Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,900,000; the new one will cost, $2,313,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $615,000 after five years. The old computer is being depreciated at a rate of $448,000 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 $657,000; in two years, it will probably be worth $195,000. The new machine will save us $413,000 per year in operating costs. The tax rate is 22 percent, and the discount rate is 11 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.) a-1. Old computer EAC New computer EAC NPV a-2

Answer 1

a-1). First we need to calculate the NPVs for both computers.

NPV = -initial investment (or opportunity cost) + PV of Operating Cash Flow (OCF) + After-tax salvage value (ASV)

After finding the NPV, we annualize the NPV over the remaining life of the computers to find the EAC.

Formulas		Old computer	New computer
n	Life	2	5
OC	Original cost	1900000	2313000
C0	Cost now	657000	2313000
D = OC/number of years left	Depreciation/year	448000	462600
SV1	Salvage value after 2 years	195000	na
SV2	Salvage value at end of life	na	615000
S	Savings/year	na	413000
T	Tax rate	22%	22%
r	Discount rate	11%	11%
Equal to OC	Initial outlay [a]	na	2313000
C0 - T*(C0 - (D*3))	Opportunity cost [a]	808140	na
(S*(1-T)) + (D*T)	Operating Cash Flow (OCF)	98560	423912
Using PV function: PV(r, n, -OCF)	PV of OCF [b]	168786.30	1566735.10
Salvage value - T*(Salvage value - Book value)	After-tax salavge value (ASV)	250660.00	479700.00
ASV/(1+r)^n	PV of ASV [c]	203441.28	284678.60
[b] + [c] - [a]	NPV	-435912.42	-461586.30
Using PMT function: PMT(r, n, - NPV)	EAC	-254543.93	-124891.55

a-2). Replacement decision NPV - It is the NPV of the incremental cash flows (cash flows associated with the new computer less cash flows associated with the old computer) over the life of the assets.

0 -2313000 903612 Formulas Year (n) -Initial outlay + OCF + after-tax salvage value New computer cash flows (CF1) -Initial outlay + OCF + after-tax salvage value old computer cash flows (CF2) CF1 - CF2 Incremental cash flow (CF) 1/(1+11%)^n Discount factor @ 11% CF*Discount factor PV of CF Sum of all PVs NPV 21 423912 3492201 74692 0.812 60621.70 423912 98560 325352 0.901 293109.91 -1504860 1.000 - 1504860.00 -25673.88 423912 0 423912 0.7311 309960.80 423912 0 423912 0.659 279243.96 903612 0.593 536249.74

423912 423912 903612 Formulas Year (n) -Initial outlay + OCF + after-tax salvage value New computer cash flows (CF1) -Initial outlay + OCF + after-tax salvage value old computer cash flows (CF2) CF1 - CF2 Incremental cash flow (CF) 1/(1+11%)^n Discount factor @ 11% CF*Discount factor PV of CF Sum of all PVS NPV -2313000 -8081401 -1504860 1.000 -1504860.00 -25673.88 423912 98560 325352 0.901 293109.91 423912 349220 74692 0.812 60621.70 423912 0.731 309960.80 423912 0.659 279243.96 903612 0.593 536249.74