Question

Alpha Systems Ltd. is considering a project with a cost of $160,000 and cash flows of $32,500 per year for the eight-year life of the project

(a) If the risk-free are is 8% and the risk premium is 4%, should the project be accepted?

(b) Suppose the firm used a firm-wide opportunity cost of capital approach. If the opportunity cost of capital is 16% and the risk premium is the same, should the project be accepted?

Answer 1

Ans. =

Project Outflows = $160000

Project Inflows = $32500 for 8 Years

Number of Periods = 8 Years

We can Find the IRR of the Project to get to know if the Project is Benificial or Not. and to Compare with the Nominal Rate of Interest or Cost of Capital of the Firm.

Firm IRR:

Present Value of Outflows = Present Value of Inflows

160000 = 32500/(1 + r)² + 32500/(1 + r)³ + 32500/(1 + r)⁴ + 32500/(1 + r)⁵ + 32500/(1 + r)⁶ + 32500/(1 + r)⁷ + 32500/(1 + r)⁸

We can get IRR by Trial and Error method :

Put IRR as 12.26, we will get Present Value of Inflows approximately equal to Present Value of Outflows.

160000 = 32500/(1.12)² + 32500/(1.12)³ + 32500/(1.12)⁴ + 32500/(1.12)⁵ + 32500/(1.12)⁶ + 32500/(1.12)⁷ + 32500/(1.12)⁸

Present Value of Inflows are Approximately equal to Outflows.

So, IRR is 12.26.

If IRR Higher than Nominal Rate of Interest then We should Accept the Project as It is above the firms cost of capital which is the minimum that we must earn.

A)

So, IRR of 12.26 is Higher than (8 + 4) = 12% Opportunity Cost.

Hence, Accept the Project.

B)

So, IRR is of 12.26 Which is lower than (16 + 4) = 20% Opportunity Cost.

Hence, Reject the Project.

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