Question & Answer

To provide a thorough analysis, let’s break this down into clear steps. Please confirm if you want me to delve into each section one at a time or if you prefer a summary of all calculations.

1. Valuation of Debt and Preferred Stock

Debt:

• Face Value: $200 million
• Market Price: 95% of par = 0.95 * $200 million = $190 million

• Preferred Stock:

  • Annual Dividend: 7% of $100 = $7 per share
  • Market Price: $90 per share
  • Market Value: 1 million shares * $90 = $90 million

  • 2. WACC Calculation

    Market Value of Equity:

    • Shares Outstanding: 10 million
    • Share Price: $50
    • Market Value of Equity: 10 million * $50 = $500 million

    Total Market Value:

    • Total Value = Equity + Debt + Preferred Stock = $500 million + $190 million + $90 million = $780million 

    • Cost of Equity (using CAPM):

      • Cost of Equity = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
      • Cost of Equity = 3% + 1.2 * (8% - 3%) = 3% + 6% = 9%

      • Cost of Debt (after tax):

        • Cost of Debt = Coupon Rate * (1 - Tax Rate)
        • Cost of Debt = 5% * (1 - 0.25) = 3.75%

        • Cost of Preferred Stock:

          • Cost of Preferred = Dividend / Price = $7 / $90 ≈ 7.78%

          WACC Calculation:

        • WACC = (E/V) * Re + (D/V) * Rd + (P/V) * Rp

          Where:

          • E = Market Value of Equity = $500 million
          • D = Market Value of Debt = $190 million
          • P = Market Value of Preferred = $90 million
          • V = Total Value = $780 million
          • Re = Cost of Equity = 9%
          • Rd = Cost of Debt = 3.75%
          • Rp = Cost of Preferred ≈ 7.78

          • WACC = (500/780) * 9% + (190/780) * 3.75% + (90/780) * 7.78%

          • WACC ≈ 5.78% + 0.89% + 0.89% ≈ 7.56%

            3. Project Valuation

            To calculate NPV, we would need the projected cash flows from the project. Assuming we have those cash flows, the formula is:

            • NPV = Σ (Cash Flow_t / (1 + WACC)^t) - Initial Investment

            Please provide the cash flows for this step.

            4. Option Pricing (Black-Scholes Model)

            The Black-Scholes formula is:

            $C=S0​N(d1​)−Xe−rtN(d2​)$

            $\mathrm{<span\; class="base"><span\; class="mclose"><br></span></span>}$

            Where:

            • $d_1 = \frac{ \ln(\frac{S_0}{X}) + (r + \frac{\sigma^2}{2})t }{ \sigma\sqrt{t} }$
            • $d_2=d_1-\sigma \sqrt{t}$
            • 
              

You'll need to provide values for the option's strike price, time to expiration, and volatility (σ) for this calculation.

• • • • • • 5. Investment Decision

            $\mathrm{<span\; class="base"><span\; class="mclose"></span></span>}$

            Compare the calculated NPV with the cost of capital and the value derived from the option pricing. If NPV > 0 and aligns with the strategic goals, the project should be undertaken.

            Sensitivity Analysis

            Evaluate how sensitive the NPV is to changes in WACC and projected cash flows. A +/- 1% change in WACC can significantly impact NPV, illustrating the project's risk profile.

            Please confirm any specific inputs for cash flows and option parameters, or if you need me to proceed with assumptions.