Question

"A firm is considering purchasing a computer system. The following data has been collected.
- Cost of the system: $125,000
- Project life: 6 years
- Salvage value at the end of year 6: $18,000
- Depreciation method: five-year MACRS
- Tax rate: 33%
- Annual revenue from project: $109,000
- Annual expenses (not including depreciation): $88,000
The firm will borrow the entire $125,000 at 5.3% interest to be repaid in 2 annual payments.
The firm's MARR is 15%. Determine the IRR for the computer system. Enter your answer as a percentage between 0 and 100."

Answer 1

In order to calculate IRR, we need to find annual cash flows from the project. The depreciation methodology for computer system is given as five-year MACRS. The annual depreciation can be calculated with the help of IRS convention – 200% declining balance switching to straight line with half-year convention for five years.

Years	IRS Convention	Declining Balance	Annual Depreciation
1	20%	1,25,000.00	25,000.00
2	32%	1,00,000.00	40,000.00
3	19.20%	60,000.00	24,000.00
4	11.52%	36,000.00	14,400.00
5	11.52%	21,600.00	14,400.00
6	5.76%	7,200.00	7,200.00

The firm is borrowing the entire $125,000 at 5.3% interest to repaid in 2 annual payments. The interest can be computed as under:

Years	Principal O/s	Interest
1	1,25,000	6,625.00
2	62,500	3,312.50

The income statement will look as under:

Particulars/ Years	1	2	3	4	5	6
Revenue	1,09,000	1,09,000	1,09,000	1,09,000	1,09,000	1,09,000
Annual Exp.	88000	88000	88000	88000	88000	88000
Depreciation	25,000.00	40,000.00	24,000.00	14,400.00	14,400.00	7,200.00
Interest	6625	3312.5	0	0	0	0
Total Expenses	119625	131312.5	112000	102400	102400	95200
PBT	-10,625	-22,313	-3,000	6,600	6,600	13,800
Tax @33%	-3,506.25	-7,363.13	-990.00	2,178.00	2,178.00	4,554.00
PAT	-7,118.75	-14,949.38	-2,010.00	-4,422.00	4,422.00	9,246.00
EBITDA	24,506.25	28,363.13	21,990.00	18,822.00	18,822.00	16,446.00

The above table doesn’t consider the tax benefit that will be received on account of the losses lodged in the earlier years.

EBITDA is calculated to arrive at the cash flow generated from the project. Considering the salvage value, the total cash flow during the years will look as under:

0	-125,000.00
1	24,506.25
2	28,363.13
3	21,990.00
4	18,822.00
5	18,822.00
6	34,446.00
IRR	4.75%