Question

"A firm is considering purchasing a computer system.

-Cost of system is $191,000. The firm will pay for the computer system in year 0.

-Project life: 5 years

-Salvage value in year 0 (constant) dollars: $13,000

-Depreciation method: five-years MACRS

-Marginal income-tax rate = 37% (remains constant over time)

-Annual revenue = $146,000 (year-0 constant dollars)

-Annual expenses (not including depreciation) = $77,000 (year-0 constant dollars) If the general inflation rate is 3.7% during the project period (which will affect all revenues, expenses, and the salvage value but not depreciation), determine the INFLATION-FREE IRR' of the computer system. Enter your answer as a percentage between 0 and 100."

Answer 1

	0	1	2	3	4	5
Net annual revenues at Year 0 constant dollars (146000-77000)		69000	69000	69000	69000	69000
Depreciation		38200	61120	36672	22003	22003
Depreciation at Year 0 constant dollar's [Depreciation/(1.037)^n]		36837	56836	32885	19027	18348
NOI at Year 0 constant dollar's		32163	12164	36115	49973	50652
Tax at 37%		11900	4501	13363	18490	18741
NOPAT at Year 0 constant dollars		20263	7663	22752	31483	31911
Add: Depreciation		36837	56836	32885	19027	18348
OCF at Year 0 constant dollars		57100	64499	55637	50510	50259
Capital expenditure	191000
Salvage value at future dollars = 13000*1.037^5 =			15590
Book value			11002
Loss on sale			-4588
Tax shield on loss at 37%			-1697
After tax salvage value = 15590+1697 =			17287
After tax salvage value at Year 0 constant dollars = 17287/1.037^5 =			14415
Annual after tax cash flows in Year 0 constant dollars	-191000	57100	78915	55637	50510	50259
ROR has to be found by trial and error. It is that discount rate for which NPV = 0.
Discounting with 17%
PVIF at 17%	1.00000	0.85470	0.73051	0.62437	0.53365	0.45611
PV at 17%	-191000	48803	57648	34738	26955	22924	68
Discounting with 18%
PVIF at 18%	1	0.8475	0.7182	0.6086	0.5158	0.4371
PV at 18%	-191000	48390	56675	33863	26052	21969	-4051
The ROR lies between 17% and 18%.
The value of ROR by simple interpolation = 17+68/(68+4051) =	17.02%