# Corporate Finance Question

From CFAI Volume 4, pg 33, question 13 Consider the two projects below. The cashflows as well as the NPV and IRR for the two projects are given. For both projects, the required rate of return is 10 percent Year 0 1 2 3 4 / NPV / IRR ProjectA -100 36 36 36 36 / 14.12 / 16.37% ProjectB -100 0 0 0 175 / 19.53 / 15.02% What discount rate would result in the same NPV for both projects? The book did not provide a good explaination in obtaining the answer. Whats the best way to solve this besides trial and error?

do a diff of the cash flows so 0 36 36 36 -139 find the IRR of this new projectâ€¦ that will be the IRR that results in the same NPV for both projectsâ€¦

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This is so simple and genious! Thanks CPK! The textbook would only show a chart of NPVs for two projects with its respective discount rates. Then point the reader to the rate where the NPVs on both projects are the same. Never had it once showed us how to find the crossover discount rate where NPVs on both projects would equate. How did you find out about this neat solution?

The reason CPKâ€™s solution method works is that the IRR is â€śthe discount rate that results in an NPV of zeroâ€ť Since youâ€™re calculating the NPV of ths â€śdifferences in cash flowsâ€ť, it results in the discount rate that make the NPV of the differences equal zero. And in this case, the NPV of the differences is the differences in the NPVs. A difference of zero in the NPV is another way of saying that the NPVs are the same. Also, search the forum for â€ścrossover rateâ€ť. There are some good discussions on it. They also go into more of the intuition of these profiles.

thanks busprof