Question

Based on the following information:

Net cash flow = R90 000 per year

Useful life = 5 years

Cost of capital = 8%

Initial investment = R300 000 calculate the internal rate of return (IRR) of the project.

(a) 0 %

(b) 15.24 %

(c) 8.00 %

(d) 12.36%

(d) None of the above

Answer 1

IRR is defined as a rate at which NPV is zero.

Firstly we shall compute NPV at 15% as shown:

= - R 300,000 + R 90,000 / 1.15 + R 90,000 / 1.15² + R 90,000/ 1.15³ + R 90,000 / 1.15⁴ + R 90,000 / 1.15⁵

= R 1,693.958821

Lets compute NPV at 16% as shown below:

= - R 300,000 + R 90,000 / 1.16 + R 90,000 / 1.16² + R 90,000/ 1.16³ + R 90,000 / 1.16⁴ + R 90,000 / 1.16⁵

= - R 5,313.57117

It denotes the IRR is between 15% and 16% because the investment is recovered between 15% and 16% and same is shown as follows:

= Lower rate + [ (Lower rate NPV / (Lower rate NPV - Higher rate NPV) ] x (Higher rate - lower rate)

= 15% + [ (R 1,693.958821) / (R 1,693.958821 - (- R 5,313.57117) ] x (16 - 15)

= 15% + [ R 1,693.958821 / R 7,007.529991 ]

= 15.24% Approximately

Hence the correct answer is option b.