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146 Part One Value
Notice that KGR’s depreciation deduction declines for the first few years and then flattens
out. That is also the case with the U.S. MACRS system of depreciation. In fact, MACRS is
just another example of the declining-balance method with a later switch to straight-line.^9(^9) Take, for example, the 10-year MACRS schedule. It allows the firm to deduct 20% of the written-down value of the asset annu-
ally. Since the IRS assumes that the asset is bought midyear, the firm deducts 10% of the investment in year 1 and writes down
the value of the asset to 100 – 10 = 90% of its purchase cost. In the second year it deducts 20% of the written-down value, that is,
.2 × 90 = 18% of purchase cost. The written-down value is now 90 – 18 = 72% of cost and, therefore, in year 3 the MACRS deduction
is .2 × 72 = 14.4% cost. By the end of year 6 the investment has been written down to 29.49% of cost, and the company switches to
straight-line depreciation for the remaining 4.5 years of the asset’s life.
6-3 Using the NPV Rule to Choose among Projects
Almost all real-world investment decisions entail either-or choices. Such choices are said
to be mutually exclusive. We came across an example of mutually exclusive investments in
Chapter 2. There we looked at whether it was better to build an office block for immediate
sale or to rent it out and sell it at the end of two years. To decide between these alternatives,
we calculated the NPV of each and chose the one with the higher NPV.
That is the correct procedure as long as the choice between the two projects does not affect
any future decisions that you might wish to make. But sometimes the choices that you make
today will have an impact on future opportunities. When that is so, choosing between compet-
ing projects is trickier. Here are four important, but often challenging, problems:
∙ The investment timing problem. Should you invest now or wait and think about it again
next year? (Here, today’s investment is competing with possible future investments.)
∙ The choice between long- and short-lived equipment. Should the company save money
today by installing cheaper machinery that will not last as long? (Here, today’s decision
would accelerate a later investment in machine replacement.)
∙ The replacement problem. When should existing machinery be replaced? (Using it
another year could delay investment in more modern equipment.)
∙ The cost of excess capacity. What is the cost of using equipment that is temporarily not
needed? (Increasing use of the equipment may bring forward the date at which additional
capacity is required.)
We will look at each of these problems in turn.
Problem 1: The Investment Timing Decision
The fact that a project has a positive NPV does not mean that it is best undertaken now. It
might be even more valuable if undertaken in the future. The question of optimal timing is not
difficult when the cash flows are certain. You must first examine alternative start dates (t) for
the investment and calculate the net future value at each of these dates. Then, to find which of
the alternatives would add most to the firm’s current value, you must discount these net future
values back to the present:
Net present value of investment if undertaken at date t = net future value at date ____t
(1 + r)t
For example, suppose you own a large tract of inaccessible timber. To harvest it, you need
to invest a substantial amount in access roads and other facilities. The longer you wait, the
higher the investment required. On the other hand, lumber prices may rise as you wait, and the
trees will keep growing, although at a gradually decreasing rate.