Question

Deriving cash flows for asset disposition. Custom Machining Company (CMC) purchased a made-to-order machine tool for grinding machine parts. The machine costs $160,000, and CMC installed it yesterday. Today, a vendor offers a machine tool that will do exactly the same work but costs only $80,000. Assume that the cost of capital is 12 percent, that both machines will last five years, that CMC will depreciate both machines on a straight-line basis for tax purposes with no salvage value, that the income tax rate is and will continue to be 40 percent, and that CMC earns sufficient income that it can offset any loss from disposing of or depreciating the ‘‘old’’ machine against other taxable income. How much, at a minimum, must the ‘‘old’’ machine fetch upon resale at this time to make purchasing the new machine worthwhile?

I have asked the question before, but I do not understand how depreciation * tax rate (for example $16,000* .4 = $64,000, instead of $4,000 or $32,000* .4= $128,000, instead of $8,000?).

Answer 1

Answers :-

If the old machine is used:

Annual depreciation = 160,000 /5 years = 32,000

Depreciation, decreases the Pre-tax income, and hence tax outlay decreases.

Thus the cash inflow due to tax benefit earned on annual depreciation = Depreciation * tax rate = 32,000 * 40%= 128,000

This tax benefit (cash inflow) is received by the company annually for 5 years.

Thus the present value of the cash inflow from tax benefit on depreciation = 128,000/(1+12%)¹ + 128,000/(1+12%)² + 128,000/(1+12%)³ + 128,000/(1+12%)⁴ + 128,000/(1+12%)⁵

= 46,141.14

If the new machine is used:

Annual depreciation = 80,000 /5 years = 16,000

Thus the cash inflow due to tax benefit earned on annual depreciation =

Depreciation * tax rate = 16,000 * 40%= 64,000

This tax benefit (cash inflow) is received by the company annually for 5 years.

Thus the present value of the cash inflow from tax benefit on depreciation = 64,000/(1+12%)¹ + 64,000/(1+12%)² + 64,000/(1+12%)³ + 64,000/(1+12%)⁴ + 64,000/(1+12%)⁵

= 23,070.57

Thus the difference in cash inflow due to tax benefit on depreciation = 23,070.57 - 46,141.14 = - 23,070.57

This difference in cash inflow is a loss, if the new machinery is purchased.

Expense, due to buying of the new machine: -80,000

Let us assume the old machinery is sold at 'X'

Gain from sale of old machinery = X - 160,000

Tax on gain from sale of old machinery = (X - 160,000)* 0.4

Total cash inflow from sale of old machinery = X - tax paid = X - (X - 160,000)* 0.4

In order to make the purchase worth while, the total cash earned from the sale of the machinery should finance the purchase of the new machinery, as well the loss in cash inflow (from tax benefit on depreciation)

Thus X - (X - 160,000)*0.4 = 23,070.57 + 80,000

=> X = 65,117.62

Therefore the old machinery need to be sold at the maximum value of 65,117.62