Your company Portfolio Manager is convening a review board in the first calendar
ID: 2778724 • Letter: Y
Question
Your company Portfolio Manager is convening a review board in the first calendar quarter to consider three projects. You have been asked to provide recommendations with respect to the capital budgeting aspects of these projects. Your recommendations will be considered by the review board along with other non-financial aspects of the projects. Initial (year 0) funding will be provided in the current year for the single project selected.
Project sponsors have provided the following estimated cash flow projections:
Project A
Project B
C
Year
Outflow
Inflow
Netflow
Outflow
Inflow
Netflow
Outflow
Inflow
Netflow
0
15000
-150000
15000
-150000
20000
-200000
1
20000
20000
130000
40000
-9000
150000
-150000
2
30000
30000
50000
50000
90000
90000
3
40000
40000
60000
60000
100000
100000
4
40000
40000
90000
90000
110000
110000
5
50000
50000
90000
90000
120000
120000
The company has not yet decided how the selected project will be financed. The cost of capital or hurdle rate will vary depending upon how the company decides to finance the project. You decide to compare projects in three areas: (1) payback period (not considering the cost of capital); NPV sensitivity (see note 1 below); and (3) Internal Rate of Return (IRR). Conduct each analysis and interpret the results.
Based on your analysis, which project would you recommend and why? Your recommendation must be based on the combination of all three factors.
Show all calculations supporting your recommendation. Calculate NPV to the nearest dollar, IRR to three decimal places, and payback period to one decimal place.
Note 1: Project NPV varies inversely with the cost of funds to perform the project (expressed as the hurdle rate or k in the NPV discount factor formula). Some project NPVs are more sensitive to changes in k than others. See the NPV Profile discussion in Gallagher, Chapter 10, pages 278-279 (Reserved Readings) for information on determining NPV sensitivity.
NPV Calculations
The NPV Profile The k value is the cost of funds used for the project. It is the discount rate used in the NPV calculation because the cost of funds for a given project is that project’s required rate of return. The relationship between the NPV of a project and k is inverse—the higher the k, the lower the NPV, and the lower the k, the higher the NPV.3 Because a project’s NPV varies inversely with k, financial managers need to know how much the value of NPV will change in response to a change in k. If k is incorrectly specified, what appears to be a positive NPV could in fact be a negative NPV and vice versa—a negative NPV could turn out to be positive. Mutually exclusive project rankings could also change if an incorrect k value is used in the NPV computations.4 To see how sensitive a project’s NPV value is to changes in k, analysts often create an NPV profile. The NPV profile is a graph that shows how a project’s NPV changes when different discount rate values are used in the NPV computation. Building an NPV profile is straightforward. First, the NPV of the project is calculated at a number of different discount rates. Then the results are plotted on the graph, with k values on one axis and the resulting NPV values on the other. If more than one project is included on the graph, the process is repeated for each project until all are depicted. To illustrate, we will build an NPV profile of Projects X and Y. We will plot Project X and then Project Y on the graph. To begin, we first calculate the NPV of Project X with a number of different discount rates. The different k values may be chosen arbitrarily. For our purposes, let’s use 0 percent, 5 percent, 10 percent, 15 percent, and 20 percent. The results of Project X’s NPV calculations follow: Discount Rate Project X NPV 0% $500.00 5% $ 57.77 10% –$326.82 15% –$663.68 20% –$960.65 Now Project X’s NPV values may be plotted on the NPV profile graph. Figure 10-1 shows the results. When the data points are connected in Figure 10-1, we see how the NPV of Project X varies with the discount rate changes. The graph shows that with a k of about 5.7 percent, the value of the project’s NPV is zero. At that discount rate, then, Project X would provide the firm’s required rate of return, no more and no less. Next, we add project Y to the NPV profile graph. We calculate the NPV of Project Y at a number of different discount rates, 0 percent, 5 percent, 10 percent, 15 percent, and 20 percent. The results follow:
Project A
Project B
C
Year
Outflow
Inflow
Netflow
Outflow
Inflow
Netflow
Outflow
Inflow
Netflow
0
15000
-150000
15000
-150000
20000
-200000
1
20000
20000
130000
40000
-9000
150000
-150000
2
30000
30000
50000
50000
90000
90000
3
40000
40000
60000
60000
100000
100000
4
40000
40000
90000
90000
110000
110000
5
50000
50000
90000
90000
120000
120000
Explanation / Answer
Project A Year 0 1 2 3 4 5 Cashflow -150000 20000 30000 40000 40000 50000 Discount 0% NPV 30000 IRR 6% Payback 5 -150000 20000 30000 40000 40000 50000 Discount 5% NPV 2896.415 IRR 1% Payback 5 -150000 19047.619 27210.88 34553.5 32908.099 39176.31 Discount 10% NPV -18605.6 IRR -4% Payback >5 -150000 18181.8182 24793.39 30052.59 27320.5382 31046.07 Discount 15% NPV -51849.2 IRR -13% Payback >5 -150000 16563.147 20575.34 22719.49 18815.3124 19477.55 Discount 20% NPV -74587.2 IRR -20% Payback >5 -150000 15151.5152 17217.63 17391.55 13175.4139 12476.72 Project B Year 0 1 2 3 4 5 Cashflow -150000 -9000 50000 60000 90000 90000 Discount 0% NPV 131000 IRR 18% Payback 3.5 -150000 -9000 50000 60000 90000 90000 Discount 5% NPV 83170.88 IRR 12% Payback 3.8 -150000 -8571.42857 45351.47 51830.26 74043.2227 70517.35 Discount 10% NPV 45573.51 IRR 7% Payback 4.8 -150000 -8181.81818 41322.31 45078.89 61471.211 55882.92 Discount 15% NPV -11687.9 IRR -2% Payback >5 -150000 -7453.41615 34292.23 34079.23 42334.4529 35059.59 Discount 20% NPV -49932 IRR -11% Payback >5 -150000 -6818.18182 28696.05 26087.32 29644.6812 22458.09 Project C Year 0 1 2 3 4 5 Cashflow -200000 -150000 90000 100000 110000 120000 Discount 0% NPV 70000 IRR 6% Payback 5 -200000 -150000 90000 100000 110000 120000 Discount 5% NPV 9679.682 IRR 1% Payback 5 -200000 -142857.143 81632.65 86383.76 90497.2722 94023.14 Discount 10% NPV -37210 IRR -4% Payback >5 -200000 -136363.636 74380.17 75131.48 75131.4801 74510.56 Discount 15% NPV -107211 IRR -12% Payback >5 -200000 -124223.602 61726.01 56798.72 51742.1091 46746.12 Discount 20% NPV -152328 IRR -20% Payback >5 -200000 -113636.364 51652.89 43478.87 36232.3882 29944.12 Project B seems to be better projet among the 3 projects in terms of NPV,IRR and payback.
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