Question

As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines.
Both machines perform the same function but differ in age. The newer machine could be sold today for $74,000. Its operating costs
are $23,200 a year, but at the end of five years, the machine will require a $18,400 overhaul (which is tax deductible).
Thereafter, operating costs will be $31,600 until the machine is finally sold in year 10 for $7,400.

The older machine could be sold today for $26,600. If it is kept, it will need an immediate $28,000 (tax-deductible) overhaul.
Thereafter, operating costs will be $36,800 a year until the machine is finally sold in year 5 for $7,400.

Both machines are fully depreciated for tax purposes. The company pays tax at 21%.Cash flows have been forecasted in real terms.
The real cost of capital is 10%.

   Equivalent Annual Cost
New machine   $ ?
Old machine   $ ?

Answer 1

New Machine
Year	0	1	2	3	4	5	6	7	8	9	10
Operating Cost		23200	23200	23200	23200	23200	31600	31600	31600	31600	31600
Overhaulling Cost						18400
Salvage value											7400
Total		23200	23200	23200	23200	41600	31600	31600	31600	31600	24200
Tax Shield @21%		4872	4872	4872	4872	8736	6636	6636	6636	6636	5082
Post Tax Cost		18328	18328	18328	18328	32864	24964	24964	24964	24964	19118
PV Factor @ 10%		0.909	0.8264	0.7513	0.683	0.6209	0.5645	0.5132	0.4665	0.4241	0.3855
PV of Cash Outflow		16660.152	15146.26	13769.83	12518.02	20405.26	14092.18	12811.5248	11645.71	10587.23	7369.989
Total of PV	135006.15
PVAF(10%.10)	6.1444
Equivalent Annual Cost	21972.23
Old Machine
Year	0	1	2	3	4	5
Operating Cost		36800	36800	36800	36800	36800
Overhaulling Cost	28000					18400
Salvage value						7400
Total	28000	36800	36800	36800	36800	47800
Tax Shield @21%	5344.92	7728	7728	7728	7728	10038
Post Tax Cost		29072	29072	29072	29072	37762
PV Factor @ 10%		0.909	0.8264	0.7513	0.683	0.6209
PV of Cash Outflow	22655.08	26426.448	24025.1	21841.79	19856.18	23446.43		138251.02
Total PV	138251.02
PVAF(10%,5)	3.7906
Equivalent Annual Cost	36472.07

Calculation of Tax shield in year 0

= 28000 *21%

=5880

this will be at the end of year

therefore, PV= 5880 *0.9090

= 5344.92