Question

Suppose that under straight-line depreciation, a corporation would be allowed to depreciate a $10,000 asset over 4 years. Under accelerated depreciation, the corporation would be allowed to depreciate 75% of the asset's value immediately in the first year and the remaining 25% in the second year. Assume that the discount rate is 10%.

(a) Suppose that the corporation normally makes $56,000 of annual profit on which it pays a 35% tax every year. What is the present discounted value of the tax deduction under accelerated depreciation?
(b) How much higher is the present discounted value of the firm's profits under accelerated depreciation than under straight-line depreciation??

Answer 1

Solution :

Asset value = $10,000 , Years = 4,

So if asset is going to depreciate using straight-line method then depreciation per year = 25% * $10,000 = $2,500

Under accelarated method of depreciation Year 1 depreciation will be 75% of 10,000 i.e. 75%*10,000 = 7500

Year 2 depreciation = 25% * 10,000 = 2,500

Tax rate = 35%, Discount rate = 10%

Question Part A )

Under accelarated method

Year 1 : Tax shield on depreciation = Depreciation * tax rate = 7500 * 35% = 2625

Discounted value = Tax shield / (1+ Discount rate ) = 2625 / (1+0.1) = 2625/1.1 = 2386.36

Year 2 : Tax shield on depreciation = Depreciation * tax rate = 2500 * 35% = 875

Discounted value = Tax shield / (1+ Discount rate )^2 = 875 / (1+0.1)^2 = 875/1.1^2 = 723.14

Net Present value = Discounted value of year 1 + Discounted value of year 2 = 2386.36 + 723.14 = 3109.50

Part B )

Under straight-line depreciation method

Year 1 : Tax shield on depreciation = Depreciation * tax rate = 2500 * 35% = 875

Discounted value = Tax shield / (1+ Discount rate ) = 875 / (1+0.1) = 875/1.1 =795.45

Year 2 : Tax shield on depreciation = Depreciation * tax rate = 2500 * 35% = 875

Discounted value = Tax shield / (1+ Discount rate )^2 = 875 / (1+0.1)^2 = 875/1.1^2 =723.14

Year 3 : Tax shield on depreciation = Depreciation * tax rate = 2500 * 35% = 875

Discounted value = Tax shield / (1+ Discount rate )^3 = 875 / (1+0.1)^3 = 875/1.1^3 =657.40

Year 4 : Tax shield on depreciation = Depreciation * tax rate = 2500 * 35% = 875

Discounted value = Tax shield / (1+ Discount rate )^4 = 875 / (1+0.1)^4 = 875/1.1^4 =597.64

Total discounted value = Sum of Discounted value of all 4 years 795.45 + 723.14 + 657.40 + 597.64 = 2773.63

Difference = 3109.50 - 2773.63 = 335.87

So using accelarated method will result in higher profits by 335.87