Discounted-Cash-Flow Analysis
Question 1
True, False, or Uncertain. Other things being equal, an increase in the volatility of the underlying asset will increase the value of the call option on that asset. Explain.
It is true that when other things are held constant, an increase in the volatility of the underlying asset will result in an increase the value of the call option on the asset. . The price of a call option depends on the volatility of the underlying asset. Volatility of price refers to the tendency of the underlying asset price to fluctuate over time. There is a direct relationship between the value of a call option and the volatility of the underlying asset. The higher the volatility of the price of the underlying asset, the higher the value of its call option will be. This is because the volatility provides the buyer of a call option a chance to earn high profits when the price of the underlying asset appreciates. On the other hand, when the price of the underlying asset depreciates, the loss of a buyer of a call option will be restricted to what the buyer paid as call premium.
The black Scholes formula which is commonly used to calculate the price of options includes volatility of the price of the underlying asset in computing the value of a call option. Volatility of the underlying asset is mathematically measurable using data of current prices of the underlying asset. In the formula, volatility is measured by the standard deviation of the price of the underlying asset over a given period of time. The formula shows a positive correlation between the value of a call option and the volatility in the price of the underlying asset. This implies that an increase in the volatility of the price of the underlying asset will result in a higher value of the call option from the Black and Scholes formula.
Question 2
How do you read an exit diagram? What type of information does the diagram provide? Explain.
Venture capitalist often evaluates investments with complicated payoff structures. In such structures, venture capitalists do not receive clear call option but instead have options that are embedded in other financial securities for example preference shares that are convertible. The exit payoff of venture capitalists is often complicated because venture capitalist can have different forms of investments. Exit diagrams are meant to simplify translation of these complicated investments into an options’ portfolio with diverse strike prices.
On an exit diagram, the x-axis represents the value of the entire company while the y-axis represents a fraction of the entire company that represents a particular investment. Time component is not included in exit diagrams because the date that an option expires is unknown. Exit diagrams are therefore read as a portfolio of options that expire randomly. To read an exit diagram, the venture capitalist starts from the left to the right; that is from the origin. At every point where there is a change in the gradient of the slope, a fraction of the call option is added or subtracted with the strike price being equal the corresponding value on the x-axis. The fraction that is added or subtracted is change in the slope at that point. A positive change in the slope is regarded as a purchase of a call option while a decrease in the slope is regarded as a sell of a call option with a strike equivalent to the corresponding value on the x-axis. The change in the slope is then multiplied by the corresponding strike price. The exit equation will be given by the sum of the products of the change in the slope and the strike price.
Question 3
What do we need to calculate to determine the cost of capital for comparable companies? Why?
Cost of capital is the opportunity cost of capital employed. Opportunity cost is forgone as a result of allocating scarce resources in a given way. Cost of capital for comparable firms is computed using the weighted average cost of capital (WACC).
Weighted average cost of capital (WACC) is the average cost of capital of a firm in which each the cost of each source of financing is weighted proportionately. These sources of capital include preferred stock, common stock, retained earnings bonds and other sources of long-term debt. Different sources of capital have different costs depending on the risks involved and their lifespan. WACC is computed in three steps. The first step is to compute the cost of each component of capital. The after-tax cost of debt is given by multiplying the yield to maturity by one minus the tax rate. The after tax cost of other sources of long-term debt is computed by multiplying the after tax interest rate by one minus the tax rate. Cost of common stock is determined using the capital asset pricing model (CAPM). The cost of common stock will be given by the risk-free rate plus beta times the market risk premium. The cost of retained earnings is presumed to be the same as the cost of common shares since it is based on expected returns by common stockholders. Cost of preference shares is determined by the preference dividends divided by the market price per preference share. The next step is determining the weight of each component of capital in the capital structure. Lastly the cost of each component of capital is multiplied by the weight and they are then summed up.
Question 4
Why do we use the Black-Scholes formula?
Black Scholes formula is a mathematical formula used in financial markets to calculate the price certain financial derivative instruments. The formula was developed in 1973 by Fisher Black and Myron Scholes. The Black Scholes formula is widely used in computation of options price.
Black Scholes formula is used because it incorporates the five major determinants of options’ prices. That is; the strike price, the current stock price, time to expiration, volatility, and the risk free short-term interest rate. Strike price refers to the specific price at which an option holder sells the underlying asset if it is a put option or buys the underlying asset if it is a call option. Current stock price refers to the prevailing stock price of a stock. Time to expiration refers to the time left before the option can be exercised; it is expressed as percentage with respect to a year. Volatility refers to the fluctuation of expected returns; it is measured by short-term returns’ standard deviation. All these variables are significant determinants of the price of an option. Black Scholes formula is easy to understand because it clearly models the relationship between all the variables that determine price of an option.
Assumptions made by the Black Scholes model are realistic. Although the assumption made by the Black Scholes model may not hold, they are close to what happens in the market. For example the model assumes that short-term returns are normally distributed and the underlying asset prices have lognormal distribution. This is close to what happens in financial markets since the underlying asset prices fluctuate from time to time. Lastly, the model can easily be modified to compute option prices for assets whose prices are non- log normally distributed.
References
Metrick, A., & Yasuda, A. (2009). Venture Capital and the Finance of Innovation (2, illustrated ed.). New York: John Wiley and Sons.
Coyle, B. (2000). Venture Capital: Corporate Finance. Chicago: Glenlake Publishing Company.
Vishwanath, S. R. (2007). Corporate Finance: Theory and Practice (2, illustrated ed.). New York: SAGE.
