Question 12: (15 Marks) company invests AED 110,000 in a project with a lifetime

Question

Question 12: (15 Marks) company invests AED 110,000 in a project with a lifetime of 35 years. The project gives an annual income of AED 12,000. The yearly maintenance costs are AED 3.500 and the salvage value for the project after 35 years is AED 20,500. There is a single extra cost at the end of ten years of AED 20,800 for renovation of the project Calculate the Internal Rate of Return for the project. Use interest rate values of 5% and 7% and interpolate the IRR linearly. Question Items A.) Calculate the present value using 5% (4 Marks) A 2o128. B.) Calculate the present value using 7%. (4 Marks) 1176:2 C.) Calculate the internal rate of return (IRR) 4 Marks) D) If the company's minimum acceptable rate of return (MARR) is 65% should the company proceed with the project? (3 Marks) e s

Explanation / Answer

Solution :- When interest rate is 5 % :-

Present value of cash inflows = (12000 - 3500) * [ 1 - (1.05)-35 ] / 0.05 - 20800 / (1.05)10 + 20500 / (1.05)35

= 8500 * [ 1 - 0.18129 ] / 0.05 - 20800 / 1.6289 + 20500 / 5.5160

= 8500 * 0.81871 / 0.05 - 12769.35 + 3716.46

= 139180.70 - 12769.35 + 3716.46

= $ 130127.81 (approx).

Present value of cash outflow = $ 110000 (Given in the question)

When interest rate is 7 % :-

Present value of cash inflows = (12000 - 3500) * [ 1 - (1.07)-35 ] / 0.07 - 20800 / (1.07)10 + 20500 / (1.07)35

= 8500 * [ 1 - 0.09366 ] / 0.07 - 20800 / 1.96715 + 20500 / 10.6766

= 8500 * 0.90634 / 0.07 - 10573.67 + 1920.09

= 110055.57 - 10573.67 + 1920.09

= $ 101401.99 (approx)

Present value of cash outflow = $ 110000 (Given in the question)

By inter-polation, Internal rate of return (IRR) of the project is calculated as follows :-

= 5 % + (7 % - 5 %) * (130127.81 - 110000) / (130127.81 - 101401.99)

= 5 % + 2 % * 20127.81 / 28725.82

= 5 % + 2 % * 0.70

= 5 % + 1.40 %

= 6.40 %

Conclusion :- Internal rate of return (IRR) for project in the given question = 6.40 %

The company should not start / proceed with the project because the internal rate of return (IRR) of project being 6.40 % is lesser than the minimum acceptable rate of return (MARR) of the company being 6.50 %. (In short, if IRR is lesser than the MARR, The project is not acceptable at all.)

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