Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,240,000; the new one will cost $1,500,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $240,000 after five years. The old computer is being depreciated at a rate of $248,000 per year. It will be completely written off in three years. If we don’t replace it now, we will have to replace it in two years. We can sell it now for $360,000; in two years, it will probably be worth $114,000. The new machine will save us $284,000 per year in operating costs. The tax rate is 40 percent, and the discount rate is 11 percent.

a. Calculate the EAC for the old computer and the new computer. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

EAC New computer $ ____

Old computer $ ____

b. What is the NPV of the decision to replace the computer now? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

NPV $ _______

Answer 1

Sol (a) EAC is Equivalent Annual Cost that can be computed by dividing the total present value of cash outflow since we are talking about cost only with the Present Value annuity factor using the Time and Discount Rate. In our case for New Machine Cash Outflow is only the Initial Outflow whose Present Value is also $ 15,00,000 and Present Value Annuity Factor for 5 years at 11% through PVIFA table gives: 3.696, thus EAC for New Machine = -$15,00,000/ 3.696 = - $ 4,05,855.46

EAC for Old Machine: The old machine costs are basically excess operating cost $2,84,000.00 for Year 1 to Year 3 thus EAC for old machine is only -$2,84,000.00

Sol (b) NPV of the decision to replace the computer now is worked as under:

Cash flow for New Machine								Calculation of Depreciation New Machine
Time	Initial Outlay	Cash Inflows	Description of Cash Flow	DF @ 11%	PV of Cash Flows			Initial Cost	1500000
0	-1500000		Cost of New Machine	1	-1500000.00			Salvage Value	240000
0		360000	Inflow from Selling Old Computer	1	360000.00			Term	5	Years
1		271200	Net Profit Notional + Depreciation	0.901	244324.32			Depreciation SLM	252000	(Initial Cost-Salvage Value)/Term
2		271200	Net Profit Notional + Depreciation	0.812	220112.00
3		271200	Net Profit Notional + Depreciation	0.731	198299.10			Savings from New Machine / Year for 5 Years	284000
4		271200	Net Profit Notional + Depreciation	0.659	178647.84			Less: Depreciation	-252000
5		271200	Net Profit Notional + Depreciation	0.593	160944.00			Notional Profit	32000
5		240000	Salvage Value after 5 year	0.593	142428.32			Tax @ 40%	12800
			NPV of the decision to replace Computer Now		4755.59			Net Profit Notional	19200
								Add Depreciation	252000
								Cash Inflow	271200