Hi spockspock!!
Thank you for asking to Google Answers.
Here is the solution to this problem:
a.
The initial investment is the sum of the investment in plant and
equipment and the required Working Capital to start the operation, for
this problem it is the 20% of the Year 1 Revenues = 20%*$40,000 =
$8,000). If we call I the initial investment, then:
I = $50,000 + $8,000 = $58,000
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b.
First of all we must define the cash flow (CF) formula:
CF = Net Operating Profit - Taxes - Net Change in Working Capital
We need to calculate other things before we are able to use the cash flow formula:
·Net Operating Profit (NOP):
For each year k (k=1 to 4) we have that the Net Operating Profit is
the difference between the revenues and the expenses of that year k:
NOP_k = R_k - E_k
where:
R_k = are the revenues for the year k
E_k = are the expenses for the year k
·Depreciation (D): (straight-line, 4 years)
D = (Invest in plant and equipment) / 4 = $12,500
·Taxes (T_k)
The taxes for each year k (for k=1 to 4) are:
T_k = T * (NOP_k - D)
where:
T = is the tax rate (for this problem 0.40)
·Net Change in Working Capital (NchWC_k):
For each year k we have that
NchWC_k = Current Working Capital - Previous Working Capital =
= Working Capital_k - Working Capital_(k-1)
Now we can write the cash flow formula for each year k (CF_k):
CF_k = NOP_k - T_k - NchWC_k
Now we can do some preliminar calculations:
E_1 = 40,000 * 0.40 = 16,000
E_2 = 30,000 * 0.40 = 12,000
E_3 = 20,000 * 0.40 = 8,000
E_4 = 10,000 * 0.40 = 4,000
NOP_1 = 40,000 - 16,000 = 24,000
NOP_2 = 30,000 - 12,000 = 18,000
NOP_3 = 20,000 - 8,000 = 12,000
NOP_4 = 10,000 - 4,000 = 6,000
T-1 = 0.40*(24,000-12,500) = 4,600
T_2 = 0.40*(18,000-12,500) = 2,200
T_3 = 0.40*(12,000-12,500) = -200
T_4 = 0.40*(6,000-12,500) = -2,600
NchWC_1 = 0.20*30,000 - 0.20*40,000 = -2,000
NchWC_2 = 0.20*20,000 - 0.20*30,000 = -2,000
NchWC_3 = 0.20*10,000 - 0.20*20,000 = -2,000
NchWC_4 = 0.20*0.00 - 0.20*10,000 = -2,000
Now we can calculate the cash flow for each year:
CF_1 = 24,000 - 4,600 - (-2,000) = $21,400
CF_2 = 18,000 - 2,200 - (-2,000) = $17,800
CF_3 = 12,000 - (-200) - (-2,000) = $14,200
CF_4 = 6,000 - (-2,600) - (-2,000) = $10,600
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c.
We need to recall some definitions:
Present Value (PV) for 4 years is:
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
Net Present Value (NPV):
NPV = PV - I
Using the calculator we find that:
PV = $52,073.90
NPV = $52,073.90 - $58,000.00 =
= -$5,926.10 ---->> NEGATIVE!! you will lose money with this
project.
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d.
IRR is the discount rate R that makes the NPV equals to zero, that is
the rate R that satisfies:
PV - I = 0
or the equivalent
PV = I
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + --------- = I
(1 + R)^1 (1 + R)^2 (1 + R)^3 (1 + R)^4
Now you must use a tool to calculate the IRR, the common way is using
the function IRR of Microsoft Excel (or similar) spreadsheet with the
following inputs:
Column A values: Column B
A1: -58,000 B1: =IRR(A1:A5)
A2: 21,400
A3: 17,800
A4: 14,200
A5: 10,600
IRR = 4.59% ---->> Less than the opportunity cost of capital!!
you will lose money with this project.
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I hope that this helps you. Please feel free to request for a
clarification if you find something obscure or wrong in the answer
before rate this answer. I will gladly respond your requests for
further assistance on this topic.
Regards.
livioflores-ga |
