Concept explainers
Equity as an Option and
- a. What is the current market value of the company’s equity?
- b. What is the current market value of the company’s debt?
- c. What is the company's continuously compounded cost of debt?
- d. The company has a new project available. The project has an NPV of $1,200,000. If the company undertakes the project, what will be the new market value of equity? Assume volatility is unchanged.
- e. Assuming the company undertakes the new project and does not borrow any additional funds, what is the new continuously compounded cost of debt? What is happening here?
a.
To compute: Current market value of the company’s equity.
Option Pricing:
Option pricing helps in determining the correct or fair price in the market. It is the value of one share on the basis of which option is traded. Black-Scholes is one of the pricing methods. Further, equity is also used as an option.
Explanation of Solution
Given,
Stock price is $9,050,000.
Exercise price is $10,000,000.
Risk free rate is 0.06.
Time to expire is 10.
Formula to calculate the value of equity by using Black Scholes model is,
Where,
- S is stock price.
- E is exercise price.
- R is risk free rate.
- T is time to expire.
Substitute $9,050,000 for S, $10,000,000 for E, 0.06for R, and 10for T.
Working Note:
Calculation of
Calculation of
Hence, current market value of the company’s equity is $5,377,390.16.
b.
To compute: Current market value of the company’s debt.
Explanation of Solution
Given,
Value of company is $9,050,000.
Value of equity is $5,377,390.16.
Formula to calculate the value of debt is,
Substitute $9,050,000 as value of company and $5,377,390.16as value of equity.
Hence, current market value of company’s debt is $3,672,609.84.
c.
To compute: Company’s continuously compounded cost of debt.
Explanation of Solution
Given,
Value of debt is $3,672,609.84.
Face value is $10,000,000.
Time to expire is 10 years.
Formula to calculate the firm’s continuously cost of debt is,
Where,
- R is firm’s continuously cost of debt.
- t is maturity time.
Substitute $3,672,609.84as value of debt, $10,000,000 as face value and 10 for t.
Simplify the above equation.
Hence, the company’s continuously cost of debt is 10.02%.
d.
To compute: New market value of equity.
Explanation of Solution
Given,
Exercise price is 10,000,000.
Risk free rate is 0.06.
Time to expire is 10 years.
Calculated stock price:
The stock price is $10,250,000.
Formula to calculate the value of equity by using Black Scholes model is,
Where,
- S is stock price.
- E is exercise price.
- R is risk free rate.
- T is time to expire.
Substitute $10,250,000for S, 10,000,000 for E, 0.06 for R, and 10 for T.
Working Note:
Calculation of
Calculation of
Calculate the revised stock price,
Hence, new market value of equity is $6,406,471.3.
e.
To compute: The new continuously compounded cost of debt.
Explanation of Solution
Given,
Value of company is $9,050,000.
Value of equity is $6,406,471.3.
Time to expire is 10 years.
Calculated value:
Value of equity is $6,406,471.3.
Value of the stock is $10,250,000.
Formula to calculate the value of debt is,
Substitute $10,250,000as value of company and $6,406,471.3 as value of equity.
Formula to calculate the new continuously cost of debt is,
Where,
- R is firm’s continuously cost of debt.
- t is maturity time.
Substitute $3,843,528.7 as value of debt, $10,000,000 as face value and 10 for t.
Simplify the above equation.
Hence, the company’s new continuously cost of debt is 9.56%.
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Chapter 22 Solutions
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