Spotless Car Wash is considering a new project whose data are shown below. The e
ID: 2774422 • Letter: S
Question
Spotless Car Wash is considering a new project whose data are shown below. The equipment to be used has a 3-year tax life, would be depreciated on a straight-line basis over the project's 3-year life, and would have a zero salvage value after Year 3. No new working capital would be required. Revenues and other operating costs will be constant over the project's life, and this is just one of the firm's many projects, so any losses on it can be used to offset profits in other units. If the number of cars washed declines by 40% from the expected level, by how much would the project's NPV decline? Construct a one way data table that shows the projects decline in NPV from the base case by varying the # of cars washed.
WACC
10.0%
Net investment cost (depreciable basis)
$60,000
Number of cars washed
2,800
Average price per car
$25.00
Fixed op. cost (excl. deprec.)
$10,000
Variable op. cost/unit (i.e., VC per car washed)
$5.375
Annual depreciation
$20,000
Tax rate
35.0%
WACC
10.0%
Net investment cost (depreciable basis)
$60,000
Number of cars washed
2,800
Average price per car
$25.00
Fixed op. cost (excl. deprec.)
$10,000
Variable op. cost/unit (i.e., VC per car washed)
$5.375
Annual depreciation
$20,000
Tax rate
35.0%
Explanation / Answer
Ans: We need to first of all prepare a table on income statment if 2800 cars are washed which is as under:
Now in order to calculate the NPV the formula is {Net Period Cash Flow/(1+R)^T} - Initial Investment.
Now if at this number of cars washed & at this net income the NPV from the project is (19669$).
If done arbitarily, the number of cars washed is increased to 3400 then the NPV from the project will be (635.73$) and then if cars is increased to 3450, then the NPV is 950.41$. Therefore, now here we need to find through permutation & combinations done arbitarily that at what level of cars washing is done such that the NPV beomces zero.
Hence at the level of 3420.1 i.e. 3421 cars washed the NOV of the project will start giving the positive NPVs. The interpreatation is if any number of cars washed is below 3421 then the project will be a loss making assignment. The one way table for the same is as under
At this level and the this level of net incomes, the NPV from the project will be 1.90$
No. of cars washed 2800 Avg. Price per car 25$ Gross Income 70000 Variable cost 15050 Fixed cost 10000 Depreciation 20000 EBT 24950 Tax@35% 8732.5 Net Income 16,218Related Questions
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