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Construction Financial Management

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Internal Rate of Return (IRR) and the Differences between IRR and NPV

The NPV ranking and the IRR ranking of the three alternatives are shown in Table 4.3.

Alternative A Alternative B Alternative C

NPV (at 6% discount rate) \$2,157,000 \$2,635,000 \$1,388,000

Ranking of NPV 2nd 1st 3rd

IRR 9.8% p.a. 9.3% p.a. 7.2% p.a.

Ranking of IRR 1st 2nd 3rd

Table 4.3 – NPV and IRR Rankings of Alternatives A, B and C

We can see that NPV and IRR methods give us different rankings of the alternatives. As said above, the NPV ranking is the correct ranking. The IRR ranking leads to wrong conclusion.

However, there is a method called Incremental IRR Analysis that will give us the result consistent with the NPV ranking (correct ranking). We are going to see how the incremental IRR analysis is used to rank the three alternatives.

First, we arrange the alternatives in an increasing order of initial capitals. In Example 4.3, we have already done this because the initial capitals of Alternatives A, B and C are \$5,000,000, \$7,000,000 and

\$11,000,000 respectively, already in an increasing order. (Otherwise, we would have to change A, B and C to, say, B, C and A, or whatever they might be).

Second, we compare Alternative A and Alternative B. The better alternative is determined by comparing the incremental IRR with the predetermined discount rate (or the minimum desirable rate of return) which is 6% p.a. in this example. The definition of incremental IRR is simply the IRR calculated from the incremental NCF. The incremental NCF is the difference of the NCF of Alternatives A and that of Alternative B, or more exactly, NCF of Alternative B minus NCF of Alternative A. If the incremental IRR is larger than 6% p.a., then Alternative B is better than Alternative A, and vice versa. Let us see how we do this below.

End of year NCFB End of year NCFA End of year Incremental NCFB-A

0 -7,000,000 0 -5,000,000 0 -2,000,000

1 700,000 1 520,000 1 180,000

2 700,000 2 520,000 2 180,000

. . minus . = . .

. . . . .

. . . . .

30 700,000 30 520,000 30 180,000

Construction Financial Management

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Internal Rate of Return (IRR) and the Differences between IRR and NPV As defined before, the incremental IRR is the IRR of the Incremental NCFB-A, and is found to be 8.1%

p.a. Since 8.1% p.a. is larger than 6% p.a., the minimum desirable rate of return, Alternative B is better than Alternative A. So, Alternative A is out and Alternative B is left behind for further consideration.

Third, we compare Alternative B and Alternative C. We repeat the process in a similar way to see whether Alternative C is better than Alternative B, or vice versa. This is done below.

End of year NCFC End of year NCFB End of year Incremental NCFC-B

0 -11,000,000 0 -7,000,000 0 -4,000,000

1 900,000 1 700,000 1 200,000

2 900,000 2 700,000 2 200,000

. . minus . = . .

. . . . .

. . . . .

30 700,000 30 700,000 30 200,000

The incremental IRR of the incremental NCFC-B is found to be 2.8% p.a. Since 2.8% p.a. is smaller than 6% p.a., Alternative B is better than Alternative C. So, Alternative B is the best overall. Therefore, the incremental IRR ranking is consistent with the NPV ranking. In the following section, we will see why NPV is more reliable in engineering economy sense.

### 4.4 IRR as Financial Indicator and NPV as Economic Indicator

As said before, IRR and NPV have intrinsic differences between one and the other. There is a more fundamental definition given to the two. The definition is: NPV is an economic indicator and IRR a financial indicator. In other words, NPV gives the society’s point of view and IRR the private investor’s point of view. Because IRR functions as a financial indicator, its value varies with the change of financial arrangement (e.g. change of equity-loan ratio) of a capital investment. NPV, however, does not vary when financial arrangement varies, because it functions as an economic indicator. Example 4.4 illustrates this.

Example 4.4 – an illustrative example

If an investor has an all-equity case investment (i.e. no borrowing from bank; the capital is totally provided by the investor) in which an initial capital outlay of \$10,000 leads to a receipt of \$5,000 each year for three years as shown in Table 4.4, the investor obtains an IRR of 23.4% p.a.

Construction Financial Management

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Internal Rate of Return (IRR) and the Differences between IRR and NPV

End of Year Cash-out Cash-in

0 10,000

1 5,000

2 5,000

3 5,000

Table 4.4 Cash Flows of An Investment

If the investor uses \$4,000 as the equity of the investment and borrows \$6,000 as a loan (paying 10% interest per annum), making a total of \$10,000 serving as the initial capital outlay of the same investment, then the net annual receipts in the next three years, having deducted the three annual principal amortizations and the annual interest payments from the gross annual receipts, are calculated to be \$2,400, \$2,600 and

\$2,800 as shown in Table 4.5 below.

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