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REPLACING AN OLD MACHINE

The previous example took the life of each machine as fixed. In practice, the point at which equipment is replaced reflects economics, not physical collapse. We usually decide when to replace. The machine will rarely decide for us.

Here is a common problem. You are operating an old machine that will last 2 more years before it gives up the ghost. It costs $12,000 per year to operate. You can replace it now with a new machine, which costs $25,000 but is much more efficient ($8,000 per year in operating costs) and will last for 5 years. Should you replace it now or wait a year? The opportunity cost of capital is 6 percent. We can calculate the NPV of the new machine and its equivalent annual cost, that is, the 5-year annuity that has the same present value.

The cash flows of the new machine are equivalent to an annuity of $13,930 per year. So we can equally well ask at what point we would want to replace our old machine, which costs $12,000 a year to run, with a new one costing $13,930 a year. When the question is posed this way, the answer is obvious. As long as your old machine costs only $12,000 a year, why replace it with a new machine that costs $1,930 more?

MUTUALLY EXCLUSIVE PROJECTS AND THE IRR RULE

Whereas the NPV rule deals easily with mutually exclusive projects, the IRR rule does not. Because of the potential pitfalls in the use of the IRR rule, our advice is always to base your final decision on the project s net present value.7

Pitfall 1: Mutually Exclusive Projects. We have seen that firms are seldom faced with take-it-or-leave-it projects. Usually they need to choose from a number of mutually exclusive alternatives. Given a choice between competing projects, you should accept the one that adds most to shareholder wealth. This is the one with the higher NPV. However, it won t necessarily be the project with the higher internal rate of return. So the IRR rule can lead you astray when choosing between projects. Think once more about the two office-block proposals. You initially intended to invest $350,000 in the building and then sell it at the end of the year for $400,000. Under the revised proposal, you planned to rent out the offices for 3 years at a fixed annual rent of $16,000 and then sell the building for $450,000. Here are the cash flows, their IRRs, and their NPVs:

Both projects are good investments; both offer a positive NPV. But the revised proposal has the higher net present value and therefore is the better choice. Unfortunately, the superiority of the revised proposal doesn t show up as a higher rate of return. The IRR rule seems to say you should go for the initial proposal because it has the higher IRR. If you follow the IRR rule, you have the satisfaction of earning a 14.29 percent rate of return; if you use NPV, you are $59,000 richer.

Figure 4.4 shows why the IRR rule gives the wrong signal. The figure plots the NPV of each project as a function of the discount rate. These two NPV profiles cross at an interest rate of 12.26 percent. So if the opportunity cost of capital is higher than 12.26 percent, the initial proposal, with its rapid cash inflow, is the superior investment. If the cost of capital is lower than 12.26 percent, then the revised proposal dominates. Depending on the discount rate, either proposal may be superior. For the 7 percent cost of capital that we have assumed, the revised proposal is the better choice. Now consider the IRR of each proposal. The IRR is simply the discount rate at which NPV equals zero, that is, the discount rate at which the NPV profile crosses the horizontal axis in Figure 4.4. As noted, these rates are 14.29 percent for the initial proposal and 12.96 percent for the revised proposal. However, as you can see from Figure 4.4, the higher IRR for the initial proposal does not mean that it has a higher NPV. In our example both projects involved the same outlay, but the revised proposal had the longer life. The IRR rule mistakenly favored the quick payback project with the high percentage return but the lower NPV.

Remember, a high IRR is not an end in itself.You want projects that increase the value of the firm. Projects that earn a good rate of return for a long time often have higher NPVs than those that offer high percentage rates of returnbut die young.

Pitfall 1a: Mutually Exclusive Projects Involving Different Outlays. A similar misranking also may occur when comparing projects with the same lives but different outlays. In this case the IRR may mistakenly favor small projects with high rates of return but low NPVs.