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You purchase a machine for $200,000 which belongs in a 30% CCA class. What is the...

You purchase a machine for $200,000 which belongs in a 30% CCA class. What is the present value of the CCA tax shield on the machine if it is sold at the end of the fifth year for $24,000, your tax rate is 35%, and the appropriate discount rate is 10%?

Select one:

a. $52,215

b. $46,202

c. $86,994

d. $66,623

e. $40,143

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Answer #1

Sol:

Cost of equipment (C) = $200,000

CCA rate (d) = 30%

Tax rate (Tr) = 35%

Discount rate (Dr) = 10%

Machine resale value (S) = $24,000

Machine life (n) = 5 years

To compute present value (PV) of the CCA tax shield

PV = [(C x d x Tr) / (Dr + d) x ( 1 + Dr / 2 )) / (1 + Dr)] - [(S x d x Tr) / (Dr + d) x ( 1/(1 + Dr)^n]

PV = [(200,000 x 30% x 35%) / (10% + 30%) x (1 + 10%/2)) / (1 + 10%)] - [(24000 x 30% x 35%) / (10% + 30%) x 1/(1 + 10%)^5]

PV = [(200,000 x 0.30 x 0.35) / (0.10 + 0.30) x (1 + 0.10/2)) / (1 + 0.10)] - [(24000 x 0.30 x 0.35) / (0.10 + 0.30) x 1/(1 + 0.10)^5]

PV = (21000 / 0.40) x (1.05/1.10) - (2520/0.40) x 1/(1.10)^5

PV = (52500 x 0.954545) - (6300 x 0.620921)

PV = 50113.636363 - 3911.8043

PV = $46,201.83 rounded to $46,202

Therefore present value (PV) of the CCA tax shield is $46,202

Answer is b. $46,202

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