# 2.18 Solutions for “Questions #3-5”

(\$)

 Project A Project B Year Cash Flows Discounted Cash Flow Cash Flows Discounted Cash Flow 0 (10,000,000) (10,000,000) (10,000,000) (10,000,000) 1 6,000,000 5,454,6000 4,000,000 3,636,400 2 8,000,000 6,611,200 4,000,000 3,305,600 NPV \$2,065,800 2 (10,000,000) (\$8,264,000) 3 6,000,000 4,507,800 4,000,000 3,005,200 4 8,000,000 5,464,000 4,00,000 2,732,000 NPV 3,773,072 2,679,200 AAA 1,190,234 845,326

The NPV for Project A – when replicated – was calculated as follows: \$2,065,800 + (2,065,800 ÷ 1.12) = \$3,773,072. If one had just added up the numbers in the column, the sum would be: \$3,773,600. The discounted cash flow numbers were calculated by using interest rate tables.

See if you can find alternate solutions to this problem. One alternate would involve using annuity factors. Since the cash flows for Project B are equal, the NPV solution could have been calculated using the annuity approach, rather than the “long” approach utilized above.[1]

When assuming equal lives, by replicating Project A, both NPV and AAA favor A. Note that “project scale” is not at issue here.

1. Many thanks to Chaim Halberstam (The Lander College for Men class of 2019) for providing the solution to this problem.

## License

Corporate Finance Copyright © 2023 by Kenneth S. Bigel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.