ANSWER KEY FOR MODULE QUIZZES
LOS 34.d: Calculate and interpret net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, and profitability index (PI) of
CFA® Program Curriculum, Volume 4, page 52
Net Present Value (NPV)
We first examined the calculation of net present value (NPV) in Quantitative Methods.
The NPV is the sum of the present values of all the expected incremental cash flows if a project is undertaken. The discount rate used is the firm’s cost of capital, adjusted for the risk level of the project. For a normal project, with an initial cash outflow followed by a series of expected after-tax cash inflows, the NPV is the present value of the expected inflows minus the initial cost of the project.
where:
CF0 = initial investment outlay (a negative cash flow) CFt = after-tax cash flow at time t
k = required rate of return for project
A positive NPV project is expected to increase shareholder wealth, a negative NPV project is expected to decrease shareholder wealth, and a zero NPV project has no expected effect on shareholder wealth.
For independent projects, the NPV decision rule is simply to accept any project with a positive NPV and to reject any project with a negative NPV.
EXAMPLE: Net present value
Using the project cash flows presented in Table 1, compute the NPV of the project and determine whether it should be accepted or rejected. Assume that the cost of capital is 9%.
Table 1: Expected Net After-Tax Cash Flows
Year Cash Flow
0 –$100
1 25
2 50
3 75
Answer:
The project has a positive NPV, so it should be accepted.
You may calculate NPV directly by using the cash flow (CF) keys on your calculator. The process is illustrated in Table 2 and Table 3.
Table 2: Calculating NPV With the TI Business Analyst II Plus
Keystrokes Explanation Display
[CF] [2nd] [CLR WORK] Clear memory registers CF0 = 0.0000 100 [+/–] [ENTER] Initial cash outlay CF0 = –100.0000
[↓] 25 [ENTER] Period 1 cash flow C01 = 25.0000 [↓] Frequency of cash flow 1 F01 = 1.0000
[↓] 50 [ENTER] Period 2 cash flow C02 = 50.0000 [↓] Frequency of cash flow 2 F02 = 1.0000 [↓] 75 [ENTER] Period 3 cash flow C03 = 75.0000
[↓] Frequency of cash flow 3 F03 = 1.0000 [NPV] 9 [ENTER] 9% discount rate I = 9.0000
[↓] [CPT] Calculate NPV NPV = 22.9335
Table 3: Calculating NPV With the HP 12C
Keystrokes Explanation Display
[f] [FIN] [f] [REG] Clear memory registers 0.0000 100 [CHS] [g] [CF0] Initial cash outlay –100.0000
25 [g] [CFj] Period 1 cash flow 25.0000 50 [g] [CFj] Period 2 cash flow 50.0000 75 [g] [CFj] Period 3 cash flow 75.0000 9 [i] 9% discount rate 9.0000 [f] [NPV] Calculate NPV 22.9335
Internal Rate of Return (IRR)
For a normal project, the internal rate of return (IRR) is the discount rate that makes the present value of the expected incremental after-tax cash inflows just equal to the initial cost of the project. More generally, the IRR is the discount rate that makes the present values of a project’s estimated cash inflows equal to the present value of the project’s estimated cash outflows. That is, IRR is the discount rate that makes the following relationship hold:
PV (inflows) = PV (outflows)
The IRR is also the discount rate for which the NPV of a project is equal to zero:
To calculate the IRR, you may use the trial-and-error method. That is, just keep guessing IRRs until you get the right one, or you may use a financial calculator.
IRR decision rule: First, determine the required rate of return for a given project. This is usually the firm’s cost of capital. Note that the required rate of return may be higher or lower than the firm’s cost of capital to adjust for differences between project risk and the firm’s average project risk.
If IRR > the required rate of return, accept the project.
If IRR < the required rate of return, reject the project.
EXAMPLE: Internal rate of return
Continuing with the cash flows presented in Table 1 for the previous example, compute the IRR of the project and determine whether it should be accepted or rejected. Assume that the required rate of return is 9%.
Answer:
The cash flows should be entered as in Table 2 or Table 3 (if you haven’t changed or cleared them, they are still there from the calculation of NPV).
With the TI calculator, the IRR can be calculated with:
[IRR] [CPT] to get 19.4377%.
With the HP 12C, the IRR can be calculated with:
[f] [IRR].
The project should be accepted because its IRR is greater than the 9% required rate of return.
MODULE QUIZ 34.1
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1. The post-audit is used to:
A. improve cash flow forecasts and stimulate management to improve operations and bring results into line with forecasts.
B. improve cash flow forecasts and eliminate potentially profitable but risky projects.
C. stimulate management to improve operations, bring results into line with forecasts, and eliminate potentially profitable but risky projects.
2. Which of the following statements concerning the principles underlying the capital budgeting process is most accurate?
A. Cash flows should be based on opportunity costs.
B. Financing costs should be reflected in a project’s incremental cash flows.
C. The net income for a project is essential for making a correct capital budgeting decision.
Use the following data for Questions 3 and 4.
An analyst has gathered the following data about two projects, each with a 12%
required rate of return.
Project Y Project Z Initial cost $15,000 $20,000
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Life 5 years 4 years
Cash inflows $5,000/year $7,500/year
3. If the projects are independent, the company should:
A. accept Project Y and reject Project Z.
B. reject Project Y and accept Project Z.
C. accept both projects.
4. If the projects are mutually exclusive, the company should:
A. reject both projects.
B. accept Project Y and reject Project Z.
C. reject Project Y and accept Project Z.
5. Which of the following statements about NPV and IRR is least accurate?
A. The IRR can be positive even if the NPV is negative.
B. When the IRR is equal to the cost of capital, the NPV will be zero.
C. The NPV will be positive if the IRR is less than the cost of capital.
Use the following data to answer Questions 6 and 7.
A company is considering the purchase of a copier that costs $5,000. Assume a required rate of return of 10% and the following cash flow schedule:
Year 1: $3,000.
Year 2: $2,000.
Year 3: $2,000.
6. What is the project’s NPV?
A. –$309.
B. +$883.
C. +$1,523.
7. The project’s IRR is closest to:
A. 10%.
B. 15%.
C. 20%.