Purpose of Assignment
The purpose of this assignment is to allow the student to calculate the project cash flow using net present value (NPV), internal rate of return (IRR), and the payback methods.
Resources: Corporate Finance
Create a 350-word memo to management including the following:
Describe the use of internal rate of return (IRR), net present value (NPV), and the payback method in evaluating project cash flows.
Describe the advantages and disadvantages of each method.
Calculate the following time value of money problems:
Calculate the project cash flow generated for Project A and Project B using the NPV method.
Which project would you select, and why?
Which project would you select under the payback method? The discount rate is 10% for both projects.
Sample Template for Project A and Project B:
“Table showing investments and returns for Project A and Project B. Project A has $10,000 initial investment with $5,000 returns in each of the first 3 years. Project B has $55,000 initial investment with $20,000 in each of the first 3 years.”
Show all work.
Submit the memo and all calculations.
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5.1 Why Use Net Present Value?
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This chapter, as well as the next two, focuses on capital budgeting, the decision-making process for accepting or rejecting projects. This chapter develops the basic capital budgeting methods, leaving much of the practical application to subsequent chapters. But we don’t have to develop these methods from scratch. In Chapter 4, we pointed out that a dollar received in the future is worth less than a dollar received today. The reason, of course, is that today’s dollar can be reinvested, yielding a greater amount in the future. And we showed in Chapter 4 that the exact worth of a dollar to be received in the future is its present value. Furthermore, Section 4.1 suggested calculating the net present value of any project. That is, the section suggested calculating the difference between the sum of the present values of the project’s future cash flows and the initial cost of the project.
The net present value (NPV) method is the first one to be considered in this chapter. We begin by reviewing the approach with a simple example. Then, we ask why the method leads to good decisions.
Net Present Value The Alpha Corporation is considering investing in a riskless project costing $100. The project receives $107 in one year and has no other cash flows. The riskless discount rate on comparable riskless investments is 2 percent.
The NPV of the project can easily be calculated as:
From Chapter 4, we know that the project should be accepted because its NPV is positive. This is true because the project generates $107 of future cash flows from a $100 investment whereas comparable investments only generate $102.
The basic investment rule can be generalized to:
Accept a project if the NPV is greater than zero.
Reject a project if the NPV is less than zero.
We refer to this as the NPV rule.
Why does the NPV rule lead to good decisions? Consider the following two strategies available to the managers of Alpha Corporation:
- Use $100 of corporate cash to invest in the project. The $107 will be paid as a dividend in one year.
- Forgo the project and pay the $100 of corporate cash to stockholders as a dividend today.
If Strategy 2 is employed, the stockholder might deposit the cash dividend in a bank for one year. With an interest rate of 2 percent, Strategy 2 would produce cash of $102 (=$100 X 1.02) at the end of the year. The stockholder would prefer Strategy 1 because Strategy 2 produces less than $107 at the end of the year.
Our basic point is:
Accepting positive NPV projects benefits the stockholders.
How do we interpret the exact NPV of $4.90? This is the increase in the value of the firm from the project. For example, imagine that the firm today has productive assets worth $V and has $100 of cash. If the firm forgoes the project, the value of the firm today would simply be:
$V + $100
If the firm accepts the project, the firm will receive $107 in one year but will have no cash today. Thus, the firm’s value today would be:
The difference between these equations is just $4.90, the net present value of Equation 5.1. Thus:
The value of the firm rises by the NPV of the project.
Note that the value of the firm is merely the sum of the values of the different projects, divisions, or other entities within the firm. This property, called value additivity, is quite important. It implies that the contribution of any project to a firm’s value is simply theNPV of the project. As we will see later, alternative methods discussed in this chapter do not generally have this nice property.
The NPV rule uses the correct discount rate.
One detail remains. We assumed that the project was riskless, a rather implausible assumption. Future cash flows of real-world projects are invariably risky. In other words, cash flows can only be estimated, rather than known. Imagine that the managers of Alpha expect the cash flow of the project to be $107 next year. That is, the cash flow could be higher, say $117, or lower, say $97. With this slight change, the project is risky. Suppose the project is about as risky as the stock market as a whole, where the expected return this year is perhaps 10 percent. Then 10 percent becomes the discount rate, implying that the NPV of the project would be:
Because the NPV is negative, the project should be rejected. This makes sense: A stockholder of Alpha receiving a $100 dividend today could invest it in the stock market, expecting a 10 percent return. Why accept a project with the same risk as the market but with an expected return of only 7 percent?
Calculating NPVs with a Spreadsheet
Spreadsheets are commonly used to calculate NPVs. Examining the use of spreadsheets in this context also allows us to issue an important warning. Consider the following:
In our spreadsheet example, notice that we have provided two answers. The first answer is wrong even though we used the spreadsheet’s NPV formula. What happened is that the “NPV” function in our spreadsheet is actually a PV function; unfortunately, one of the original spreadsheet programs many years ago got the definition wrong, and subsequent spreadsheets have copied it! Our second answer shows how to use the formula properly.
The example here illustrates the danger of blindly using calculators or computers without understanding what is going on; we shudder to think of how many capital budgeting decisions in the real world are based on incorrect use of this particular function.