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: