Question

Ms. T. Potts, the treasurer of Ideal China, has a problem. The company has just ordered a new kiln for $544,000. Of this sum, $68,000 is described by the supplier as an installation cost. Ms. Potts does not know whether the Internal Revenue Service (IRS) will permit the company to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $68,000 straight-line over 5 years. The tax rate is 30% and the opportunity cost of capital is 5%. a. What is the present value of the cost of the kiln if the installation cost is treated as a separate current expense? b. What is the present value of the cost of the kiln if the installation cost is treated as a part of the capital investment? (Round your answer to the nearest whole dollar amount.) a. Present value Present value

Answer 1

Present value is today's value of tomorrow's money discounted using the time value of money.
Particulars
Total cost incurred by Ideal China				$      544,000
Installation cost				$        68,000
Capital investment made for new kiln				$      476,000
(544000-68000)
Depreciation method				Straight Line Method
Life of the asset in years				5
Tax rate				30%
Discounting factor (Opportunity cost of capital)				5%
Notes: Listing down the details given in the question

a. Calculation of present value of the cost of kiln if installation cost is treated as current expense
Particulars		Cash Flows (A)	Year	Discounting factor @ 5% (B)	Present value of cash flows (A X B)
A.Initial investment		$      476,000	0	1	$        476,000
B. Installation cost	68000
Less Tax deduction (68000*30%)	20400	$        47,600	1	0.952	$          45,333
C. Depreciation (476000/5)	95200
Less Tax deduction (95200*30%)	28560	$        66,640	1	0.952	$          63,467
		$        66,640	2	0.907	$          60,444
		$        66,640	3	0.864	$          57,566
		$        66,640	4	0.823	$          54,825
		$        66,640	5	0.784	$          52,214
					$        288,516
Total present value of cash flows					$        809,850
(A+B+C)
Notes
1) Initial investment occurs immediately ie at the current point of time, hence year is 0 and discounted at 1
2) Installation cost is tax deductible at the end of the year, hence year is 1
3) Discounting factor for 5% can be referred from the Present Value Table or by using a calculator
(year 1- 1/1.05, year 2- 1/1.05^2 and so on). The values have been rounded off to 3 decimal points for accuracy.
4) Depreciation is calculated on SLMbasis,the formula of which is
(Cost of the asset- Salvage value)/Life of the asset
Depreciation is operational cash outflow hence it has be discounted for 5 years.

b. Calculation of present value of the cost of kiln if installation cost is treated as capital investment
Particulars		Cash Flows (A)	Year	Discounting factor @ 5% (B)	Present value of cash flows (A X B)
A.Initial investment		$      476,000	0	1	$        476,000
B. Installation cost		$        68,000	0	1	$          68,000
C. Depreciation (544000/5)	108800
Less Tax deduction (108800*30%)	32640	$        76,160	1	0.952	$          72,533
		$        66,640	2	0.907	$          60,444
		$        66,640	3	0.864	$          57,566
		$        66,640	4	0.823	$          54,825
		$        66,640	5	0.784	$          52,214
					$        297,583
Total present value of cash flows					$        841,583
(A+B+C)
Notes:
1) Initial investment and installation cost occurs immediately ie at the current point of time, hence year is 0 and discounted at 1
2) Installation cost is treated as capital cost, hence there is no impact on tax
3) Discounting factor for 5% can be referred from the Present Value Table or by using a calculator
(year 1- 1/1.05, year 2- 1/1.05^2 and so on). The values have been rounded off to 3 decimal points for accuracy.
4) Depreciation is operational cash outflow hence it has be discounted for 5 years.
Depreciation should be calculated on the total capital investment i.e. 544000