Florida Car Wash is considering a new project, which requires an initial investm
ID: 2726364 • 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%.
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?
Please help me understand with use of the following categories:
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
CALCULAITON OF NPV:
_____________________________________________________________________________________________
YEAR 0 1 2 3
1. INITIAL INVESTMENT $60,000 -- -- --
2. WORKING
(RECEIVABLES+INVENTORIES) -- 16,858 17,701 18.586
3. CHANGE IN WORKING CAPITAL 16,858 843 885
4. REVENUES (2800 X 25)+5% EVERY YEAR - 70,000 73,500 77,175
5. EXPENSES(VARIABLE@20%+FIXED) -- 24,000 24,700 25,435
6. DEPRECIATION (60,000/3) - 20,000 20,000 20,000
7. PRETAX PROFITS (4-5-6) 26,000 28,800 31,740
8. TAX @35%(35% X 7) -- 9,100 10,080 11,109
9. PROFITS AFTER TAX (7-8) 16,900 18,720 20,631
10. NET OF THE TAX PROCEEDINGS
(SALE OF ASSET) (10,000-15%) -- -- 8,500
11. CASH FLOWS (9+6-3+10) -- 20,042 37,877 48,246
12. PRESENT VALUE FACTOR @9% 0.9174 0.8417 0.7722
13. DISCOUNTED CASH FLOWS (60,000) 18,387 31,881 37,256
CALCULATION OF NPV:
______________________________________________________________________
TOTAL PRESENT VALUE OF CASH INFLOWS ( 18,387+31,881+37,256) = $87,524
LESS: INITIAL INVESTMENT = 60,000
DECISION: SINCE, NPV IS POSITIVE PROJECT WILL BE ACCEPTED
CALCULATION OF IRR:
___________________________________________________________________________________________
YEARS 1 2 3 TOTTAL
1. DISCOUNTED CASH FLOWS 20,042 37,877 48,246
2. PRESENT VALUE FACTOR
@30%(TRIAL & ERROR) 0. 7692 0.5917 0.4552
3. PRESENT VALUE (1X2) 15,416 22,418 21,962
4. TOTAL PRESENT VALUE 59,796
5. LESS: INITIAL INVESTMENT 60,000
6. NPV (4-5) (204)
CALCULATION OF IRR:
PRESENT VALUE REQUIRED = 60,000
PRESENT VALUE @9% = 87,524
PRESENT VALUE @30% = 59,796
BY INTERPOLATION
IRR = LOWER RATE+ (PRESNT VALUE AT LOWER RATE - PRESENT VALUE REQUIRED/PRESENT VALUE AT LOWER RATE - PRESENT VALUE AT HIGHER RATE) X DIFFERENCE BETWEEN LOWER AND HIGHER RATE
IRR = 9% + (87254 - 60,000)/87,254 - 59,796) X 21%
= 9% + (27,254/27,458) X 21
= 9% + (0.99 X 21)
=9%+20.79%
= 29.79%
DECISION : SICE,PROJECT IRR 29.79% IS GREATER THAN OPPORTUNITY COST 9%, PROJECT WILL BE ACCEPTED
CALCULATION OF NPV IF CAR WASHES ARE REDUCED TO HALF I.E 1400
________________________________________________________________________________________
YEARS 0 1 2 3
1. INITIAL INVESTMENT 60,0000 --- --
2. WORKING CAPITAL
(RECEIVABLE + INVENTORIES) -- 8,430 8,851 9,294
3. CHANGE IN WORKING CAPITAL -- 8,430 421 443
4. REVENUES ( 14,00 X 25) + 5% 35,000 36,750 38,588
5. EXPENSES (VARIABLE @20%+FIXED) 17,000 17,350 17,718
6. DEPRECIAITON (60,000/3) 20,000 20,000 20,000
7. PRETAX PROFIT (2,000) (600) 870
8. TAX @ 35% NIL NIL 305
9. PROFITS AFTER TAX (2,000) (600) 565
10. NET OF TAX PROCEEDS
(SALE OF ASSET) -- -- 8,500
11. CASH FLOWS (9+6-3+10) -- 28,430 18,979 20,122
12. PRESENT VALUE FACTOR@9% 0. 9174 0.8417 0.7722
13. DISCOUNTED CASHFLOWS (11 X 12) 26,082 15,975 15,538
TOTAL DISCOUNTED CASH FLOWS (26,082 + 15,875+15,538) = 57,495
LESS: INITIAL INVESTMENT = 60,000
NPV (2,505)
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