Question

Suppose Backwoods Chemical Limited is financed partly by a zero-coupon bond that has a two-year maturity. The market value of the company's total assets is $1,290, and the annual standard deviation of its assets value (o) is 43%. The risk-free interest rate is 5%. The company's book-value balance sheet is: Backwoods Chemical Company (Book Values) Net working capital 490 S 1,690 $ 2,180 $ 1,090 S 1,090 S 2,180 Debt Equity (net worth) Total value Net fixed assets Total assets QUESTIONS 1. Consider the shareholder's investment in the equity of Backwoods as a financial option. What type of option (call or put) is this option? What is shareholder's position (long or [2 marks] short) in this option?

Answer 1

Q1: Shareholders' position in equity of backwoods is "Long" and the option type is "Call". The underlying argument according to Merton Model is that - If a company in question has asset value more than the market value of debt, then only a shareholder gets his share of investment in case of liquidation. Thus the underlying for option is "Asset Value" and the strike price for the option is the "Market Value of Debt", and underlying value has to increase to get the payoff. The basic option criteria satisfying all the above condition is "Call" option.

Q2. Underlying asset - Market value of firms asset,

Exercise Price - Face Value of firms' Debt (ZCB).

Value of Firms Total Asset   $1,290

Face Value of Debt = $1,090

As, Value of asset > Face value of Debt [Underlying value > Exercise price in a call option], the option is "In The Money (ITM)".

Ques 3. Using Merton Formula:

Value of Equity:

Here, N(d) is cumulative normal distribution function.

substituting, value in the equation we get, d = 0.5271 (see calculation image attached below)

and Market value of asset ~ $443 (442.917)

Ques 4. Market value of Blackwoods Debt = Market value of total asset - Market value of Equity

= 1290 - 443 = $ 847.

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