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Managers of the Jonathan Co

Accounting

Managers of the Jonathan Co. realize that the present value of the depreciation tax benefit is affected by the discount rate, the tax rate, and the depreciation rate. They have recently purchased a machine for $100,000 and they are trying to decide which depreciation method to use. There are only two alternatives available, and they must make an irrevocable selection of one method or the other right now. They have no uncertainty about the company's discount rate (it is 10 percent), but they are highly uncertain about the direction of future tax rates. The company's uncertainty stems from the fact that the existing tax rate is 30 percent, but congress is presently debating tax legislation that would dramatically increase the rate. If the legislation is passed it would go into affect in two years (after the Jonathan Co. has claimed two years of depreciation). How high would tax rates need to be in two years for the Jonathan Co. to be indifferent between depreciation Method 2 and depreciation Method 1 below?

 

 

Method 1

Method 2

Difference

Year 1

$30,000

$10,000

$(20,000)

Year 2

$40,000

$15,000

$(25,000)

Year 3

$10,000

$25,000

$ 15,000 

Year 4

$10,000

$25,000

$ 15,000 

Year 5

$10,000

$25,000

$ 15,000 

 

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Answer:

No matter what happens, the tax rate for the next two years is 30 percent. Using the differences in depreciation amounts, one can determine the difference in present values between the two methods at the end of year 2 when the tax rate is expected to change.

Present value calculations for years 1 and 2:

Year 1 ($20,000) ´ .30 ´ .9091 =

$ (5,455)

Year 2 ($25,000) ´ .30 ´ .8265 =

$ (6,199)

Total present value difference at end

$(11,654)

So, after the first two years, Method 1 has generated $11,654 more present value than Method 2. This simply means that at the point of indifference, Method 2 would be required to generate $11,654 more present value than Method 1 in the last three years. For the last three years of the project's life, the difference in depreciation amounts is $15,000. This $15,000 amount can be used in the following equation to solve for the tax rate that yields a present value of $11,654:

$11,654 = $15,000 ´ tax rate ´ (.7513 + .6830 + .6209)

$11,654 = $30,828 ´ tax rate

Tax rate = $11,654/$30,828

Tax rate = 37.8%

Thus, an increase in the tax rate to about 37.8 percent would cause management to be indifferent between the two depreciation methods.