Question

Your firm is contemplating the purchase of a new $625,000 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $105,000 at the end of that time. You will save $196,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $120,000 (this is a one-time reduction).

If the tax rate is 25 percent, what is the IRR for this project? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Initial Investment

Initial Investment = Cost of the Asset + One Time Reduction in Working Capital

= -$625,000 + 120,000

= -$505,000

Annual Cash Inflow

Operating Cash Flow = Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= $196,000(1 – 0.25) + [($625,000 / 5 Years) x 0.25]

= $147,000 + $31,250

= $178,250

Year 1-5 Cash Flow = $178,250

Year 6 Cash Flow = Annual cash flow – Working Capital Outflow + After tax Salvage Value

= $178,250 – 120,000 + [$105,000 x (1 – 0.25)]

= $137,000

Internal Rate of Return (IRR) Calculation

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 21%

Year	Annual Cash Flow ($)	Present Value factor at 21%	Present Value of Cash Flow ($)
1	1,78,250	0.82645	1,47,314.05
2	1,78,250	0.68301	1,21,747.15
3	1,78,250	0.56447	1,00,617.48
4	1,78,250	0.46651	83,154.94
5	1,37,000	0.38554	52,819.43
TOTAL			5,05,653.05

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $5,05,653.05 - $505,000

= $653.05

Step – 2, NPV at 21% is positive, Calculate the NPV again at a higher discount rate, Say 22%

Year	Annual Cash Flow ($)	Present Value factor at 22%	Present Value of Cash Flow ($)
1	1,78,250	0.81967	1,46,106.56
2	1,78,250	0.67186	1,19,759.47
3	1,78,250	0.55071	98,163.50
4	1,78,250	0.45140	80,461.89
5	1,37,000	0.37000	50,689.90
TOTAL			4,95,181.32

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $4,95,181.32 - $505,000

= -$9,818.68 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.21 + [$653.05 x (0.22 – 0.21)]

              $653.05 – (-$9,818.68)

= 0.21 + 0.0007

= 0.2107

= 21.07%

“Therefore, the Internal Rate of Return (IRR) = 21.07%”