Question

Spherical Manufacturing recently spent $ 14 million to purchase some equipment used in the manufacture of disk drives. This equipment has a CCA rate of 45 % and​ Spherical's marginal corporate tax rate is 28 %.

a. What are the annual CCA deductions associated with this equipment for the first five​ years?

b. What are the annual CCA tax shields for the first five​ years?

c. What is the present value of the first five CCA tax shields if the appropriate discount rate is 12 % per​ year?

d. What is the present value of all the CCA tax shields assuming the equipment is never sold and the appropriate discount rate is 12 % per​ year?

e. How might your answer to part​ (d) change if Spherical anticipates that its marginal corporate tax rate will increase substantially over the next five​ years?

Answer 1

Solution:

a)Statement showing annual CCA deductions associated with this equipment for the first five​ years

For the first year CCA deduction is allowed at half rate.

Year	Opening balance(a)	Depreciation(a*rate)(b)	Closing balnce(a-b)
1	14000,000	7000,000*45%=$3,150,000	10850,000
2	10850,000	10850,000*45%=$4,882,500	5,967,500
3	5,967,500	5,967,500*45%=$2,685,375	3,282,125
4	3,282,125	3,282,125*45%=$1,476,956.25	1,805,168.75
5	1,805,168.75	1,805,168.75*45%=812,325.94	992,842.81
CCA deductions for first 5 year	$13,007,157.19

b)Statement showing tax sheild for the first five​ years

Year	Depreciation($)	Tax shield(Depreciation*Tax rate)
1	3,150,000	3,150,000*28%=$882,000
2	4,882,500	4882,500*28%=$1,367,100
3	2,685,375	2,685,375*28%=$751,905
4	1,476,956.25	1,476,956.25*28%=$413,547.75
5	812,325.94	812,325.94*28%=$227,451.26
Tax sheild for the first five​ years	$3642004.01

c)Present Value of Tax sheild

=Tax sheild/(1+Discount rate)^no. of year

=882,000/(1+0.12)^1+1,367,100/(1+0.12)^2+751,905/(1+0.12)^3+413,547.75/(1+0.12)^4+227,451.26/(1+0.12)^5

=$2804,414.00

d)Calculation of present value of all the CCA tax shields(PVCCATS)

d=CCA rate

C=cost of asset

T=tax rate

k=discount rate

Since there is no salvage value and there is no replacement of equipment,hence PVCCATS is calculated using following formula;

PVCCATS=C*(dT/k+d)*(1+0.5K/1+K)

=$14000,000*(0.45*0.28/0.12+0.28)*(1+0.5*0.12/1+0.12)

=$14000,000*0.315*0.946429

=$4,173,750.00