An investment project has an initial cost, and then generates inflows of R50 a year for the next five years.The project has a payback period of 3.6 years.What is the project's internal rate of return?

Question

Quizplus · Accepted Answer

To calculate the internal rate of return (IRR) of this project, we need to find the discount rate that makes the net present value (NPV) of the project equal to zero. We can use the trial-and-error method or a financial calculator to find the IRR.

Using the trial-and-error method, we can start with a discount rate of 10% and calculate the NPV of the project as follows:
- Year 0: -initial cost = -100
- Year 1: R50/(1+10%) = R45.45
- Year 2: R50/(1+10%)^2 = R41.32
- Year 3: R50/(1+10%)^3 = R37.56
- Year 4: R50/(1+10%)^4 = R34.15
- Year 5: R50/(1+10%)^5 = R31.08

NPV = -100 + 45.45 + 41.32 + 37.56 + 34.15 + 31.08 = -10.44

Since the NPV is negative, we need to increase the discount rate. Let's try a discount rate of 11%:
- Year 0: -initial cost = -100
- Year 1: R50/(1+11%) = R45.05
- Year 2: R50/(1+11%)^2 = R40.54
- Year 3: R50/(1+11%)^3 = R36.41
- Year 4: R50/(1+11%)^4 = R32.63
- Year 5: R50/(1+11%)^5 = R29.18

NPV = -100 + 45.05 + 40.54 + 36.41 + 32.63 + 29.18 = -0.19

Since the NPV is still negative, we need to increase the discount rate further. Let's try a discount rate of 12%:
- Year 0: -initial cost = -100
- Year 1: R50/(1+12%) = R44.64
- Year 2: R50/(1+12%)^2 = R39.94
- Year 3: R50/(1+12%)^3 = R35.59
- Year 4: R50/(1+12%)^4 = R31.56
- Year 5: R50/(1+12%)^5 = R27.84

NPV = -100 + 44.64 + 39.94 + 35.59 + 31.56 + 27.84 = 0.57

Since the NPV is now positive, we can conclude that the IRR of the project is between 11% and 12%. To narrow down the range, we can interpolate as follows:

IRR = Lower Discount Rate + (NPV at Lower Discount Rate / (NPV at Lower Discount Rate - NPV at Higher Discount Rate)) * (Higher Discount Rate - Lower Discount Rate)
IRR = 11% + (-10.44 / (-10.44 - 0.57)) * (12% - 11%)
IRR = 12.05%

Therefore, the best choice is B, with an IRR of 12.05%.

An Investment Project Has an Initial Cost, and Then Generates