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An investor is considering three projects, A, B and C summarized in the table below.  Investment cost Annual operating profit Project life (years)Project A -70000 17000 5Project B -90000 15000 8Project C -60000 13000 6Suppose the investor can borrow funds at an interest rate of 6%, by using the NPV rule with a 5% discount rate, he should choose project _____. When using the IRR rule, he should ____ this project.

Question

An investor is considering three projects, A, B and C summarized in the table below.  Investment cost Annual operating profit Project life (years)Project A -70000 17000 5Project B -90000 15000 8Project C -60000 13000 6Suppose the investor can borrow funds at an interest rate of 6%, by using the NPV rule with a 5% discount rate, he should choose project _____. When using the IRR rule, he should ____ this project.

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Solution

First, let's calculate the Net Present Value (NPV) for each project. The NPV is calculated by subtracting the initial investment cost from the present value of the annual operating profit over the project's life. The present value of the annual operating profit is calculated using the formula for the present value of an annuity:

PVA = C * [(1 - (1 + r)^-n) / r]

where C is the annual cash flow, r is the discount rate (5% or 0.05), and n is the number of periods (years).

  1. Project A: PVA = 17000 * [(1 - (1 + 0.05)^-5) / 0.05] = 72,097.75NPV=PVAInitialInvestmentCost=72,097.75 NPV = PVA - Initial Investment Cost = 72,097.75 - 70,000=70,000 = 2,097.75

  2. Project B: PVA = 15000 * [(1 - (1 + 0.05)^-8) / 0.05] = 92,643.27NPV=PVAInitialInvestmentCost=92,643.27 NPV = PVA - Initial Investment Cost = 92,643.27 - 90,000=90,000 = 2,643.27

  3. Project C: PVA = 13000 * [(1 - (1 + 0.05)^-6) / 0.05] = 64,618.79NPV=PVAInitialInvestmentCost=64,618.79 NPV = PVA - Initial Investment Cost = 64,618.79 - 60,000=60,000 = 4,618.79

Based on the NPV rule, the investor should choose Project C because it has the highest NPV.

Next, let's consider the Internal Rate of Return (IRR) rule. The IRR is the discount rate that makes the NPV of a project equal to zero. If the IRR of a project is greater than the cost of capital (in this case, the interest rate of 6%), the project should be accepted. If the IRR is less than the cost of capital, the project should be rejected.

Without knowing the exact IRRs of the projects, we can't definitively say which project the investor should choose or reject based on the IRR rule. However, since Project C has the highest NPV at a discount rate of 5%, it's likely that its IRR is also the highest and thus greater than the cost of capital. Therefore, the investor should also choose Project C based on the IRR rule.

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