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Chapter 13

Q. 13.9

Some new production machinery has a first cost of $100,000 and a useful life of 10 years. Its estimated operating and maintenance (O&M) costs are $10,000 the first year, which will increase annually by $4000. The asset’s before-tax market value will be $50,000 at the end of the first year and then will decrease by $5000 annually. This property is a 7-year MACRS property. The company uses a 6% after-tax MARR and is subject to a combined federal/state tax rate of 28%.

Calculate the after-tax cash flows.

Step-by-Step

Verified Solution

To find this new production machinery’s minimum cost life, we first find the after-tax cash flow (ATCF) effect of the O&M costs and depreciation (Table 13–1). Then, we find the ATCFs of disposal if the equipment is sold in each of the 10 years (Table 13–2). Finally in the closing section on spreadsheets, we combine these two ATCFs (in Figure 13–5) and choose the minimum cost life.

In Table 13–1, the O&M expense starts at $10,000 and increases at $4000 per year. The depreciation entries equal the 7-year r_{t} MACRS depreciation values
given in Table 11–2 multiplied by the $100,000 first cost. The taxable income, which is simply the O&M costs minus the depreciation values, is then multiplied by minus the tax rate to determine the tax savings. The O&M expense plus the tax savings is the Table 13–1 portion of the total ATCF.

Regarding the market value data in this problem, it should be pointed out that the initial decrease of $50,000 in Year 1 is not uncommon. This is especially true for custom-built equipment for a particular and unique application at a specific plant. Such equipment would not be valuable to others in the marketplace. Also, the $100,000 first cost (cost basis) could have included costs due to installation, facility modifications, or removal of old equipment. The $50,000 may be optimistic for the market value of one-year-old equipment.

The next step is to determine the ATCFs that would occur in each possible year of disposal. (The ATCF for Year 0 is easy; it is − $100, 000.) For example, as shown in Table 13–2, in Year 1 there is a $35,710 loss as the book value exceeds the market value. The tax savings from this loss are added to the salvage (market) value to determine the ATCF (if the asset is disposed of during Year 1).

Table 13-1 ATCF for O&M and Depreciation for Example 13–9

O&M Depreciation ATCF Tax Savings (at 28%) Taxable Income MACRS
Depreciation,
d_{t}
O&M Expense Year, t
−$3,199 $6,801 −$24,290 $14,290 −$10,000 1
−3,223 10,777 −38,490 24,490 −14,000 2
−8,063 9,937 −35,490 17,490 −18,000 3
−12,343 9,657 −34,490 12,490 −22,000 4
−16,220 9,780 −34,930 8,930 −26,000 5
−19,102 10,898 −38,920 8,920 −30,000 6
−21,980 12,020 −42,930 8,930 −34,000 7
−26,111 11,889 −42,460 4,460 −38,000 8
−30,240 11,760 −42,000 0 −42,000 9
−33,120 12,880 −46,000 0 −46,000 10

 

Table 13-2 ATCF in Year of Disposal for Example 13–9

ATCF if Disposed of Gain or Loss (at 28%) Gain/Loss Tax Book
Value
Market Value Year, t
$59,999 $9,999 −$35,710 $85,710 $50,000 1
49,542 4,542 −16,220 61,220 45,000 2
41,044 1,044 −3,730 43,730 40,000 3
33,947 −1,053 3,760 31,240 35,000 4
27,847 −2,153 7,690 22,310 30,000 5
21,749 −3,251 11,610 13,390 25,000 6
15,649 −4,351 15,540 4,460 20,000 7
10,800 −4,200 15,000 0 15,000 8
7,200 −2,800 10,000 0 10,000 9
3,600 −1,400 5,000 0 5,000 10

These tables assume that depreciation is taken during the year of disposal and then calculates the recaptured depreciation (gain) or loss on the year-end book value.

Spreadsheets are very useful in nearly all after-tax calculations. However, they are absolutely required for optimal life calculations in after-tax situations, because bonus plus MACRS is the tax law, and after-tax cash flows are different in every year. Thus, the NPV function and the PMT function are both needed to find the minimum EUAC after taxes. Figure 13–5 illustrates the calculation of the minimum cost life for Example 13–9.

In Figure 13–5, the NPV finds the present worth of the irregular cash flows from Period 1 through Period t for t = 1 to life. Then PMT can be used to find the EUAC over each potential life. Before-tax replacement analysis was done this way in Example 13–2. The spreadsheet block function NPV is used to find the PW of cash flows from Period 1 to Period t. Note that the cell for Period 1 is an absolute address and the cell for period t is a relative address. This allows the formula to be copied.

Some new production machinery has a first cost of $100,000 and a useful life of 10 years. Its estimated operating and maintenance (O&M) costs are $10,000 the first year, which will increase annually by $4000. The asset’s before-tax market value will be $50,000 at the end of the first year and then