Question

Alpha company wants to replace its equipment system (class 8, 20%). The existing equipment can be sold today for $40,000. In another five years it will have a resale value of zero. The new equipment costs $250,000, has a five-year life, and has a $47,000 resale value in five years. The tax rate is 45%, and the opportunity cost of capital is 12%. Due to increased worker productivity and morale, the estimated benefits before tax(∆CFBT) are $65,000 per year. Should the equipment be replaced?

Answer 1

Sale value of existing equipment = 40,000

Cost of New Equipment= 250,000

Resale value of this equipment = 47,000

Tax Rate = 45%

Interest rate/Opportunity cost = 12%

Benefit before tax = 65,000

Now, the decision to replace the equipment will depend on the benefits and cost. If the benefits are more than the cost, the equipment should be replaced.

Total cost= cost of equipment+ Opportunity cost of the capital

= 250,000 + 12% * capital for 5 years

	Capital at beginning of year	% Interest	Interest	Capital at the end of year
1st Year	250000	0.12	30000	280000
2nd	280000	0.12	33600	313600
3rd	313600	0.12	37632	351232
4th	351232	0.12	42147.84	393379.8
5th	393379.8	0.12	47205.58	440585.4
Total			190585.4

So, Total cost is 250,000 + 190,585.4=440585, depreciation will not be added as the salvage value is given and depreciation is adjusted there.

Total Benefit: Salvage Value of 1st equipment + Salvage value of second equipment + CFBT after tax for 5 years+ opportunity cost of capital received.

= 40,000+47,000+(65000-45%)*5+ opportunity cost

But, since the opportunity cost is given, the same will also be calculated for 40,000 that we received by selling the 1st equipment and on CFBT after tax every year.

	Capital at beginning of year	% Interest	Interest	Capital at the end of year
1st Year	40000	0.12	4800	44800
2nd	44800	0.12	5376	50176
3rd	50176	0.12	6021.12	56197.12
4th	56197.12	0.12	6743.654	62940.77
5th	62940.77	0.12	7552.893	70493.67
Total			30493.67

It is assumed that the equipment was sold at the beginning of the year

	Capital at beginning of year	% Interest	Interest	Capital at the end of year
2nd	35750 (65000-45%)	0.12	4290	40040
3rd	75790 (40040+65000-45%)	0.12	9094.8	84884.8
4th	120634.8 (84884.8+65000-45%)	0.12	14476.18	135111
5th	170861 (135111+65000-45%)	0.12	20503.32	191364.3
Total			48364.29

Interest will be earned on CFBT from second year as it is assumed that income is earned at the end of year

No interest will be earned on 47,000 as it is sold at the end of 5 years

Total Benefit= 40000+47000+65000-45%*5+30493.67+48364.29=344608

Since the benefit is less than the cost, equipment should not be replaced.