Question

"A firm purchases a new machine for $159,000. It borrows $63,600 at 6.3% annual interest to be repaid in 2 years. The machine is depreciated using a 5-year MACRS. At the end of 3 years, the firm sells the machine for $49,000. The firm's tax rate is 33%. How much does the firm pay or save in taxes from selling this machine at the end of 3 years? In other words, what is the gains tax?
If the firm will have to pay taxes from selling this machine, enter your answer as a positive number. If the firm will save money in taxes from selling the machine, enter the answer as a negative number. "

Answer 1

Tax is always calculated on the profit, more the profit more the tax amount. Non-cash expenses and losses serve as tax beneficial because they reduce the profit without actual reduction in cash. Cash expenses also reduce profit but with actual cash payments. After the machine was bought there were two deductions from the profit depreciation and interest payments on the borrowed money to purchase the machine.

Loan repayment schedule is below that gives us the total interest paid in the two-year repayment period. It is assumed that the annual interest is compounded monthly and the monthly interest comes to 0.063 / 12 = 0.00525 which is 0.525%.

Monthly payment = P x r / (1 - ((1 + r) ^-n))

Where,

P = Initial loan amount

r = rate of interest according to periods and intervals

n = number of periods

The total interest payment in 2 years comes to $4257.50.

Now let’s calculate the total depreciation amount that reduced the profit till the machine was sold. The below table calculates with the MACRS depreciation rate.

The total depreciation in the machine was (159000 – 69889) $89111.

As we can see the book value at the end of the year 3 was $69889 and the machine was sold below it at $49000 which means that there was a loss of (69889 – 49000) $20889 which also reduces the profit.

Hence the total tax savings that resulted was [($4257.50 + $89111 + $20889) x 0.33] $37704.975.

Depreciation schedule
EOY	Dep rate	Dep amount	Book Value
0			159000
1	20%	31800	127200
2	32%	40704	86496
3	19.20%	16607.232	69888.768

Loan repayment schedule
Month	Payment	Interest	Principal	Balance
1	$2,827.40	$333.90	$2,493.50	$61,106.50
2	$2,827.40	$320.81	$2,506.59	$58,599.92
3	$2,827.40	$307.65	$2,519.75	$56,080.17
4	$2,827.40	$294.42	$2,532.98	$53,547.20
5	$2,827.40	$281.12	$2,546.27	$51,000.92
6	$2,827.40	$267.75	$2,559.64	$48,441.28
7	$2,827.40	$254.32	$2,573.08	$45,868.20
8	$2,827.40	$240.81	$2,586.59	$43,281.61
9	$2,827.40	$227.23	$2,600.17	$40,681.45
10	$2,827.40	$213.58	$2,613.82	$38,067.63
11	$2,827.40	$199.86	$2,627.54	$35,440.09
12	$2,827.40	$186.06	$2,641.34	$32,798.75
13	$2,827.40	$172.19	$2,655.20	$30,143.55
14	$2,827.40	$158.25	$2,669.14	$27,474.41
15	$2,827.40	$144.24	$2,683.16	$24,791.25
16	$2,827.40	$130.15	$2,697.24	$22,094.01
17	$2,827.40	$115.99	$2,711.40	$19,382.61
18	$2,827.40	$101.76	$2,725.64	$16,656.97
19	$2,827.40	$87.45	$2,739.95	$13,917.02
20	$2,827.40	$73.06	$2,754.33	$11,162.69
21	$2,827.40	$58.60	$2,768.79	$8,393.90
22	$2,827.40	$44.07	$2,783.33	$5,610.57
23	$2,827.40	$29.46	$2,797.94	$2,812.63
24	$2,827.40	$14.77	$2,812.63	$0.00
Total interest		$4,257.50