1) Explain why the NPV of a relatively long-term project, defined as one for whi

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Question

1) Explain why the NPV of a relatively long-term project, defined as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in the cost of capital than is the NPV of a short-term project.

b) When two mutually exclusive projects are being compared, explain why the short term project might be ranked higher under the NPV criterion if the cost of capital is high whereas the long-term project might be deemed better if the cost of capital is low. Would changes in the cost of capital ever cause a change in the IRR ranking of two such projects? why or why not?

c) Suppose a firm is considering two manually exclusive projects. One has a life of 6 years and the other a life of 10 years. Would the failure to employ some type of replacement chain analysis bias an NPV analysis against one of the projects? Expain

Explanation / Answer

a) Explain why the NPV of a relatively long-term project, defined as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in the cost of capital than is the NPV of a short-term project.

Ans:

The NPV of a project is the excess of PV of Incremental Cash Inflows over the PV of Incremental Cash Outflows resulting from the project.

In order to find the PV of the cash flows, the cash flows are discounted using the Overall Cost of Capital.

The discounting formula used is PV = CFt/(1-k)t , where CFt is the cash flow occurring in the year ‘t’ and ‘k’ is the discounting rate (which rate is the cost of capital).

This discounting formula compounds the discount rate used over time, with the result that,

for the same discount rate, the PV decreases for the later years. Such difference in PV is more pronounced with changes in discount rates. These are evident from the table given below, which gives the PV of Re 1 at different rates over a period of time.

Year

PV @ 5%

PV @ 6%

PV @ 7%

.952

.943

.935

.907

.890

.873

.864

.840

.816

.823

.792

.763

.784

.747

.713

.745

.705

.666

.711

.665

.623

.677

.627

.582

.645

.592

.544

.614

.558

.508

This has the effect of giving less weightage to cash flows occurring in the later years and more weightage to the cash flows occurring in the earlier years. Besides, as the rate of discount is varied, the increase or decrease in PV for every 1% change in discount rate, is more than proportionate for the same year. As a result, the NPV of a relatively long-term project, defined as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in the cost of capital than is the NPV of a short-term project

The discounting of cash flows for finding out the PV, as explained above, gives more weightage

to the earlier cash flows than the later cash flows and a higher discount rate compounds the problem making the disparity more pronounced.

Where the discount rate is high, the later cash flows are at a higher disadvantage, and hence a long term project might be ranked lower than a short term project. On the other hand, when the discount rate is low, the difference in PVs for earlier and later cash flows is not that pronounced, with the result that the long term project might get a higher ranking.

But, in contrast, the IRR for two projects is not affected by the change in cost of capital, as the IRR of a project (that discount rate which equals the PV of Cash inflows with the PV of Cash outflows) is that projects rate of return, which will be the same irrespective of the COC.

If some method of replacement chain analysis is not employed in such cases, it would work against the project having lower life.

In this particular example, if we compare the NPVs of the two projects without considering reinvestment in the case of the shorter project after 6 years, which is possible, we would be ignoring the possible benefits that may arise in the years 7 to 10 if the project is repeated.