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## 13.3 Net Present Value

PLEASE NOTE: This book is currently in draft form; material is not final.

### Learning Objectives

1. Define and calculate Net Present Value.
2. Apply the accept/reject decision rule of NPV.
3. Explain the limitations of Net Present Value.

Our next capital budgeting method we introduced when we discussed time value of money, and have used it to value stocks and bonds. Discounting all of the cash flows for an investment to the present, adding inflows and subtracting outflows, is called finding the net present value (NPV)Discounting all of the cash flows for an investment to the present, adding inflows and subtracting outflows.. The larger the NPV, the more financial value the project adds to our company; NPV gives us the project amount of value that a project will add to our company. Projects with a positive NPV add value, and should be accepted. Projects with negative NPVs destroy value, and should be rejected. It is generally regarded as the single best criterion for screening projects.

NPV considers the time value of money, because the cash flows are discounted back at the firm’s rate of capital (r). This rate, also called the discount rate or the required return, is the minimum return a firm must earn on a project to have the firm’s market value remain unchanged. If the amount earned on the project exceeds the cost of capital, NPV is positive, so the project adds value and we should do the project.

NPV decision criteria (independent projects):

• If the NPV is greater than zero (NPV > 0) than accept the project
• If the NPV is less than zero (NPV < 0) than reject the project.

If funds are unlimited then we would accept any project with a positive NPV. With mutually exclusive projects, we pick the highest NPV (or the least negative, if we need to pick one and all are below zero). Under capital rationing, we usually want to pick the set of projects with the highest combined NPV that we can afford.

Let’s look at the NPV for the two Gator Lover’s Ice Cream projects. Assume a discount rate of 10%.

Project A

NPV Project A = ($48,000) +$13,636.36 + $12,396.69 +$11,269.72 + $10,245.20 +$9,313.82 = $8,861.80 Also written as: NPV Project A =$13,636.36 + $12,396.69 +$11,269.72 + $10,245.20 +$9,313.82 − $48,000 =$8,861.80

NPV can be calculated by hand, by a financial calculator, or in a spreadsheet. The keystrokes for a financial calculator are as follows:

<CF> <2ND> <CLR WORK> −48000 <ENTER> <DOWN ARROW> 15000 <ENTER> <DOWN ARROW> 5 <ENTER> <NPV> 10 <ENTER> <DOWN ARROW> <CPT>

Note: Excel and other spreadsheet programs are tricky with regard to year 0. The NPV function expects flows to start at year 1. So any cash flows from year 0 need to be added separately.

To solve in a spreadsheet, the corresponding spreadsheet formula is:

=NPV(periodic rate, cash flows from period 1 to n) + net of initial cash flows

Using the numbers for Project A, the spreadsheet function looks like this:

=NPV(.10, 15000, 15000, 15000, 15000, 15000) + (−48000) = 8861.80

Project B

NPV Project B = ($52,000) +$16,363.64 + $16,528.93 +$11,269.72 + $8,196.16 +$6,209.21 = $6,567.66 In this case, Project A has the higher NPV by$2,294.14 ($8,861.80−6,567.66). So we would pick Project A over Project B if they are mutually exclusive. If they are independent, we would accept both projects, since both NPVs are positive. Figure 13.3 Project A NVP Figure 13.4 Project B NVP Net Present Value is the preferred tool by many financial managers, as it properly accounts for the time value of money and the cost of capital. The NPV rule easily handles both mutually exclusive and independent projects. ## Shortfalls of NPV NPV is a little less intuitive than payback period, so it might be more difficult to explain to others who aren’t as well versed in finance. To use NPV requires a discount rate; if we don’t have an accurate guage of the cost of capital, it can be difficult to calculate an NPV. ### Key Takeaways Net Present Value is the most important tool in capital budgeting decision making. It projects the financial value of the project for the company. • Net Present Value is the discounted value of all cash flows. • It is considered to be the best single criterion. • Positive NPV adds value to a company. • Accept any project with positive NPV for independent projects. • Accept the highest NPV project from mutually exclusive projects. ### Exercises 1. Calculate the NPV for the following projects with a discount rate of 12%: Project 1 costs$100,000 and earns $50,000 each year for three years. Project 2 costs$200,000 and earns $150,000 in the first year, and then$75,000 for each of the next two years.

Project 3 costs $25,000 and earns$20,000 each year for three years.

2. If the projects are mutually exclusive, which should we accept?
3. If the projects are independent, which should we accept?