Question

A processing plant has a first cost of $700,000 and an expected life of 15 years with no salvage value. Money is borrowed at 5 percent compounded annually, and the first cost is paid off with 15 equal annual payments. The expected annual income is $200,000, and annual operating expenses are $40,000. Corporation income tax is 50 percent of the profits, and the SYD method of depreciation is applicable on the tax life of the facility, which is 11 years with no salvage value. Compute the income tax for (a) the first year and (b) the second year.
(Ans.. (a) $4167 (b) $10281.)

Tip:
The depreciation method SYD is described at page 41 in chapter 3
Tax is paid on the “real” annual profit (Incomes-Expenses-Interest- Depreciation)

Answer 1

SYD depreciaition is a method of accelerated depreciaiotn . It results in greater depreciation in the earlier years of an asset's useful life and less in the later years.
Base for the deprecition will calculated uisng n(n+1)/2
where n is number of years
As n is 11 years from taxation point of view
base = 11(12)/2
= 66

Depreciation in first year will be 11/66
Depreciation in second  year will be 10/66
Depreciation in second  year will be 9/66 and so on


Income tax first year
EBIT = income- operating expense-depreciation - interest
= 200000-40000- 11/66*700000-35000
= 8333
Earnings after tax = 50% of EBIT = 8333/2
= 4166.5
= 4167 (round off)

Income tax second year
EBIT = income- operating expense-depreciation - interest
= 200000-40000- 10/66*700000-33378
= 160000-106060-33378
=20562
Earnings after tax = 50% of EBIT = 20562/2
= 10281