Answer:
a. $57,000
b.
- CF1 = $23,650
- CF2 = $18,850
- CF3 = $14,050
- CF4 = $9,250
c. - $3,047.64
d. IRR = 7%
Explanation:
<em>a. What is the initial investment in the product?</em>
We have: the initial investment in the product is the sum of investment in plant, equipment and the initial required working capital.
+) Investment in plant and equipment is given as $49,000
+) Required working capital each year is 20% of revenue of the following year
=> The initial working capital required is 20% of revenue of year 1
=> Initial working capital required = 20% x 40,000 = $8,000
So that: The initial investment = $49,000 + $8,000 = <u>$57,000</u>
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<em>b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 20%, what are the project cash flows in each year?</em>
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We have the formula to calculate the cash flow of each year as following:
<em>CF = Net Operating Profit - Taxes - Net Change in Working Capital = P - T - </em>ΔCw
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According to the straight-line depreciation, as the plant and equipment are depreciated over 4 years, so that the depreciation of investment in plant and equipment each year is:
<em>D = Depreciation = (Total Investment in Plant and Equipment)÷Its useful life = $49,000 ÷4 = $12,250</em>
We have, expenses (E) are expected to be 40% of revenues (R).
=> Expense of each year is: E = 0.4 R
Net profit of each year (P)= Revenue - Expense
=> <u>Net profit of each year is: P = R - E = R - 0.4 R = 0.6R</u>
The tax each year is imposed on the profit of the company after depreciation, so that taxes each year of the company with the rate of 20% is:
<u>T = 0.2(P - D) = 0.2 (0.6R - 12,250) = 0.12R - 2,450</u>
We have, working capital change for each year is the difference in working capital of current and the previous year.
We have, working capital (Cw) of each year is:
+) Initial Cw = $8,000
+) Cw1 = 20% x Revenue Year 2 = 0.2 x 30,000 = $6,000
+) Cw2 = 20% x Revenue Year 3 = 0.2 x 20,000 = $4,000
+) Cw3 = 20% x Revenue Year 4 = 0.2 x 10,000 = $2,000
+) Cw4 = 20% x Revenue Year 5 = 0.2 x 0 = 0
So that the change in Cw each year is:
+) ΔCw1 = Cw1 - Initial Cw = 6,000 - 8,000 = -2,000
+) ΔCw2 = Cw2 - Cw1 = 4,000 - 6,000 = -2,000
+) ΔCw3 = Cw3 - Cw2 = 2,000 - 4,000 = -2,000
+) ΔCw4 = Cw4 - Cw3 = 0 - 2,000 = -2,000
Now we can write the cash flow formula as following:
<em>CF = P - T - </em>ΔCw = 0.6R - (0.12R -2,450) - (-2000) = 0.48R +4,450
- CF1 = 0.48R1 + 4,450 = 0.48 x 40,000 + 4,450 = $23,650
- CF2 = 0.48R2 + 4,450 = 0.48 x 30,000 + 4,450 = $18,850
- CF3 = 0.48R3 + 4,450 = 0.48 x 20,000 + 4,450 = $14,050
- CF4 = 0.48R4 + 4,450 = 0.48 x 10,000 + 4,450 = $9,250
<em>c. If the opportunity cost of capital is 10%, what is project NPV? </em>
Assume that cost of capital is <em>r</em>, so that r = 10% = 0.1
We have:
PV = ∑[CF Year i/(1+r)^i] (with i = 1 to 4) = ∑[CF Year i/(1+0.1)^i]
= CF1/(1+0.1)^1 + CF2/(1 + 0.1)^2 + CF3/(1+0.1)^3 + CF4/(1+0.1)^4
Replace the value of CF as the previous part in the equation, we have:
PV ≈ $53,952.36
We have,Net Present Value (NPV) = Present Value (PV) - Initial Investment (I)
=> NPV = $53,952.36 - $57,000 = - $3,047.64
<em>d. What is project IRR?</em>
IRR is the discount rate r in the equation:
<em>+) PV = ∑[CF Year i/(1+r)^i] (with i = 1 to 4)</em>
The value of IRR has to satisfy the equation:
NPV = 0
⇔ PV - I = 0
+) <em>PV = ∑[CF Year i/(1+r)^i] = Initial Investment = $57,000</em>
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However, the IRR can only be calculated by tool. Here, we can use Excel spreadsheet to calculate the value of IRR.
<em>The input can be describe as following:
</em>
Column A values: Column B
A1: -57,000 (Initial Investment) B1: =IRR(A1:A5)
A2: 23,650 (CF1)
A3: 18,850 (CF2)
A4: 14,050 (CF3)
A5: 9,250 (CF4)
=> IRR = B1 = 7%
