Question

You have to evaluate two mutually exclusive projects Alpha and Beta. Both projects have a cost fo capital is 12%. Both projects have an economic life of 5 years.

Project Alpha has a cost of $14,000. Its expected cash flows are an annuity of $4,500 per annum.

Project Beta has a cost of $14,000. It has one expected cash flow at the end of period 5 $30,000.

We must figure out the NPR, IRR and CHOICE for both Alpha and Beta.

Complete the following table:

Project:   NPR IRR CHOICE

Alpha-   

Beta-

Answer 1

NPV is calculated by discounting the cashflows

PV = C/(1+r)^n

C - Cashflow

r - Discount rate

n - years to the cashflow

Project Alpha:

NPV = -14000 + 4500/(1+0.12)^1 + 4500/(1+0.12)^2 + 4500/(1+0.12)^3 + 4500/(1+0.12)^4 + 4500/(1+0.12)^5 = $2221.49

Project Beta:

NPV = -14000 + 30000/(1+0.12)^5 = $3022.81

Choose project Beta, as it has higher NPV

IRR is the rate at which NPV = 0

Project Alpha:

0 = -14000 + 4500/(1+IRR)^1 + 4500/(1+IRR)^2 + 4500/(1+IRR)^3 + 4500/(1+IRR)^4 + 4500/(1+IRR)^5

By trail and error, IRR = 18.23%

Project Beta

0 = -14000 + 30000/(1+IRR)^5

IRR = 16.47%

Choose project Alpha, as it has higher IRR.