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McCann Catching, Inc. has 2.00 million shares of stock outstanding. The stock currently sells for $12.85 per share. The firm’s debt is publicly traded and was recently quoted at 89.00% of face value. It has a total face value of $13.00 million, and it is currently priced to yield 8.00%. The risk free rate is 4.00% and the market risk premium is 8.00%. You’ve estimated that the firm has a beta of 1.30. The corporate tax rate is 37.00%.

The firm is considering a $41.22 million expansion of their production facility. The project has the same risk as the firm overall and will earn $11.00 million per year for 8.00 years.

What is the NPV of the expansion? (answer in terms of millions, so 1,000,000 would be 1.0000)

5 answers

To calculate the Net Present Value (NPV) of the expansion project, we follow these steps:

  1. Calculate the Cost of Equity using the Capital Asset Pricing Model (CAPM): \[ R_e = R_f + \beta \times (R_m - R_f) \] Where:

    • \( R_f = 4.00% \) (risk-free rate)
    • \( \beta = 1.30 \)
    • \( R_m - R_f = 8.00% \) (market risk premium)

    So: \[ R_e = 0.04 + 1.30 \times 0.08 = 0.04 + 0.104 = 0.144 = 14.40% \]

  2. Calculate the Cost of Debt: Given that the debt yields 8.00%, we use this rate to find the after-tax cost of debt: \[ R_d = 8.00% \] \[ R_d(1 - T) = 0.08 \times (1 - 0.37) = 0.08 \times 0.63 = 0.0504 = 5.04% \]

  3. Calculate the Market Value of Equity (E): \[ E = \text{Stock Price} \times \text{Shares Outstanding} \] \[ E = 12.85 \times 2,000,000 = 25,700,000 \]

  4. Calculate the Market Value of Debt (D): The market value of the debt is obtained by calculating the market price. \[ \text{Market Value of Debt} = \text{Face Value} \times \text{Quote Percentage} \] \[ D = 13,000,000 \times 0.89 = 11,570,000 \]

  5. Calculate the Total Value of the Firm (V): \[ V = E + D = 25,700,000 + 11,570,000 = 37,270,000 \]

  6. Calculate the WACC (Weighted Average Cost of Capital): \[ WACC = \frac{E}{V} \times R_e + \frac{D}{V} \times R_d(1 - T) \] \[ WACC = \left(\frac{25,700,000}{37,270,000} \times 0.144\right) + \left(\frac{11,570,000}{37,270,000} \times 0.0504\right) \]

    First, we calculate the components: \[ \frac{E}{V} = \frac{25,700,000}{37,270,000} \approx 0.688 \] \[ \frac{D}{V} = \frac{11,570,000}{37,270,000} \approx 0.312 \] Now calculate WACC: \[ WACC \approx 0.688 \times 0.144 + 0.312 \times 0.0504 \] \[ WACC \approx 0.099072 + 0.01574784 \approx 0.11481984 = 11.48% \]

  7. Calculate the Cash Flows from the Project: Cash flows are \( 11.00 \) million per year for \( 8 \) years. Therefore, the cash flows \( C \) will be: \[ C = 11.00 \text{ million} \]

  8. Calculate the NPV: The NPV formula is: \[ NPV = \sum_{t=1}^{n} \frac{C}{(1 + WACC)^t} - \text{Initial Investment} \] Given \( n = 8 \) and \( \text{Initial Investment} = 41.22 \) million: \[ NPV = \sum_{t=1}^{8} \frac{11.00}{(1 + 0.1148)^t} - 41.22 \]

    First, we calculate the total present value of cash inflows using the Present Value of Annuity formula, because the cash flows are constant: \[ PV = C \times \left( \frac{1 - (1 + WACC)^{-n}}{WACC} \right) \] \[ PV = 11.00 \times \left( \frac{1 - (1 + 0.1148)^{-8}}{0.1148} \right) \] Calculating \( (1 + 0.1148)^{-8} \): \[ (1 + 0.1148)^{-8} = 0.3710 \quad \text{(approximately)} \] Now plug it back: \[ PV = 11.00 \times \left( \frac{1 - 0.3710}{0.1148} \right) \] \[ PV = 11.00 \times \left( \frac{0.6290}{0.1148} \right) \approx 11.00 \times 5.48 \approx 60.28 \]

    Finally, calculate the NPV: \[ NPV = PV - Initial Investment = 60.28 - 41.22 \approx 19.06 \]

Thus, the NPV of the expansion is approximately 19.0600 million.

