation tax shield?

1. Calculating Project OCF [LO1] Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of \$2.7 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate \$2,080,000 in annual sales, with costs of \$775,000. If the tax rate is 35 percent, what is the OCF for this project?

1. Break-Even LO3] Assume a firm is considering a new project that requires an initial investment and has equal sales and costs over its life. Will the project reach the accounting, cash, or financial break-even point first? Which will it reach next? Last? Will this ordering always apply?

1. Capital Rationing [LO5] Going all the way back to Chapter 1, recall that we saw that partnerships and proprietorships can face difficulties when it comes to raising capital. In the context of this chapter, the implication is that small businesses will generally face what problem?

1. Calculating Costs and Break-Even [LO3] Night Shades, Inc. (NSI), manufactures biotech sunglasses. The variable materials cost is \$10.48 per unit, and the variable labor cost is \$6.89 per unit.
2. What is the variable cost per unit?
3. Suppose NSI incurs fixed costs of \$870,000 during a year in which total production is 280,000 units. What are the total costs for the year?
4. If the selling price is \$49.99 per unit, does NSI break even on a cash basis? If depreciation is \$490,000 per year, what is the accounting break-even point?

1. Computing Average Cost [LO3] K-Too Everwear Corporation can manufacture mountain climbing shoes for \$31.85 per pair in variable raw material costs and \$22.80 per pair in variable labor expense. The shoes sell for \$145 per pair. Last year, production was 120,000 pairs. Fixed costs were \$1,750,000. What were total production costs? What is the marginal cost per pair? What is the average cost? If the company is considering a one-time order for an extra 5,000 pairs, what is the minimum acceptable total revenue from the order? Explain.

1. Scenario Analysis [LO2] Olin Transmissions, Inc., has the following estimates for its new gear assembly project: price = \$1,400 per unit; variable costs = \$220 per unit; fixed costs = \$3.9 million; quantity = 85,000 units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?

It will frequently turn out that the crucial variable for a project is sales volume. If we are thinking of creating a new product or entering a new market, for example, the hardest thing to forecast accurately is how much we can sell. For this reason, sales volume is usually analyzed more closely than other variables.

Break-even analysis is a popular and commonly used tool for analyzing the relationship between sales volume and profitability. There are a variety of different break-even measures, and we have already seen several types. For example, we discussed (in Chapter 9) how the payback period can be interpreted as the length of time until a project breaks even, ignoring time value.

All break-even measures have a similar goal. Loosely speaking, we will always be asking, “How bad do sales have to get before we actually begin to lose money?” Implicitly, we will also be asking, “Is it likely that things will get that bad?” To get started on this subject, we first discuss fixed and variable costs.

[LO3] FIXED AND VARIABLE COSTS

In discussing break-even, the difference between fixed and variable costs becomes very important. As a result, we need to be a little more explicit about the difference than we have been so far.

Variable Costs By definition, variable costs change as the quantity of output changes, and they are zero when production is zero. For example, direct labor costs and raw material costs are usually considered variable. This makes sense because if we shut down operations tomorrow, there will be no future costs for labor or raw materials.

variable costs
Costs that change when the quantity of output changes.

We will assume that variable costs are a constant amount per unit of output. This simply means that total variable cost is equal to the cost per unit multiplied by the number of units. In other words, the relationship between total variable cost (VC), cost per unit of output (v), and total quantity of output (Q) can be written simply as:

1. Calculating Break-Even [LO3] In each of the following cases, calculate the accounting break-even and the cash break-even points. Ignore any tax effects in calculating the cash break-even.