Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,780,000; the new one will cost, $2,257,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $525,000 after five years. The old computer is being depreciated at a rate of $400,000 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 $603,000; in two years, it will probably be worth $177,000. The new machine will save us $377,000 per year in operating costs. The tax rate is 21 percent, and the discount rate is 8 percent. a-1. Calculate the EAC for the 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.) a-2. 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.)

Answer 1

a-1). To calculate the EAC, NPV for each computer has to be calculated first.

NPV = -initial investment + Operating cash flows + after-tax salvage value where

initial investment = cost of new computer; opportunity cost for not selling the selling the old computer now

Operating cash flows = savings*(1-Tax rate) + (depreciation*Tax rate)

After-tax salvage value = salvage value - Tax rate*(salvage value - book value)

After calculating NPV, it is annualized over the remaining life of the computers to get the EAC.

Formulas		Old computer	New computer
n	Life	2	5
OC	Original cost	1780000	2257000
C0	Cost now	603000	2257000
D = OC/number of years left	Depreciation/year	400000	451400
SV1	Salvage value after 2 years	177000	na
SV2	Salvage value at end of life	na	525000
S	Savings/year	na	377000
T	Tax rate	21%	21%
r	Discount rate	8%	8%
Equal to OC	Initial outlay [a]	na	2257000
C0 - T*(C0 - (D*3))	Opportunity cost [a]	728370	na
(S*(1-T)) + (D*T)	Operating Cash Flow (OCF)	84000	392624
Using PV function: PV(r, n, -OCF)	PV of OCF [b]	149794.24	1567633.79
Salvage value - T*(Salvage value - Book value)	After-tax salavge value (ASV)	223830.00	414750.00
ASV/(1+r)^n	PV of ASV [c]	191898.15	282271.88
[b] + [c] - [a]	NPV	-386677.61	-407094.33
Using PMT function: PMT(r, n, - NPV)	EAC	-216836.91	-101959.40

a-2). To find the NPV of the decision to replace the computer now, incremental cash flows have to be found, discounted back to the present and then added together to get the NPV.

Formulas	Year (n)	0	1	2	3	4	5
-Initial outlay + OCF + after-tax salvage value	New computer cash flows (CF1)	-2257000	392624	392624	392624	392624	807374
-Opportunity cost + OCF + after-tax salvage value	Old computer cash flows (CF2)	-728370	84000	307830	0	0	0
CF1 - CF2	Incremental cash flow (CF)	-1528630	308624	84794	392624	392624	807374
1/(1+8%)^n	Discount factor @ 8%	1.000	0.926	0.857	0.794	0.735	0.681
CF*Discount factor	PV of CF	-1528630.00	285762.96	72697.19	311677.59	288590.36	549485.18
Sum of all PVs	NPV	-20416.72