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Calculating NPVs and IRRs of given projects

Suppose we have two mutually exclusive land development projects. The first is a office building which can be constructed for an initial outlay of $20 million and sold a year later for $24 million. The other use of the land is for a parking lot where an initial outlay of $10,000 will produce a cash inflow of $10,000 per year forever. The NPV of the building project is given by: NPVB = -$20,000,000 + [$24,000,000/(1 + i)] where i is the cost of capital. The NPV of the perpetuity producing parking project is given by the expression: NPVp = -$10,000 + ($10,000/i).

1. Calculate the NPVs of both projects at a 15% cost of capital.

2. Calculate the IRRs of both projects.

Solution Preview

1.
Let us calculate NPV for building project.
PV of cash inflow after one year=24,000,000/(1+15%)^1=20869565.22
NPV of buiding project=NPVB=-Initial outlay+PV of cash flows=-20000000+20869565.22=$869,565.22

Let us calculate NPV for parking lot project.

It is case of perpetuity.

Annual cash ...

Solution Summary

NPV and IRR are two important capital budgeting parameters and help us in selecting suitable project/s. Solution to the given problem explains the methodology to find the NPVs and IRRs of given projects and then it selects the better project.

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