Question

23) ABC Inc.has a choice between two machines A and B. The company requires a return of 15% percent and uses straight-line depreciation to a zero book value over a machine's life. Machine A has a cost of $300,000, annual operating costs of $9,000, and a life of 3 years. Machine B costs $225,000, has annual operating costs of $12,000, and a life of 2 years. Whichever machine is purchased will be replaced at the end of its useful life. Which machine should ABC purchase and why? Assume a tax rate of 21%.

Please show the calculations. Thank you in advance :)

Answer 1

ABC inc,has two choice

Machine A cost = 300000    3 years

Annual cost = 9000

Machine B cost = 225000     last for 2 years

Operating cost = 12000

Required return =15%

Tax rate = 21%

Depreciated both straight line

Which machine should ABC purchase and why? For answer it through calculating EAC (equivalent annual cost ).

* ABC purchase, Machin A becuse it has Lowest EAC

Equivalent annual cost (EAC) is the annual cost of maintaining an asset determined by dividing the net present value of the asset purchase, operations and maintenance cost by the present value of annuity factor. It is a capital budgeting decision tool used by companies to compare assets with unequal useful lives..

Calculate EAC of each machine

EAC = Net Present value of cash flow / PV of annuity $1 factor discounted

Machine A

So first calculate Present value of cash flow

Operating cash flow

Operating cost	(9000)
- Tax benefits of cost. @ rate 21%	1890
= cost after tax (excluding dep.)	(7110)
+ depreciation tax shield (calculation is below)	21000
= operating cash flow	= 13890

Machine A costs $300000,

Dep = 300000 / 3 = 100000

Tax shield = 100000 * 21% = 21000

years	Cash flow	PV of $ 1 factor @ 8%	Present value
0th year(initial )	300000	( 1 /1+15%)0 = 1	300000
1 to 3 years OCF	13890	( 1 /1+15%)3GT =2.283225	317114

NPV = PV of cash flow - initial investment

NPV =     317114   - 300000    = -268286

PV of annuity due $1 @ 15% for 3 period = (1/1+15%)3GT = 2.283225

EAC = - 268286  / 2.283225   =   - $117503.10

Machine B costs 225000     last for 9 years

Dep = 225000 /   2 = 112500

Tax shield = 112500 * 21% = 23625

Annual operating cash flow

Operating cost	(12000)
- Tax benefits of cost. @ rate 21%	2520
= cost after tax (excluding dep.)	(9480)
+ depreciation tax shield (calculation is below)	23625
= operating cash flow	= 14145

years	Cash flow	PV of $ 1 factor @ 8%	Present value
0th year(initial )	225000	( 1 /1+15%)0 = 1	225000
1 to 2 years OCF	14145	( 1 /1+15%)2GT =1.62571	22995.65

NPV = 22995.65   - 225000   = - 202004.35

PV of annuity due $1 @ 15% for 2 period = (1/1+15%)2GT = 1.62571

EAC = - $202004.35  / 1.62571   = - $124256.07

EAC

Machine A	- $117503
Machine B	- $124256

Here Machine A is Lower EAC of - $117503, so take this project. It is profit than Machine B

** The minus (−) sign indicates that it is a cost and not a benefit. Since Machine A have lower equivalent annual cost, they should be the preferred option.