## Timing

Assume that there are two mutually exclusive investments both requiring the same initial outlay. This case seems to be different from the one we have just discussed because there is no incremental investment. Actually, the difference is superficial. Consider investments Y and Z, described in Table 2. Suppose that Y and Z are mutually exclusive investments for a company whose cost of money is 5%. The IRR of Y is 20%, whereas that of Z is 25%. If we take the present value of each investment at 5%, however, we find that the ranking is in the opposite order. The present value of Z is less than the present value of Y.

Cash flows for period
| IRR (%)
| NPV at 5%
| |||

Investment | 0 | 1 | 2 | ||

Y | −$100.00 | $20.00 | $1200.00 | 20 | $27.89 |

Z | −100.00 | 100.00 | 31.25 | 25 | 23.58 |

Period 0 | 0.00 | Cash flows identical |

Period 1 | −$80.00 | Cash flow of Y is less than that of Z |

Period 2 | $88.75 | Cash flow of Y exceeds that of Z |

Suppose that we attempt to make an incremental comparison, as shown in Table 3. We see that the cash flow of Y is $80.00 less in year 1 and $88.75 more than Z in year 2. As before, we can compute the IRR on the incremental cash flow. An outlay of $80.00 that returns $88.75 one year later has an IRR of 10.9%. An investment such as this would be desirable for a company whose cost of money is less than 10.9%. Again, we are really dealing with a problem of the scale of the investment, but in this case, the opportunity for the additional investment occurs one year later.

The same result can be reached by a somewhat different route if we ask how much cash the company would have on hand at the end of the second year if it accepted investment Y or if it accepted investment Z. Both investments give some cash proceeds at the end of the first year. The value of the investment at the end of the second year will depend on what is done with cash proceeds of the first year. Assume that the cash proceeds of the first year could be reinvested to yield 5%. Then investment Y would result in a total cash accumulation by the end of the year of $141 (105% of $20 plus $120). Investment Z would result in a cash accumulation of only $136.25 (105% of $100 plus $31.25).

Figure 2 shows that investment Y is to be preferred as long as the appropriate discount rate is less than 10.9%. If the rate is in excess of 10.9, then Z is to be preferred.

One disadvantage associated with the use of the IRR method is the necessity of computing the IRR on the incremental cash proceeds in order to determine which of a pair of mutually exclusive investments is preferable. If there are more than two mutually exclusive investments, we shall have to conduct an elimination tournament among the mutually exclusive investments. Taking any pair, we compute the IRR on the incremental cash flow and attempt to decide which of the two investments is preferable. The winner of this round would then be compared in the same manner with one of the remaining investments until the grand champion investment is discovered. If there are 151 investments being considered, there will have to be 150 computations, because 150 investments would have to be eliminated.

## Why IRR Is Popular

Managers like the IRR method, since they consider it important to know the differential between the proposed investment’s IRR and the required return. This is a measure of safety that allows an evaluation of the investment’s return compared to its risk. If an investment has an IRR of 0.30 when the required return is 0.12, this is a large margin that allows for error. An NPV measure does not give the same type of information to management.

## Case Study

### A Decision in Mexico

A major Mexican steel corporation had a major decision. It could stand relatively pat (a marginal investment of $50,000,000) with its present steel making facilities and earn indefinitely (after maintenance capital expenditures) $8,000,000 per year. This is an IRR of 0.16. The pesos have been translated to dollars.

The alternative is to invest $10,000,000,000 and earn $1,500,000,000 per year indefinitely, an IRR of 0.15.

What should the corporation do if it has a cost of capital of 0.10 for steel making facilities?

The solution is:

NPV (stand pat) = 8,000,000 ÷ 0.10 – 50,000,000 = 80,000,000 – 50,000,000 = $30,000,000

NPV (major investment) = 1,500,000,000 ÷ 0.10 – 10,000,000,000 = 15,000,000,000 – 10,000,000,000 = $5,000,000,000

IRR says stand pat (0.16 is larger than 0.15). NPV says rebuild ($5 billion is larger than $30 million).

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