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Integrative—Determining relevant cash flows Lombard Company is contemplating the purchase of a new high-speed widget grinder to replace the existing grinder. The existing grinder was purchased 2 years ago at an installed cost of $60,000; it was being depreciated under MACRS using a 5-year recovery period. The existing grinder is expected to have a usable life of 5 more years. The new grinder costs $105,000 and requires $5,000 in installation costs; it has a 5-year usable life and would be depreciated under MACRS using a 5-year recovery period. Lombard can currently sell the existing grinder for $70,000 without incurring any removal or cleanup costs. To support the increased business resulting from purchase of the new grinder, accounts receivable would increase by $40,000, inventories by $30,000, and accounts payable by $58,000. At the end of 5 years, the existing grinder is expected to have a market value of zero; the new grinder would be sold to net $29,000 after removal and cleanup costs and before taxes. The firm pays taxes at a rate of 40% on both ordinary income and capital gains. The estimated profits before depreciation and taxes over the 5 years for both the new and the existing grinder are shown in the following table. (Table 3.2 on page 100 contains the applicable MACRS depreciation percentages.)
TABLE 3.2
Rounded Depreciation Percentages by Recovery Year Using MACRS for First Four Property Classes
Percentage by recovery yeara
Recovery year
3 years
5 years
7 years
10 years
1 33%
20%
14%
10%
2 45
32
25
18
3 15
19
18
14
4
7
12
12
12
5
12
9
9
6
5
9
8
7
9
7
8
4
6
9
6
10
6
11
___
___
___
4
Totals
100%
100%
100%
100%
Profits before
depreciation and taxes
Year
New grinder
Existing grinder
1. $43,000
$26,000
2. 43,000
24,000
3. 43,000
22,000
4. 43,000
20,000
5. 43,000
18,000
a. Calculate the initial investment associated with the replacement of the existing grinder by the new one.
b. Determine the incremental operating cash inflows associated with the proposed grinder replacement. (Note: Be sure to consider the depreciation in year 6.)
c. Determine the terminal cash flow expected at the end of year 5 from the proposed grinder replacement. d. Depict on a time line the relevant cash flows associated with the proposed grinder replacement decision.

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Answer:

a. Calculate the initial investment associated with the replacement of the existing grinder by the new one.

initial investment = cost of new grinder + cost of installing new grinder - after tax cost of selling old grinder + increase in net working capital

  • cost of new grinder = $105,000
  • cost of installing new grinder = $5,000
  • after tax cost of selling old grinder = $70,000 - ($70,000 - {$60,000 x (1 - 52%)] x 40%} = $70,000 - $16,480 = $53,520
  • increase in net working capital = $40,000 + $30,000 - $58,000 = $12,000

initial investment = $105,000 + $5,000 - $53,520 + $12,000 = $68,480

b. Determine the incremental operating cash inflows associated with the proposed grinder replacement. (Note: Be sure to consider the depreciation in year 6.)

cash flows new grinder:

  • year 1 = [($43,000 - $22,000) x (1 - 40%)] + $22,000 = $34,600
  • year 2 = [($43,000 - $35,200) x (1 - 40%)] + $35,200 = $39,880
  • year 3 = [($43,000 - $21,120) x (1 - 40%)] + $21,120 = $34,248
  • year 4 = [($43,000 - $12,672) x (1 - 40%)] + $12,672 = $30,868.80
  • year 5 = [($43,000 - $12,672) x (1 - 40%)] + $12,672  + $18,000 (NWC) + $19,934.40 (after tax salvage value) = $68,803.20

cash flows old grinder:

  • year 1 = [($26,000 - $11,520) x (1 - 40%)] + $11,520 = $20,208
  • year 2 = [($24,000 - $6,912) x (1 - 40%)] + $6,912 = $15,964.80
  • year 3 = [($22,000 - $6,912) x (1 - 40%)] + $6,912 = $15,964.80
  • year 4 = [($20,000 - $3,456) x (1 - 40%)] + $3,456 = $13,382.40
  • year 5 = $18,000 x (1 - 40%) = $10,800

incremental cash flows:

year 1 = $34,600 - $20,208 = $14,392

year 2 = $39,880 - $15,964.80 = $23,915.20

year 3 = $34,248 - $15,964.80 = $18,283.20

year 4 = $30,868.80 - $13,382.40 = $17,486.40

year 5 = $68,803.20 - $10,800 = $58,003.20

c. Determine the terminal cash flow expected at the end of year 5 from the proposed grinder replacement.

terminal cash flow = recovering net working capital + after tax salvage value = $18,000 + $19,934.40 = $37,934.40

d. Depict on a time line the relevant cash flows associated with the proposed grinder replacement decision.

year 0 = -$68,480

year 1 = $34,600

year 2 = $39,880

year 3 = $34,248

year 4 = $30,868.80

year 5 = $68,803.20

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