In general, we say that two projects with cash flows \(x_{i}\) and \(y_{i}, i=0,1,2, \ldots\), \(n\), cross if \(x_{0}\sum_{i=0}^{n} y_{i}\). Let \(P_{x}(d)\) and \(P_{y}(d)\) denote the present values of these two projects when the discount factor is \(d\).

(a) Show that there is a crossover value \(c>0\) such that \(P_{x}(c)=P_{y}(c)\).

(b) For Exercise 13, calculate the crossover value \(c\).

Data from Exercises 13

Consider the two projects whose cash flows are shown in Table 2.7. Find the IRRs of the two projects and the NPVs at 5\%. Show that the IRR and NPV figures yield different recommendations. Can you explain this?

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TABLE 2.7 Years 0 1 2 3 4 5 Project 1-100 30 30 30 30 30 Project 2 -150 42 42 42 42 42