The forecast net cash flows of two mutually exclusive projects, A and B, are sho

Question

The forecast net cash flows of two mutually exclusive projects, A and B, are shown in
the following table.

Year (end) Project A Project B
0 ? $55,000 ? $35,000
1 $26,000 $25,100
2 $12,500 $16,900
3 $44,400 $17,500
4 $26,200 $11,600
5 $13,200 $8,250

The NPV and IRR methods must give conflicting ranks for these projects if:

a) The required rate of return is less than 25% pa.
b) The required rate of return is greater than 25% pa.
c) The required rate of return is between 35% pa and 45% pa.
d) None of the above.

Explanation / Answer

Here's the detailed solution:

Hence by IRR method, the rank is Project B > Project A

Hence we need an interval when NPVA>NPVB i.e. NPV(A-B) > 0

When A is compared to B, the NPV of A-B ie A with respect to B has MIRR = 23.7144%. Hence NPV of A-B is +ve for rate of return <= 23.7144% ie A will be preferred if rate of return < = 23.7144% (and not 25%).. Hence the answer is d) None of the above.

Formula Case -> A B A-B Cash flow PV of Cash flow Year Cash flow Cash flow Cash flow A A/(1+r)^0 0 -55,000 -35,000 -20,000 B B/(1+r)^1 1 26,000 25,100 900 C C/(1+r)^2 2 12,500 16,900 -4,400 D D/(1+r)^3 3 44,400 17,500 26,900 E E/(1+r)^4 4 26,200 11,600 14,600 F F/(1+r)^5 5 13,200 8,250 4,950 IRR r if npv = sum of above = 0 34.9957% 44.9998% 23.7144%

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