Company X has only debt and equity in its capital structure. The total market va

Question

Company X has only debt and equity in its capital structure. The total market value of the firm's assets is $25 million. The total market value of debt is $10 million. The total market value of equity is $15 million. All of the debt matures in 15 years, and has a face value of $20 million. After the current debt matures, the company intends to issue new debt with a 10 year maturity. Is the equity value in this company equivalent to a call option or is it equivalent to a put option? What is the strike price of the option? What is the time to expiry of the option? The current price of an asset is $1.5 million. Next year it may be worth $2 million if the economy does well, or it may be worth only $1 million, if the economy does badly. The risk-free rate is 8%. Calculate the price of a one-year call option on the asset, with an strike price of $1.2 million.

Explanation / Answer

part a:-

1. the company at any cost has to repay $20million in next 15years.

currently balancesheet appears as follows:-

liabilities assets

debt - $10million assets - $25million

equity - $ 15million

1. the company at any cost has to repay $20million in next 15years. so liability has to be created towards liabilities side and it comes around $35million whereas right side i.e. on assets side it is $25million. so options has to be purchased for the balancing amount of $ 10million.

liabilities assets

debt - $10million assets - $25million

equity - $ 15million options - $10million

liability - $10million

so here comes the confusion whether the options purchased to be call option or put option. call option means what ever the price in the market after a specified agreed period you have to purchase stock from me at a particular pre determined price which is called strike price. and put option means what ever the market rate writer has to pay strike price.

the company enters with writer that what ever the price in the market i will sell my debt (callable bonds) for $20million. as company must require 20$ million after 15years. so company holds put option

putoption value not equals to equity value here.

option value is $10million and equity value is $15million.

2. strike price is the price at which we agreed to pay or receive from writer after maturity of option and the agreed price for callable bonds i.e. debt is $20million.

3. the option gets expired in 15years as they require money only after 15years.

part b:-

call option value = spot price - present value of strike price

call option = $1.5million - e-rt   * strike price

r = rate of interest

t = term

ert   = 1 + x/1! + x2/2! + x3/3!+.........

rt = 8%*1year

= 0.08

=1 + 0.08/1 +(0.08)2/2!+......

= 1.0832

e-rt = 1 / ert = 1/1.0832 = 0.923

call option = 1.5 - 0.923*1.2

= 1.5 - 1.1076

= $0.3924 million

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