The first trial of an IRR interpolation used an interest rate of 15% and produced a NPV of ($81,450) and the second trial of IRR at 6% produced an NPV of $56,000. Assuming a straight-line relationship between IRR and NPV, what percent reduction from 15% would result in the project's IRR?

Question

Quizplus · Accepted Answer

The NPV changes by $137,450 ($56,000 - (-$81,450)) for a 9% change in the interest rate (15% - 6%). Therefore, a 1% change in the interest rate would change the NPV by $15,272 ($137,450 / 9). Since the NPV is negative at 15% and positive at 6%, the IRR must be between 6% and 15%. To find the IRR, we can use the following formula:IRR = Lower interest rate + (NPV at lower interest rate / (NPV at lower interest rate - NPV at higher interest rate)) * (Higher interest rate - Lower interest rate)IRR = 6% + ($56,000 / ($56,000 - (-$81,450))) * (15% - 6%)IRR = 6% + ($56,000 / $137,450) * 9%IRR = 6% + 0.407 * 9%IRR = 6% + 3.663%IRR = 9.663%Therefore, the percent reduction from 15% would be 5.337% (15% - 9.663%).

The First Trial of an IRR Interpolation Used an Interest