In: Accounting
The firm in above is considering a new project, which requires an initial investment in equipment of 90,000 and also an initial investment in working capital of 10,000 (at t = 0). You expect the project to produce sales revenue of 120,000 per year for three years. You estimate manufacturing costs at 60% of revenues. (Assume all revenues and costs occur at year‐end) The equipment fully depreciates using straight‐line depreciation over three years. At the end of the project, the firm can sell the equipment for 10,000 and also recover the investment in net working capital. a. Find the project’s payback period, IRR, NPV and profitability index. b. Should the company invest in the project? Explain. c. Does your decision in (b) depend on the way the project is financed? If so, how?
PS:I wrote the first question because the second question will be solved using the data from the first quesion. Sorry for posting 2 questions.
Solution
The company has a Debt of $12 Million. Pre-tax Cost of Debt
being 15%. Rate of Tax is 20%.
Therefore, Post-Tax Cost of Debt (kd) = 15% x (1 - 0.2)
= 15% x 0.8
= 12%
Now, Company has 1 Million outstanding common stock currently
being traded at $10 per share.
Therefore, Value of Common Stock outstanding = $10 Million
Again, we have been given that Risk-free rate (Rf) is 8%, Market
Return (Rm) being 18%, and CAPM Beta (B) is 1.50.
Therefore, Required rate of return on equity, or Cost of Equity
(ke) = Rf + [(Rm - Rf) x B]
= 8% + [(18% - 8%) x 1.50]
= 8% + 15%
= 23%
Now as we have the required information, we can calculate the Weighted Average Cost of Capital (WACC) as follows,
Particulars | Value ($ in Millions) | Weight | Cost | Weighted Cost |
Common Stock | 10 | 0.455 | 23% | 10.465 |
Debt | 12 | 0.545 | 12% | 6.540 |
TOTAL | 22 | 1.000 | 17.005 |
Therefore, the Weighted Average Cost of Capital (WACC) will be 17.005%.
Now let us move to the next part.
Initial Investment = $90000
Initial Working Capital Requirement (will be recovered at the end)
= $10000
Therefore, Total Initial Outlay = $100000
Again,
Revenue per year = $120000
Manufacturing Cost (60% of Revenue) = $72000
Net revenue per year = $48000
Depreciation per year = (Initial Investment - Scrap Value) /
Number of years
= (90000 - 10000) / 3
= 26666.67 (Approx.)
Terminal Value = Recovery of Working Capital + Scrap Value
= $(10000 + 10000)
= $20000
Therefore,
Initial Outflow = $100000
Annual Cash Flow After Tax (CFAT) = [(Net Revenue - Depreciation) x
(1 - Tax Rate)] + Depreciation
= [(48000 - 26666.67) x (1 - 0.2)] + 26666.67
= 17066.67 + 26666.67
= $43733.34
Terminal Value = $20000
Therefore, Cash Flow at 3rd Year will be ($43733.34 + $20000) =
$63733.34
Now,
We will making our calculations as follows,
Project PBP:
We need to require the following table,
Year | Cash Flows | Cumulative Cash Flows |
1 | $ 43,733.34 | $ 43,733.34 |
2 | $ 43,733.34 | $ 87,466.68 |
3 | $ 63,733.34 | $ 151,200.02 |
At PBP, we know that the Investor will be able to recover its Initial Outlay. Here, the Initial Outlay is $100000, which will be recovered somewhere in between 2 to 3 years. The exact value can be determined using interpolation as follows,
(PBP - 2) / (3 - 2) = (100000 - 87466.68) / (151200 -
87466.68)
Or, PBP - 2 = 12533.32 / 63733.32
Or, PBP = 2.197 (Approx.)
Therefore Project PBP will be 2.197 Years
Project IRR:
The calculation will be made using Trial-and-Error method. For our
calculation we are using 22% and 23%. The calculation is as
follows,
Year | Cash Flows | PVIF @ 22% | Discounted Cash Flow | PVIF @ 23% | Discounted Cash Flow |
0 | $ (100,000.00) | 1.0000 | $ (100,000.00) | 1.0000 | $ (100,000.00) |
1 | $ 43,733.34 | 0.8197 | $ 35,847.00 | 0.8130 | $ 35,555.56 |
2 | $ 43,733.34 | 0.6719 | $ 29,382.79 | 0.6610 | $ 28,906.96 |
3 | $ 63,733.34 | 0.5507 | $ 35,098.39 | 0.5374 | $ 34,249.27 |
$ 328.18 | $ (1,288.21) |
At IRR, Intial Outflow will be equal to Discounted Cash Flows. Therefore, it is clear from above that IRR will be somewhere in between 22% and 23%. The exact value will be calculated using interpolation as follows,
(IRR - 22) / (23 - 22) = (0 - 328.18) / (- 1288.21 -
328.18)
Or, IRR - 22 = 328.18 / 1616.39
Or, IRR = 22.203 (Approx.)
Therefore, Project IRR will be 22.203%.
Project NPV (Using Discounting rate (WACC) = 17.005%):
Year | Cash Flows | PVIF @ 17.005% | Discounted Cash Flow |
0 | $ (100,000.00) | 1.0000 | $ (100,000.00) |
1 | $ 43,733.34 | 0.8547 | $ 37,377.33 |
2 | $ 43,733.34 | 0.7305 | $ 31,945.07 |
3 | $ 63,733.34 | 0.6243 | $ 39,788.12 |
NET PRESENT VALUE | $ 9,110.51 |
Therefore, Net Present Value will be $9110.51.
Profitability Index:
Profitablity Index = PV of Future Cash Flows / Initial
Outflow
= (43733.34 + 43733.34 + 63733.34) / 100000
= 1.512 (Approx.)
From the calculated results, it can be concluded that as the NPV is positive, and the IRR is also more than the Required Rate of Return, the project should be accepted.
It is true that the investment decision depends upon the level of financing. As given, the investment is financed by 15% Debt and Common Stock. The ratio of weights between the mode of financing is 0.455 : 0.545. If the financing modes are altered, for example reducing the Debt quantum, or Increase in Common Stock will definitely affect the WACC, resulting to which the NPV calculation will be affected. Therefore, we can say that investment decision depends upon the level of financing.