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) Show graphically and explain the impact on a firm’s investment of accelerated depreciation (as opposed to straight-line depreciation) that is show whether it will invest more or less with accelerated depreciation

Answer 1

Value of assets would be $ 10000*4= $40000. Assuming the salvage value is Nil

Depreciation under accelerated method in first yr would be $ 40000*75% = $ 30000

Depreciation under accelerated method in second yr would be $ 40000*25% = $10000

In 3rd and 4th year there would be Nil depreciation

Assuming that the $56000 annual profit is after considering the depreciation under straight line method

In $	Yr 1	Yr 2	Yr 3	Yr 4
Annual Profit	56000	56000	56000	56000
Add: Depreciation under straight line method	10000	10000	10000	10000
Less: Depreciation under accelerated method	30000	10000	0	0
Annual profit if accelerated depreciation method is adopted	36000	56000	66000	66000
Tax Rate	35%	35%	35%	35%
Tax Amount	12600	19600	23100	23100
Discount Rate	10%	10%	10%	10%
Present discounted value of taxation deduction	11,454.55	16,198.35	17,355.37	15,777.61
Present value = Cash flow in nth year/ (1 + Discount rate)^n
Where n refers to year

The above chart explains that if company adopts accelerated depreciation that the amount available to invest is more as annual profit after tax increases as compared to straight line method

In $	Yr 1	Yr 2	Yr 3	Yr 4
Annual Profit under Straight line method(after Tax) = annual profit less tax amount	36400	36400	36400	36400
Annual Profit under Accelerated line method(after Tax) = annual profit less tax amount	23400	36400	42900	42900