Question

Spherical Manufacturing recently spent

$18

million to purchase some equipment used in the manufacture of disk drives. This equipment has a CCA rate of

30%

and​ Spherical's marginal corporate tax rate is

32%.

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 equiment 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

a) Annual CCA deduction for 1st year = $18 million *30 % = $5.4 million

Annual CCA deduction for 2nd year = $18 million *0.7 * 30 % = $3.78 million

Annual CCA deduction for 3rd year = $18 million *0.7^2 * 30 % = $2.646 million

Annual CCA deduction for 4th year = $18 million *0.7^3 * 30 % = $1.8522 million

Annual CCA deduction for 5th year = $18 million *0.7^4 * 30 % = $1.29654 million

b) Annual CCA tax shield for 1st year = $5.4 million * 32% =$1.728 million

Annual CCA tax shield for 2nd year = $3.78 million * 32% =$1.2096 million

Annual CCA tax shield for 3rd year = $2.646 million * 32% =$0.84672 million

Annual CCA tax shield for 4th year = $1.8522 million * 32% =$0.592704 million

Annual CCA tax shield for 5th year = $1.29654 million * 32% =$0.414893 million

c) present value of the first five CCA tax shields (million $)

=1.728/1.12+1.2096/1.12^2+0.84672/1.12^3+0.592704/1.12^4+0.414893/1.12^5

=3.721916853

So, present value of the first five CCA tax shields = $3.721916853 million or $3,721,916.85

d) The Present value of all the CCA Tax shields (million $)

=1.728/1.12+1.2096/1.12^2+0.84672/1.12^3+0.592704/1.12^4+0.414893/1.12^5+ .....

=1.728/1.12 + 1.728*0.7/1.12^2+1.728*0.7^2/1.12^3+1.728*0.7^3/1.12^4+.........

Applying the formula for sum of Infinite GP

= (1.728/1.12) / (1-0.7/1.12)

= 4.114285714

So, present value of the All CCA tax shields = $4.114285714 million or $4,114,285.71