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Solutions+Problem+Set+5

# Solutions+Problem+Set+5 - E120 Principles of Engineering...

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Fall 2010 Problem Set #5 Solutions 1. NPV= (1/1.08)×30/0.08-100=\$247.22million, so we should make the investment The IRR solves (1/1+r)×30/r-100=0 => r=24.16% So, the cost of capital can be underestimated by 16.16% without changing the decision. 2. Computing the NPV of the cash flow stream: NPV=-120+20/r × (1-1/(1+r) 10 )-2/r ×1/(1+r) 10 You can verify that r=0.02924 or 0.08723 gives an NPV of zero. There are two IRRs, so you cannot apply the IRR rule. Let’s see what the NPV rule says. Using the cost of capital of 8% gives NPV=-120+20/r × (1-1/(1+r) 10 )-2/r ×1/(1+r) 10 =2.621791 So the investment has a positive NPV of \$2,621,791. In this case the NPV as a function of the discount rate is n shaped. If the opportunity cost of capital is between 2.93% and 8.72%, the investment should be undertaken. 3. a. NPV A =2/r-10 Setting NPV A =0 and solving for r IRR A =20% NPV B =1.5/(r-0.02)-10 Setting NPV B =0 and solving for r IRR B =17% Based on the IRR you always pick project A. b. Substituting r = 0.07 into the NPV formulas derived in part (a) gives

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Solutions+Problem+Set+5 - E120 Principles of Engineering...

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