How do I solve it on a finance calculator? What value do i Enter for F0,C0,C1,C2,C3,C4, V5, C6, C7,C8 and I to solve for NPV do you know?

To solve for the NPV of the project using a financial calculator, you'll need to input the cash flows of the project appropriately. Here's how to set it up based on the details we've calculated.

Input Values for the Financial Calculator:

  1. F0 (Initial Investment): This is the cash outflow for the expansion project.

    • Input Value: \(-41.22\) million (Note the negative sign indicates a cash outflow).

  2. C1, C2, C3, C4, C5, C6, C7, C8 (Annual Cash Flows): These are the cash inflows from the project. Since the project is expected to earn $11 million per year for 8 years:

    • Input Values:
      • C1 = 11 million
      • C2 = 11 million
      • C3 = 11 million
      • C4 = 11 million
      • C5 = 11 million
      • C6 = 11 million
      • C7 = 11 million
      • C8 = 11 million

Steps to Enter Values in the Calculator:

  1. Set Financial Calculator to Cash Flow Mode: Depending on the calculator, you may have to press a button labeled "CF" or "CFO".

  2. Enter Initial Investment:

    • C0 = \(-41.22\)
    • This is often done by entering the value then pressing the "Enter" key.

  3. Enter Annual Cash Flows:

    • C1 = 11 (then press "Enter" or the "down" arrow).
    • C2 = 11 (then press "Enter" or the "down" arrow).
    • C3 = 11 (then press "Enter" or the "down" arrow).
    • C4 = 11 (then press "Enter" or the "down" arrow).
    • C5 = 11 (then press "Enter" or the "down" arrow).
    • C6 = 11 (then press "Enter" or the "down" arrow).
    • C7 = 11 (then press "Enter" or the "down" arrow).
    • C8 = 11 (then press "Enter" or the "down" arrow).

  4. Calculate NPV:

    • Find the "NPV" button on your calculator.
    • Enter the WACC as your interest rate, which is 11.48%. (Depending on the calculator, you may need to enter it as 0.1148 or 11.48).
    • After setting up the interest rate, press the "NPV" button to compute the result.

Result:

Upon completing these steps, the calculator should compute the NPV of the project. Based on prior calculations, you should see an NPV of approximately 19.06 million. If you don't, check that all cash flows and the initial investment were entered correctly.

the calculator ask for I.do you know how to caculate I?

Certainly! The value for \( I \) on a financial calculator typically refers to the interest rate or discount rate used to calculate the NPV of future cash flows. In this case, we want to use the Weighted Average Cost of Capital (WACC) that we previously calculated.

Recap on WACC Calculation

From our previous calculations, we found the WACC to be approximately:

\[ WACC \approx 11.48% \quad (\text{or } 0.1148 \text{ when expressed as a decimal}) \]

Setting the Value of \( I \) on the Financial Calculator:

  1. Convert the WACC to a Decimal:

    • Since many calculators ask for the rate as a decimal, you will enter \( I \) as 0.1148 if the calculator accepts decimal form.

  2. If the Calculator Requires a Percentage:

    • If your financial calculator requires the interest rate as a whole number (percentage), simply input it as 11.48.

Steps to Input \( I \):

  1. Look for a button labeled "I" or "I/Y" on your financial calculator.
  2. Enter 0.1148 (or 11.48 depending on your calculator).
  3. Confirm the entry (press "Enter" or whatever button is necessary to save the rate).

Summary of Inputs for Your Financial Calculator:

  • F0 (Initial Investment): \(-41.22\)
  • C1, C2, ..., C8 (Annual Cash Flows): \(11\) (for each of the 8 cash flows)
  • I (Interest Rate / Discount Rate): \(0.1148\) (or \(11.48\))

Once you've entered these values, proceed to calculate NPV, and it should yield the result based on the inputs provided!