Florida Car Wash is considering a new project, which requires an initial investm
ID: 2726143 • Letter: F
Question
Florida Car Wash is considering a new project, which requires an initial investment of $60,000. The equipment to be used has a 3-year tax life, would be depreciated on a straight-line basis over its 3-year life to zero salvage value. The equipment can be sold for $10,000 at the end of year 3. With the new equipment, the company is expected to wash 2,800 cars per year for all 3 years. The price per car will be $25 for the first year, and growing at a constant rate of 5% due to inflation. . The variable cost is 20% of the revenue, and the fixed cost is $10,000 each year. Suppose Florida Car Wash allows its customers to pay their bills with an average 1-month delay, and its inventories are 15% of next year’s revenue. If the opportunity cost of capital is 9%, corporate tax rate is 35%, and capital gain tax is 15%.
a. What is the project’s NPV?
b. Should you accept the project based on its NPV? What is the project’s IRR?
c. Will your answer change based on the IRR method? How much would the project’s NPV change if the number of cars washed reduces to half?
Explanation / Answer
Initial Investment = $60,000
Depreciation per year = $60,000/3 = $20,000
After-tax salvage value of equipment = $10,000 x (1-Capital gain tax rate) = $8,500
Year
1
2
3
Sales
$70,000.00
$73,500.00
$77,175.00
Less: Variable Cost
$14,000.00
$14,700.00
$15,435.00
Less: Fixed Cost
$10,000.00
$10,000.00
$10,000.00
Less: Depreciation
$20,000.00
$20,000.00
$20,000.00
EBT
$26,000.00
$28,800.00
$31,740.00
Less: Tax @ 35%
$9,100.00
$10,080.00
$11,109.00
Net Income
$16,900.00
$18,720.00
$20,631.00
Add: Depreciation
$20,000.00
$20,000.00
$20,000.00
Less: NWC
$11,025.00
$11,576.25
$0.00
Add: After tax salvage value
$0.00
$0.00
$8,500.00
Operating Cash flow
$25,875.00
$27,143.75
$40,631.00
NPV = -$60,000 + [($25,875)/(1.09)] + [($27,143.75)/(1.09)2] + [($40,631)/(1.10)3] = $17,959.47
As the NPV is positive, we should accept the project.
IRR:
0 = -$60,000 + [($25,875)/(IRR)] + [($27,143.75)/(IRR)2] + [($40,631)/(IRR)3] = 23.83%
Based on IRR method, we should accept the project as IRR is higher than the opportunity cost.
NPV with half number of cars:
Year
1
2
3
Sales
$35,000.00
$36,750.00
$38,587.50
Less: Variable Cost
$7,000.00
$7,350.00
$7,717.50
Less: Fixed Cost
$10,000.00
$10,000.00
$10,000.00
Less: Depreciation
$20,000.00
$20,000.00
$20,000.00
EBT
-$2,000.00
-$600.00
$870.00
Less: Tax @ 35%
-$700.00
-$210.00
$304.50
Net Income
-$1,300.00
-$390.00
$565.50
Add: Depreciation
$20,000.00
$20,000.00
$20,000.00
Less: NWC
$5,512.50
$5,788.13
$0.00
Add: After tax salvage value
$0.00
$0.00
$8,500.00
Operating Cash flow
$13,187.50
$13,821.88
$20,565.50
NPV = -$60,000 + [($13,187.50)/(1.09)] + [($13,821.88)/(1.09)2] + [($20,565.50)/(1.10)3] = -$20,387.44
In this case, NPV is negative, so project should not be accepted in this scenario.
Year
1
2
3
Sales
$70,000.00
$73,500.00
$77,175.00
Less: Variable Cost
$14,000.00
$14,700.00
$15,435.00
Less: Fixed Cost
$10,000.00
$10,000.00
$10,000.00
Less: Depreciation
$20,000.00
$20,000.00
$20,000.00
EBT
$26,000.00
$28,800.00
$31,740.00
Less: Tax @ 35%
$9,100.00
$10,080.00
$11,109.00
Net Income
$16,900.00
$18,720.00
$20,631.00
Add: Depreciation
$20,000.00
$20,000.00
$20,000.00
Less: NWC
$11,025.00
$11,576.25
$0.00
Add: After tax salvage value
$0.00
$0.00
$8,500.00
Operating Cash flow
$25,875.00
$27,143.75
$40,631.00
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