Question

7. A firm is considering a mining project with the following cash flows (with the final cash flow being negative, perhaps due to an extensive land reclamation in the project’s final year):

C0 = –$420, C1 = $420, C2 = $462, C3 = $546, C4 = $420, and C5 = –$1554. (a) From among the following multiple-choice answers, calculate this project’s internal rate(s) of return: 5.070%, 25.225%, 33.333%, 51.909%, 82.425%. (2 pts.) (b) If the required return is 30.000%, should the project be rejected or accepted? Briefly, clearly justify and explain your reasoning. (2 pts.)

Answer 1

IRR is calculated by solving for the follwing equation:

NPV will be 0 when we discount using the IRR as IRR is the rate at which the cash inflows = cash outflows

• Now basically, we need to use either hit and trial method or the the goal seek function for finding out the IRR which satisfies the above equation.
• But as this is a multiple choice question we can use the given values and substitute them in the above equation to find out the right value.
• We also need to consider that there can be multiple IRRs as the cash flow series in unconventional.

Starting with the discount rate = 5.070%

As NPV is positive this is not the correct IRR,

If the discount rate = 25.225%

As NPV is positive this is not the correct IRR

If the discount rate = 33.333%

As NPV is positive this is not the correct IRR

If the discount rate = 51.909%

As NPV is positive this is not the correct IRR

If the discount rate = 82.425%

As NPV = 0 so this is the correct IRR

Now coming to the other part in the question, whether this project is worth investing in if the discount rate is 30%, if the cash flows are conventional then we actually dont need to solve the above equation again because there will only be one IRR and till the time the discount rate is less than the IRR, we will have a positive NPV and we should invest. But the CF are unconventional in this case so there is a chance of multiple IRR and so we will have to resolve the above equation to verify:

As NPV is positive, we should invest in this project, ie the project should be accepted.