Example: Computing the IRR Example 4.11: Suppose a veterinarian is considering buying new equipment. The equipment will cost him or her $16,000. This cost and the net annual benefits over a five-year life are displayed on the following time line. Compute the IRR. Now Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5 $-16,000 $+4,500 $+4,500 $+4,500 $+4,500 $+4,500 Example 4.11: Solution IRR is the discount rate at which: PVcash inflows - PVcash out flows = 0 $4,500 *(1 + i)-1 + $4,500 + (1 + i)-2 + $4,500 (1 + i)-3 + $4,500 - (1 + i)*4 + $4,500 * (1 + i)-S - $16,000 = 0 Tryi= 12% $4,500 - (1 + 0.12)-1 + $4,500 + (1 + 0.12)-2 + $4,500 - (1 +0.12)-3 + $4,500 (1 + 0.12) -4 + $4,500 + (1 + 0.12)-5 - $16,000 = 0 -$221.49 0 Not close enough! Try i = 12.5% = $22.567 0 Not close enough! Try i = 12.6% = -$16.76 0 Not close enough! Therefore, IRR = 12.55% Note: Using a financial calculator, IRR = 12.55733% Example 4.11: Alternative Solution Note there are equal period cash inflows of $4,500 from the end of year 1 through the end of year 5, making this an ordinary annuity. (1-(1+i)-R PVA ordinary =PMT IRR is the discount rate at which: PVcash inslows - PVcash outflows = 0 The formula above simplifies to: PVA-PV Initial cash outflow = 0 |- $16,000 = 0 $4,500 + (1-(1+0)--) - $16,000 = 0 PMT PMT (1-(1 +9**) $16000=0 Tryi= 12% $4,500 - (1 - (1+0.12)-S) - $16,0 -$221.49 +0 Not close enough! Try i = 12.5% = $22.56 0 Not close enough! Try i = 12.6% -$16.76 0 Not close enough! Therefore, IRR = 12.55% What is the internal rate of return (to the nearest one-half percent) on an investment costing $500,000 and having expected future after-tax net cash flows of: Year Net Cash Flow ($) 100,000 150,000 150,000 300,000 (includes salvage) Use the trial-and-error method and write out all your work. Hint: Start at 11%. (Points: 20)