In: Finance
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% |
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. | ||||||