To analyze McCann Catching, Inc.'s potential expansion of their production facility, we can follow these steps:
Step 1: Calculate the value of the firm's equity and debt.
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Equity:
- Shares Outstanding = 2.00 million
- Price per Share = $12.85 \[ \text{Equity Value} = \text{Shares Outstanding} \times \text{Price per Share} = 2,000,000 \times 12.85 = 25,700,000 \]
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Debt:
- Face Value of Debt = $13.00 million
- Quoted Price = 89% of Face Value \[ \text{Market Value of Debt} = \text{Face Value} \times \text{Quoted Price} = 13,000,000 \times 0.89 = 11,570,000 \]
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Total Firm Value: \[ \text{Total Firm Value} = \text{Equity Value} + \text{Market Value of Debt} = 25,700,000 + 11,570,000 = 37,270,000 \]
Step 2: Calculate the weighted average cost of capital (WACC).
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Cost of Equity (using the CAPM model): \[ \text{Cost of Equity} = \text{Risk-Free Rate} + \beta \times \text{Market Risk Premium} = 0.04 + 1.30 \times 0.08 = 0.04 + 0.104 = 0.144 \text{ or } 14.40% \]
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Cost of Debt: The yield on the debt is 8.00% and tax-adjusted is given by: \[ \text{After-tax Cost of Debt} = \text{Cost of Debt} \times (1 - \text{Tax Rate}) = 0.08 \times (1 - 0.37) = 0.08 \times 0.63 = 0.0504 \text{ or } 5.04% \]
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Weights:
- Weight of Equity: \[ W_e = \frac{\text{Equity}}{\text{Total Value}} = \frac{25,700,000}{37,270,000} \approx 0.689 \]
- Weight of Debt: \[ W_d = \frac{\text{Debt}}{\text{Total Value}} = \frac{11,570,000}{37,270,000} \approx 0.311 \]
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WACC Calculation: \[ \text{WACC} = W_e \times \text{Cost of Equity} + W_d \times \text{After-tax Cost of Debt} \] \[ \text{WACC} = 0.689 \times 0.144 + 0.311 \times 0.0504 \approx 0.0993 + 0.0157 = 0.1150 \text{ or } 11.50% \]
Step 3: Evaluate the project under NPV criteria.
- Annual Cash Flows: $11 million for 8 years.
- Discount cash flows using WACC:
- Cash Flow = $11,000,000
- Number of Periods = 8
- WACC = 11.50% or 0.115
\[ \text{NPV} = \sum_{t=1}^{8} \frac{\text{Cash Flow}}{(1 + \text{WACC})^t} - \text{Initial Investment} \] Using the formula for the present value of an annuity, which is: \[ \text{PV} = C \times \left(1 - (1 + r)^{-n}\right) / r \] Where:
- \( C \) = cash flow per period = $11,000,000
- \( r \) = WACC = 0.115
- \( n \) = number of periods = 8
Calculating the present value of cash flows: \[ \text{PV} = 11,000,000 \times \left(1 - (1 + 0.115)^{-8}\right) / 0.115 \] \[ = 11,000,000 \times \left(1 - (1.115)^{-8}\right) / 0.115 \] \[ = 11,000,000 \times \left(1 - 0.3740\right) / 0.115 \] \[ = 11,000,000 \times 0.6260 / 0.115 \] \[ \approx 11,000,000 \times 5.452 = 60,972,000 \text{ (approximately)} \]
Now, calculate NPV: \[ \text{NPV} = \text{PV of future cash inflows} - \text{Initial Investment} = 60,972,000 - 41,220,000 = 19,752,000 \]
Conclusion
The NPV of the project is approximately $19.75 million, which is positive. This indicates that the project is expected to generate value for McCann Catching, Inc. and thus may be a worthwhile investment.