Question

Energy Dynamic is a company with 10 million shares outstanding. The current asset value is $90m and it has a zero-coupon corporate debt of $100m face value due in 5 years. Suppose company’s asset volatility is 25% and the risk-free interest rate is 6% per annum with continuous compounding. The company makes no dividend payment.

1)Apply the BlackScholes model to estimate company’s equity value. What is the share price?

2)what is the yield to maturity on the debt?

Answer 1

1. Black - Scholes Formula:

For Using Black Scholes Formula, we need five key inputs which in this case would be as follows:

Spot Price (Current Assets Value) = $90 Million

Strike Price (Zero - Coupon Debt Maturity Value) = $100 Million

Time to Maturity (Zero - Coupon Expiry Time) = 5 Years

Volatility (Company's Assets Volatility) = 25%

Risk Free Rate = 6% p.a. Continuously Compounded

While inputing these inputs and using black scholes formula in excel whose screenshot is as follows:

Following is the result of above formulas:

As seen in the above screenshot, Value of Call Option is $27.07 million. This is the value of equity as per Black Scholes Formula.

Company's Equity Value = $27.07 million

No. of Equity Shares Outstanding = 10 million

Value per share = 27.07 / 10 = $2.707 per share

2. Value of company's assets = $100 million

Value of company's Equity = $27.07 million

Value of Zero - Coupon Debt = 100 - 27.07 = $72.93 million

This is the present Value of future repayment of $100 million. By using the follwoing formula, we can calculate the YTM of this bond.

YTM of bond =

YTM of Bond = [(100 / 72.93)^(1/5) - 1] * 100 = 6.52%.