Florida Car Wash is considering a new project, which requires an initial investm
ID: 2726233 • 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%. Calculate without using Excel and use the following chart.
What is the project’s NPV? Should you accept the project based on its NPV?
What is the project’s IRR? 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?
Year 0
Year 1
Year 2
Year 3
Cost for new machine
Working Capital
Change in Working Capital
Revenues
Expense
Depre
Pretax Profit
Taxes
Profit
Net-of-tax Proceeds
Cash Flows
Discounted Cash Flows
Year 0
Year 1
Year 2
Year 3
Cost for new machine
Working Capital
Change in Working Capital
Revenues
Expense
Depre
Pretax Profit
Taxes
Profit
Net-of-tax Proceeds
Cash Flows
Discounted Cash Flows
Explanation / Answer
____________________________________________________________________________________________-
Year 0 Year 1 Year 2 Year 3
1.Cos of Equipment (60,000) - - -
2. Working Capital (receivables+inventory) 16,858 17,481 18,005
3. Change in Working Capital -- 16,858 623 524
4 Revenue (2,800 x 25) + 3% - 70,000 73,500 75,705
5. Expenses (variable+fixed) -- 24,000 24,700 25,141
6. Depreciaiton (60,000/3) -- 20,000 20,000 20,000
7. Pretax profit (4-5-6) 26,000 28,800 30,564
8. Tax ( 7 x 35% ) 9,100 10,080 10,698
9. Profit after tax (7 - 8) 16,900 18,720 19,866
10. Net of tax proceeds (10,000 - 15%) -- -- 8,500
11.Cash flows (9+6-3+10) -- 20,042 38,097 47,862
12. Present value factor (3 years @ 9%) 0.9174 0.8417 0.7722
14. Discounted cash flows ( 11 x 12) 18,387 32,066 36,959
CALCULATION OF NPV
TOTAL DISCOUNTED CASH FLOWS ( 50,732+96,435+106,201) = $ 87,392
LESS: iNITIAL INVESTMENT 60,000
NET PRESENT VALUE (87,392 - 60,000) = 27,392
Decision; Since, NPV is positive, Project can be accepted
CALCULATION OF IRR:
YEAR 1 YEAR 2 YEAR 3 Total
Cash flows 20,042 38,097 47,862
Present value factor @ 30% 0.7692 0.5917 0.4552
Discounted cash flows 15,416 22,542 21,787
Total discounted cash flows -- -- -- 59,745
Less: Initial investment 60,000
Net present Value (255)
CALCULATION OF IRR
PRESENT VALUE REQUIRED 60,000
TOTAL PRESENT VALUE @9% 87,392
TOTAL PRESENT VALUE @30% 59,745
BY INTERPOLATION,
IRR = LOWER RATE + TOTAL PRESENT VALUE AT LOWER RATE - PRESENT VALUE REQUIRED /TOTAL PRESENT VALUE AT LOWER RATE - TOTAL PRESENT VALUE AT HIGHER RATE x DIFF. BETWEEN LOWR AND HIGHER RATE
IRR = 9% + 87,392 - 60,000/87,392 - 59,745 x 21 = 9% + 27,392/27,647 x 21 = 9% + 20.81% = 29.81%
Hence, IRR is 29.81%.
Decision: No, Since Project IRR ie. 29.81% is more than opportunity cost ie. 9%, project will be accepted
IF CAR WASHES REDUCED TO HALF I.E 1400
_______________________________________________________________________________________________
YEAR 0 YEAR 1 YEAR 2 YEAR 3
3. Change in working capital 8,325 249 257
4. Revenues -- 35,000 36,050 37,132
5. Expenses (variable + fixed) 17,000 17,210 17,426
6. Depreciation (60,000/3) 20,000 20,000 20,000
7. Pretax profit (4-5-6) 2,000 (1,160) (294)
8. Tax @35% 700 -- --
9. Profit after tax 1,300 (1,160) (294)
10. Net of tax proceeds (10,000-15%) -- -- 8,500
11. Cash flows (9+6-3+10) 12,975 18,591 27,949
12. Present Value factor @9% 0.9174 0.8417 0.7722
13. Discounted cash flows 11,903 15,648 21,582
CALCULATION OF NPV:
__________________________________________________________________________
TOTAL DISCOUNTED CASH FLOWS (11,903+15,648+21,582) $49,133
LESS: INITIAL INVESTMENT 60,000
WHEN CAR WASHES REDUCED TO HALF REVENUES FALL BY 50% AND NPV BECOME NEGATIVE AS NPV REDUCED BY $38,259
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