# 1.28 IRR Practice Problems (Solutions)

Problem #1:

NPV= \$10,000 x (PVAF 5%; n = 10) – Cost

= (\$10,000) (7.7217) – \$61,446

= 77,217 – 61,446

= \$15,771

As we did before, we will start out assuming a 0% discount rate. Thus, we simply add the ten \$10,000 payments and divide by the cost of \$61,446 (less one): [\$100,000 ÷ \$61,446] – 1 = 0.627.

Possible Range for IRR: 5% to 62.7%

Since the NPV at a 5% discount rate was positive, the IRR must be greater than that. The upper limit is 62.7%. This is a wide range. You could start guessing, using perhaps a first guess of 30% and taking it from there. Alternatively, if you have tables, you might try using them!

Since we are dealing with a round number of \$10,000, you could look across the Present Value Annuity table – on the 10-period row – for a multiplier that comes closest to being a multiple of the cost figure (\$61,446). A multiple of exactly 6.1446 appears in the 10% column! Thus, (\$10,000) (6.1446) = \$61,446, making the NPV = 0.

Mathematically the solution for this is: (\$10,000) (PVAF) = \$61,446; PVAF = 6.1446.

IRR = 10%

Problem #2:

 Period Free Cash Flow PVF @ 3% PVCF 0 (\$1,500,000) 1.0000 (\$1,500,000) 1 725,000 0.9709 703,902.5 2 830,000 0.9426 782,358.0 3 840,000 0.9251 768,684.0 4 625,000 0.8885 555,312.5 5 225,000 + 35,000 0.8626 224,276.0 NPV= \$1,534,533

## License

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