Car Wash is considering a new project whose data are shown below. The equipment

Question

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 declined by 40% from the expected level, by how much would the project's NPV change? (Hint: Note that cash flows are constant at the Year 1 level, whatever that level is.) What is DPB period of the project?

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. depr.)-$10,000
Variable op. cost/unit (i.e., VC per car washed)-$5.375
Annual depreciation--$20,000
Tax rate-35.0%


Please, help especially with calculation of DPB. Explain, how could it be calculated in this task? What could be used as as discount rate?
Note, that this is in class task, so Excel is prohibited to use. In this regards, please, explain how to calculate all the figures by hand.

Explanation / Answer

WACC-10.0%

Net investment cost (depreciable basis)-$60,000

Annual Cash Flow =( (Average price per car - VC per car washed)*Number of cars washed - Fixed op. cost (excl. depr.))*(1-tax rate) + Annual depreciation*Tax rate

Annual Cash Flow = ((25-5.375)*2800-10000)*(1-35%) + 20000*35%

Annual Cash Flow = $ 36,217.50

Using PV Factor from table

From Cummulative of PV of Cash Flow column we get that DPB is greater than year 1 & lower than year 2

Discounted PayBack Period (DPB) = 1 + 27075.03/29931.95

Discounted PayBack Period (DPB) = 1.90 Years

Note : As you are saying  this is in class task , PV table are generally provided, if that is too not provided

You can calculate PV factor :

Year 0 = 1/(1+discount rate)^0 = 1/1.10^0 = 1.00000

Year 1 = 1/(1+discount rate)^1 = 1/1.10^1 = 0.90909

Year 2 = 1/(1+discount rate)^2 = 1/1.10^2 = 0.82645

Year 3 = 1/(1+discount rate)^3 = 1/1.10^3 = 0.75131

Year Cash Flow PV Factor @ 10% PV of Cash Flow Cummulative of PV of Cash Flow [a] [b] [c =a*b] [d] 0 -60000 1.00000 -60000.00 -60000.00 1                  36,217.50 0.90909 32924.97 -27075.03 2                  36,217.50 0.82645 29931.95 2856.92 3                  36,217.50 0.75131 27210.57 30067.49

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