Question

Last year, Michelson Manufacturing reported $10,250 of sales, $3,500 of operating costs other than depreciation, and $1,250 of depreciation. The company had no amortization charges, it had $3,500 of bonds outstanding that carry a 6.5% interest rate, and its federal-plus-state income tax rate was 25%. This year’s data are expected to remain unchanged except for one item, depreciation, which is expected to increase by $725. By how much will the depreciation change cause the firm’s net after-tax income to change? Note that the company uses the same depreciation calculations for tax and stockholder reporting purposes.

Answer 1

Solution:

The formula for calculating the Net income after tax is

= ( Sales – Operating costs – Depreciation – Interest expense ) * ( 1 – Tax rate )

Calculation of Net income after tax for last year:

As per the information given in the question we have

Sales = $ 10,250 ; Operating costs = $ 3,500 ; Depreciation = $ 1,250 ; Tax rate = 25 % = 0.25

Bonds outstanding = $ 3,500 ; Interest rate on bonds = 6.5 %

Thus Interest expense = Bonds outstanding * Interest rate on bonds

= $ 3,500 * 6.5 %

= $ 227.50

Thus the Interest expense = $ 227.50

Applying the above information in the formula for Net income after tax we have

= ( $ 10,250 - $ 3,500 - $ 1,250 - $ 227.50 ) * ( 1 – 0.25 )

= $ 5,272.50 * ( 1 – 0.25 )

= $ 5,272.50 * 0.75

= $ 3,954.3750

Thus the Net Income after tax for last year = $ 3,954.3750

Calculation of Net income after tax for this year:

As per the information given in the question we have

Sales = $ 10,250 ; Operating costs = $ 3,500 ; Depreciation = $ 1,250 + $ 725 = $ 1,975 ;

Tax rate = 25 % = 0.25

Bonds outstanding = $ 3,500 ; Interest rate on bonds = 6.5 %

Thus Interest expense = Bonds outstanding * Interest rate on bonds

= $ 3,500 * 6.5 %

= $ 227.50

Thus the Interest expense = $ 227.50

Applying the above information in the formula for Net income after tax we have

= ( $ 10,250 - $ 3,500 - $ 1,975 - $ 227.50 ) * ( 1 – 0.25 )

= $ 4,547.50 * ( 1 – 0.25 )

= $ 4,547.50 * 0.75

= $ 3,410.6250

Thus the Net Income after tax for this year = $ 3,410.6250

The change in the firm’s net after-tax income from last year to this year due to a change in amount of depreciation = Net Income after tax for last year - Net Income after tax for this year

= $ 3,954.3750 - $ 3,410.6250

= $ 543.75

Thus the change in the firm’s net after-tax income from last year to this year due to a change in amount of depreciation = $ 543.75