Question

In: Finance

Brock Florist Company buys a new delivery truck for $29,000. It is classified as a light-duty...

Brock Florist Company buys a new delivery truck for $29,000. It is classified as a light-duty truck. Brock is in a 30% tax bracket and has a cost of capital of 8%. Assume that Brock will sell its delivery truck after three years of service for $15,000. a. Calculate the NPV of the equipment purchase using a five-year life with straight-line depreciation to zero salvage. b. Calculate the NPV of the equipment purchase using a five-year life and MACRS depreciation. c. Which of the two depreciation methods would Brock prefer?

Year

3-year

Class

5-year

Class

7-year

Class

1

33.33%

20.00%

14.29%

2

44.45%

32.00%

24.49%

3

14.81%

19.20%

17.49%

4

7.41%

11.52%

12.49%

5

11.52%

8.93%

6

5.76%

8.92%

7

8.93%

8

4.46%

Solutions

Expert Solution

Answer a
Calculation of NPV of the equipment purchase using a five-year life with straight-line depreciation to zero salvage.
Year 0 1 2 3 NPV
Purchase cost of new delivery truck -$29,000.00
Depreciation tax shield $1,740.00 $1,740.00 $1,740.00
After tax sale value of delivery truck $13,980.00
Net Cash flow -$29,000.00 $1,740.00 $1,740.00 $15,720.00
x Discount factor @ 8% 1 0.925925926 0.85733882 0.793832241
Present Value -$29,000.00 $1,611.11 $1,491.77 $12,479.04 -$13,418.08
NPV of the equipment purchase using a five-year life with straight-line depreciation to zero salvage = -$13,418.08
Working
Depreciation per year using straight line method = $29000/5 years = $5800
Depreciation tax shield per year = Depreciation per year x Tax rate = $5800 x 30% = $1740
Calculation of after tax sale value of delivery truck
Sale value $15,000.00
Less : Book value after 3 years $11,600.00
Gain on sale $3,400.00
Tax @ 30% on Gain $1,020.00
After tax sale value [Sale value - tax] $13,980.00
Answer b
Calculation of NPV of the equipment purchase using a five-year life and MACRS depreciation
Year 0 1 2 3 NPV
Purchase cost of new delivery truck -$29,000.00
Depreciation tax shield $1,740.00 $2,784.00 $1,670.40
After tax sale value of delivery truck $13,005.60
Net Cash flow -$29,000.00 $1,740.00 $2,784.00 $14,676.00
x Discount factor @ 8% 1 0.925925926 0.85733882 0.793832241
Present Value -$29,000.00 $1,611.11 $2,386.83 $11,650.28 -$13,351.78
NPV of the equipment purchase using a five-year life and MACRS depreciation -$13,351.78
Working
Calculation of depreciation tax shield
Year Cost of new delivery truck 5 Year Class MACRS rates Depreciation Depreciation tax shield @ 30%
1 $29,000.00 20% $5,800.00 $1,740.00
2 $29,000.00 32% $9,280.00 $2,784.00
3 $29,000.00 19.20% $5,568.00 $1,670.40
Calculation of after tax sale value of delivery truck
Sale value $15,000.00
Less : Book value after 3 years $8,352.00
Gain on sale $6,648.00
Tax @ 30% on Gain $1,994.40
After tax sale value [Sale value - tax] $13,005.60
Answer c
Brock should prefer MACRS depreciation method as it gives lower net present value of cash flows.

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