Question

The J. Miles Corp. has 25 million shares outstanding with a share price of $ 20 per share. Miles also has outstanding​ zero-coupon debt with a 5​-year ​maturity, a face value of $ 900 ​million, and a yield to maturity of 9 %. The​ risk-free interest rate is 5 %.

a. What is the implied volatility of​ Miles' assets?

b. What is the minimum profitability index required for equity holders to gain by funding a new investment that does not change the volatility of​ Miles' assets?

c. Suppose Miles is considering investing cash on hand in a new investment that will increase the volatility of its assets by 10 %. What is the minimum NPV such that this investment will increase the value of​ Miles' shares?

The J. Miles Corp. has 25 million shares outstanding with a share price of $ 20 per share. Miles also has outstanding​ zero-coupon debt with a 5​-year ​maturity, a face value of $ 900 ​million, and a yield to maturity of 9 %. The​ risk-free interest rate is 5 %.

a. What is the implied volatility of​ Miles' assets?

b. What is the minimum profitability index required for equity holders to gain by funding a new investment that does not change the volatility of​ Miles' assets?

c. Suppose Miles is considering investing cash on hand in a new investment that will increase the volatility of its assets by 10 %. What is the minimum NPV such that this investment will increase the value of​ Miles' shares?

Answer 1

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Answer:

a.

Market value of the equity = $20 * 25,000,000 shares = $500,000,000

Market value of zero-coupon bond = $900,000,000 / 1.09^5 = $584,938,247.66

Total market value = $584,938,247.66 + $500,000,000 = $1,084,938,247.66

Here, Spot price (S) = $1,084,938,247.66

Strike price (K) = $900,000,000

Market value of option (C) = $500,000,000

Time to maturity (T) = 5 years

Risk-free rate (R) = 5%

By using the Black-Scholes Implied Volatility calculator, we get the value = 34.62%

b.

By using the same parameters as mentioned above, we can also compute the delta (δ) of the option. Same calculator should be put in use to compute the delta (δ). Thus, δ = 0.827.

Profitability index = [1 - δ] / δ = 0.173 / 0.827 = 0.209

c.

If we raise the implied volatility on the asset to 44.62%, then the total market value of the asset would fall to $1,009,000,000 (approx)

Thus, Net Present Value (NPV) = $1,009,000,000 - $1,084,938,247.66 = -$75,938,247.66