Your boss now wants you to help Higgs Bassoon Corporation. Higgs Bassoon Corpora

Question

Your boss now wants you to help Higgs Bassoon Corporation. Higgs Bassoon Corporation is a custom manufacturer of bassoons and other wind instruments. Its current value of operations, which is also its value of debt plus equity, is estimated to be $200 million. Higgs has zero coupon debt outstanding that matures in 3 years with $110 million face value. The risk-free rate is 5%, and the standard deviation of returns for similar companies is 60%. The owners of Higgs Bassoon view their equity investment as an option and would like to know its value. Start with the attached partial model, and answer the following questions: Using the Black-Scholes option pricing model, how much is the equity worth? techniques to reduce its volatility to 45%? Can you explain this? from $10 to $160 million. value of the debt is $100 million. . How much is the debt worth today? What is its yield? . How would the equity value change if the company used risk management . Graph the cost of debt versus the face value of debt for values of the face value . Graph the values of debt and equity for volatilities from 0.10 to 0.90 when the face

Explanation / Answer

Solution:

Answer to Question a.

Total value of the firm = $200.00 million (This is the current value of operations)

Face value of debt = $100.00 million (200 * 5% = 10, 110 – 10 = 100)

Risk free rate (r) = 5% = 0.05

Maturity of debt (years) = 3 years

Standard deviation (s) = 0.45 (This is sigma - also known as volatility)

d1 = [In (S/K) + (r + s2/2) * t] / s * ?t

    = [In (200/100) + (0.05 + 0.452/2) * 3] 0.45 * ?3

d1 = 1.4715

Here,

In = Natural log

S = Current stock price

K = Option striking price

t = time until option exercise

d2 = d1 - s * ?t

    = 1.4715 - 0.45 * ?3

d2 = 0.6920

N(d1) = 0.9294 (Use the Normsdist function in the function wizard)

N(d2) = 0.7555

Call price = Equity price

                 = S * N(d1) – Ke-rt N(d2)

                = 200 * 0.9294 – 100e-0.05 * 3 0.7555

                = $120.85 million

Answer to Question b.

Debt value = Total value – Equity value = $79.15 million ($200 million - $120.85 million)

Debt yield = 8.107%

Answer to Question c.

Equity value at 60% volatility = $128.76748 million

Total value of the firm = $200.00 million (This is the current value of operations)

Face value of debt = $100.00 million (200 * 5% = 10, 110 – 10 = 100)

Risk free rate (r) = 5% = 0.05

Maturity of debt (years) = 3 years

Standard deviation (s) = 0.60 (This is sigma - also known as volatility)

d1 = [In (S/K) + (r + s2/2) * t] / s * ?t

    = [In (200/100) + (0.05 + 0.602/2) * 3] 0.60 * ?3

d1 = 1.4374

d2 = d1 - s * ?t

    = 1.4374 - 0.60 * ?3

d2 = 0.3982

N(d1) = 0.9247 (Use the Normsdist function in the function wizard)

N(d2) = 0.6548

Call price = Equity price

                 = S * N(d1) – Ke-rt N(d2)

                = 200 * 0.9247 – 100e-0.05 * 3 0.6548

                = $128.76748 million

Equity value at 45% volatility = $120.85314 million (Calculated above)

Percent change = -6.1%

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.