The IRR is the discount rate that causes the NPV = 0. For Project A: NPV (A) = 2/r − 10 = 0
2/r= 10,
IRR (A)= 20%
For Project B: NPV (B) = 1.5/(r − 0.02) −10 = 0
1.5 = (r − 0.02) × 10
0.15 = r − 0.02
IRR (B) = 17%
Thus, Project A has a higher IRR.
Which investment has the higher NPV when the cost of capital is 7%?
NPV (A) = (2/0.07) − 10 = $18.571 million
NPV (B) = 1.5/(0.07 − 0.02) − 10 = $20 million
The crossover point can be solved by setting the NPVs equal to one another: NPV (A) = NPV (B)
2/r − 10 = 1.5/(r − 0.02) − 10
2(r − 0.02) = 1.5 r
0.5r = 0.04
r = 0.08 = 8%
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