NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA

Basic

3. (LO2) Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 of recapturing the initial investment, so the payback for Project A is:

Payback = 1 + ($21,000 / $25,000) = 1.84 years

Project B has cash flows of:

Cash flows = $14,000 + 17,000 + 24,000 = $55,000

during this first three years. The cash flows are still short by $18,000 of recapturing the initial investment, so the payback for Project B is:

B: Payback = 3 + ($5,000 / $270,000) = 3.02 years

6. (LO4) Our definition of AAR is the average net income divided by the average book value. The average net income for this project is:

Average net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325

And the average book value is:

Average book value = ($15,000,000 + 0) / 2 = $7,500,000

So, the AAR for this project is:

AAR = Average net income / Average book value = $1,836,325 / $7,500,000 = .2448 or 24.48%

10. (LO5) The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:

0 = –$19,500 + $9,800/(1+IRR) + $10,300/(1+IRR)2 + $8,600/(1+IRR)3

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 22.64%

11. (LO1) The NPV of a project is the PV of the outflows minus the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is:

NPV = –$19,500 + 9,800 + 10300 + 8,600 = $9,200

The NPV at a 10 percent required return is:

NPV = –$19,500 + $9,800/1.1 + $10,300/1.12 + $8,600/1.13 = $4382.79

The NPV at a 20 percent required return is:

NPV = –$19,500 + $9,800/1.2 + $10,300/1.22 + $8,600/1.23 = $796.30

And the NPV at a 30 percent required return is:

NPV = –$19,500 + $9,800/1.3 + $10,300/1.32 + $8,600/1.33 = –$ 1,952.44 Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project.

14. (LO5) a. The equation for the NPV of the project is: NPV = –$45,000,000 + $78,000,000/1.12 – $14,000,000/1.122 = $13,482.142.86

The NPV is greater than 0, so we would accept the project.

b. The equation for the IRR of the project is:

0 = –$45,000,000 + $78,000,000/(1+IRR) – $14,000,000/(1+IRR)2

From Descartes rule of signs, we know there are two IRRs since the cash flows change signs twice. From trial and error, the two IRRs are:

IRR = 53%, –79.67%

When there are multiple IRRs, the IRR decision rule is ambiguous. Both IRRs are correct, that is, both interest rates make the NPV of the project equal to zero. If we are evaluating whether or not to accept this project, we would not want to use the IRR to make our decision.

19. (LO6) The MIRR for the project with all three approaches is:…