Question

Please show work step by step, No Excel. Thank you!

Suppose miller motors can either expense or capitalize an asset it has just purchased for $9,000. if it capitalizes the asset, it will depreciate the asset to a book value of zero on a straight line basis of three years. The firm has a marginal tax rate of 38%, and the cost of capital for this asset is 12%. What is the present-value difference to the firm between expensing and capitalizing the asset? Assume the firm will have sufficient income over the next three years to use all possible tax credits.

Answer 1

If the firm treats it as an expense, the whole amount goes into P&L in the first year and the same expense is tax deductible:

Profit and Loss Statement Extract
Gross Profit	X
Less: Expense on purchase of an asset	9000
Net profits	X-9000
Less: Taxes	38%*(X-9000)
Tax savings	38%*9000= 3420
PV of Tax Savings	=9000/1.12
PV of Tax Savings	3053

Profit and Loss Statement Extract	Year 1	Year 2	Year 3
Gross Profit	X	Y	Z
Less: Depreciation on Asset	=9000/3= 3000	3000	3000
Net profits	X-3000	Y-3000	Z-3000
Less: Taxes	38%*(X-3000)	38%*(Y-3000)	38%*(Z-3000)
Tax savings	38%*3000= 1140	38%*3000= 1140	38%*3000= 1140
PV of Tax Savings	=1140/(1.12)^1	=1140/(1.12)^2	=1140/(1.12)^3
PV of Tax Savings	1018	909	811

Sum of PV of Tax savings in Case 2: $2738

PV of Tax Savings in Case 1: $3053

Difference= $315

Thus,treating the asset as an expense leads to higher tax savings but the profits will be volatile with very low profits in the 1st year and higher profits in the subsequent years.

The remaining balance of the asset that is capitalised will be shown in the Balance Sheet at Book Value less Accumulated Depreciation