Solutions to Tutorial week 2:
CQ5.4; QP5.12; QP5.16; QP6.10; QP6.14; QP6.18 Note: You might see small differences for some solutions, it is because I’m using excel spread sheet and PVIFA formula to do the calculations. And you may have a little bit different answers when you used calculator.
A project has perpetual cash flows of C per period, a cost of I, and a required return of R. What is the relationship between the project’s payback and its IRR? What implications does your answer have for long- lived projects with relatively constant cash flow?
For a project with future cash flows that are an annuity:
Payback = I / C
And the IRR is:
0 = – I + C / IRR
Solving the IRR equation for IRR, we get:
IRR = C / I
Notice this is just the reciprocal of the payback. So:
IRR = 1 / PB For long-lived projects with relatively constant cash flows, the sooner the project pays back, the greater is the IRR, and the IRR is approximately equal to the reciprocal of the payback period.
Problems with profitability index. The Robb Computer Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (I) Cash Flow (II)
0 -$30,000 -$12,000 1 18,000 7,500 2 18,000 7,500 3 18,000 7,500
a. If the required return is 10 percent and Robb Computer applies the profitability index decision rule, which project should the firm accept?
b. If the company applies the NPV decision rule, which project should it take?
c. Explain why our answer in (a) and (b) are different?
a. The profitability index is the PV of the future cash flows divided by the initial investment. The cash flows for both projects are an annuity, so:
PII = $18,000(PVIFA10%,3 ) / $30,000 = 1.493
PIII = $7,500(PVIFA10%,3 ) / $12,000 = 1.555
The profitability index decision rule implies that we accept project II, since PIII is greater than the PII.
b. The NPV of each project is:
NPVI = – $30,000 + $18,000(PVIFA10%,3 ) = $14,777.16
NPVII = – $12,000 + $7,500(PVIFA10%,3 ) = $6,657.15
The NPV decision rule implies accepting Project I, since the NPVIis greater than the NPVII.
c. Using the profitability index to compare mutually exclusive projects can be ambiguous when the magnitudes of the cash flows for the two projects are of different scales. In this problem, project I is roughly 3 times as large as project II and produces a larger NPV, yet the profit-ability index criterion implies that project II is more acceptable.
Comparing investment criteria. Consider the following cash flows if two mutually exclusive projects for AZ-Motorcars. Assume the discount rate for AZ-Motorcars is 10 percent.
Year AZM Mini-SUV AZF Full-SUV
0 -$450,000 -$800,000
1 320,000 350,000
2 180,000 420,000
3 150,000 290,000
a. Based on the payback period, which project should be accepted?
b. Based on the NPV, which project should be accepted?
c. Based on the IRR, which project should be accepted?
d. Based on this analysis, is incremental IRR analysis necessary? If yes, please conduct the analysis.
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