Refer to Example 13–4, where we calculated the before-tax marginal costs for a new piece of production machinery. Calculate the asset’s after-tax marginal costs considering this additional information. • Depreciation is by the straight-line method, with S = $0 and n = 5 years, so dt = ($25,000-$0)

Question

Refer to Example 13–4, where we calculated the before-tax marginal costs for a new piece of production machinery. Calculate the asset’s after-tax marginal costs considering this additional information.

• Depreciation is by the straight-line method, with S = $0 and n = 5 years, so [latex]d_{t}[/latex] = ($25,000−$0)/5 = $5000.
• Ordinary income, recaptured depreciation, and losses on sales are taxed at a combined state and federal rate of 28%.
• The after-tax MARR is 10%.

Some classes skip or have not yet covered Chapter 10’s explanation of expected value. Thus, the expected cost for risk of breakdowns is described here as an insurance cost.

Accepted Answer

The after-tax marginal cost of ownership will involve the following elements : incurred or forgone loss or recaptured depreciation, interest on invested capital, tax savings due to depreciation, and annual after-tax operating/maintenance and insurance. Figure 13–6 shows example cash flows for the marginal cost detailed in Table 13–3.

As a refresher of the recaptured depreciation calculations in Chapter 12:

The market value in Year 0 = 25,000.
The market value decreases to $18,000 at Year 1.
The book value at Year 1 = 25,000 − 5000 = $20,000.
So loss on depreciation = 20,000 − 18,000 = $2000.
This results in a tax savings of (2000)(0.28) = $560.

Table 13-3 Marginal Costs of Ownership

	After-Tax	Taxes or	Recaptured	Book	Market
	Market Value	Tax Savings	Depr. or Loss	Value	Value	Year
	$25,000			$25,000	$25,000	0
	18,560	–$560	–$2000	20,000	18,000	1
	13,560	–560	–2000	15,000	13,000	2
	9,280	-280	–1000	10,000	9,000	3
	5,720	280	1000	5,000	6,000	4
	2,880	1120	4000	0	4,000	5
	2,160	840	3000		3,000	6
	1,800	700	2500		2,500	7
= C + D+ F – B	Col. F		Col. D	Col. C	Col. B
Marginal	After-Tax	O&M and	Tax Savings	Beg.Yr	After-Tax
Cost	Annual Expense	Insurance Cost	from Depr. Deduct.	Value× (1 +i)	Market Value	Year
					$25,000	0
$12,580	$5,040	$7,000	–$1400	$27,500	18,560	1
10,856	5,400	7,500	–1400	20,416	13,560	2
9,996	5,760	8,000	–1400	14,916	9,280	3
10,288	7,200	10,000	–1400	10,208	5,720	4
10,652	8,640	12,000	–1400	6,292	2,880	5
11,088	10,080	14,000	0	3,168	2,160	6
12,096	11,520	16,000	0	2,376	1,800	7

The marginal cost in each year is much lower after taxes than the pretax numbers shown in Example 13–4. This is true because depreciation and expenses can be subtracted from taxable income. However, the pattern of declining and then increasing marginal costs is the same, and Year 3 is stil the year of lowest marginal costs.

Question 13.10: Refer to Example 13–4, where we calculated the before-tax ma...

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