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## What is asset beta and unlevered beta?

The asset beta of the company will depend on whether the business is financed through the debt or the equity. Most cases the firm will be financed by both the equity and the debt. A firm will be known as leveraged when it has the debt capital and unleveraged when it does not have debt capital. it means that unleveraged firm fully financed through the equity finance. The unleveraged beta of a firm is also known as the asset beta and it will be the beta of the company that does not show the impact of the debt. The asset beta will measure the volatility of the returns of the company without taking into account its financial leverage. The asset beta of the company will compare the risk of an unleveraged firm to the risk of the market. it is commonly known as the asset beta because the volatility of the company that is not financed b y the debt is the result of only the assets. The asset beta can be computed using the following formula;

Equity beta is determined by slope of the returns of ship portfolio and the excess market risk. Beta coefficient is computed using the following formula;

Beta = . Using Microsoft Excel, the beta value is the slope which is equal to 1.268504

The firm is assumed to have zero tax rate and hence t= 0

is defined as the D/E ratio. For the purpose of this analysis Damodaran’s industry average D/E ratio is used and it is 0.75.

With the information above, the asset beta will be computed as follows;

Asset beta =  = 1.268504/1+0.75 = 1.268504/1.75 = 0.725

As was said before, beta is a measure of market risk that examines the regression of a stock in comparison to the market index, which is most usually referred to as the S&P 500. When determining a firm's beta, the debt-to-equity ratio of the company is typically given a great deal of weight to consider (this is measured by leverage). Unlevered Beta, on the other hand, evaluates the market risk of a firm without taking into consideration either the degree of leverage it uses nor the impact of the debt it carries. A measurement that is unlevered leaves out any advantages or disadvantages that are associated with debt. The phrase "systematic risk" refers to threats that a company is unable to eliminate or mitigate on its own. Systemic risks are exceedingly difficult to avoid or lessen in any meaningful sense because of their pervasive nature. One sort of risk that can be difficult to control is known as systemic risk. Some examples of this type of risk include war, inflation, and natural disasters. Beta is another statistic that may be used to illustrate the level of systematic risk or volatility that a stock or portfolio has been subjected to in the past. The risk is proportional to the stock's volatility; the lower the volatility, the lower the risk. Conversely, the higher the volatility, the lower the risk. If a firm has a beta of one, it suggests that its total risk is equivalent to that of the market. Because beta was less than 1, as was the case in our scenario, this indicates that the company's volatility was lower than the volatility of the whole market. If a firm has a beta of 2, it shows that their level of volatility is higher than the overall market.

## The formula for computing asset beta

The amount of debt that a company carries can have an impact on its performance, which in turn makes the firm more susceptible to fluctuations in its stock price. Although the company being evaluated does have debt, the unlevered beta model evaluates it as though it did not since it eliminates any references to debt from the calculation. Due to the fact that different companies have differing capital structures and debt levels, analysts are able to utilize unlevered beta to analyze enterprises relative to one another or the market. If the assets (equity) of a corporation are sensitive to changes in the market, then only then will they be taken into consideration.

There are several methods of valuing the option. Some of the models used in valuing the stock option includes the black-Scholes model. This is one of the most important modern financial theories that is used to value the asset. The model is considered because it accounts for the time value of the money by considering the risk-free rate and time. The model is considered to be one of the best because it does not ignore the volatility of the return. The stock volatility is measured using the standard deviation. It means that the asset valuation using the Black and Scholes model will incorporate the standard deviation.

When computing the option price using the Black and Scholes option pricing method, the analyst will be required to make the following assumptions;

The firm has not paid out the dividends during the life of the option. This means that company is retaining all the earnings of the company and has 0% dividend payout ratio.

The market is assumed to be perfect competitive market and there is no government intervention. It means that the price mechanism is brought about by the law of demand and supply.

The options are assumed to be European options and they can only be exercised at the expiration time.

The other assumption we need to make when calculating the value of the option using the Black and Scholes model is that the returns of the assets are log-normally distributed.

The trading of the options is assumed to be free from the transaction cost. This means the buyer of the option will not incur the cost of transaction.

In the option computation, we shall assume that the risk-free rate and the volatility of the assets or the security will be known and constant through out the analysis period.

The following formula is used to determine the value of the asset;

C =

Where P is the option price

P is the stock current price or the underlying price

E is used to represent the exercise price and r represents the risk-free interest rate.

T is the time to maturity and N is used as the formula of computing the cumulative normal distribution.

In determination of the option value using the Black and Scholes option pricing model, the following steps will be used;

Step 1: Computation of d1 and d2.

## Importance of beta in measuring market risk

d 1 =

Step 2: Computation of the cumulative normal distribution

= 0.5+ 0.4967 = 0.9967

= 0.5- 0.4918 = 0.0082

Step 3: Using the computed values above compute the value of the option using the formula for option

C =

= 8091.21 – 29.403 = 8061.81

We show that statistically equivalent patterns may be produced in the context of a dynamic capital structure model, which assumes that companies routinely reevaluate the merits of their investment and financing choices. We are following in the footsteps of Hennessy and Whited (2005, 2007), who developed the workhorse model for dynamic corporate and investment-based asset price analyses. Merton's compound option pricing formula (1973) and Toft and Prucyk's (1997) pricing of an equity option on a corporation that faces taxes and bankruptcy costs are two fundamental works that directly inform the application of a dynamic model of the firm to option pricing. Both of these authors price an equity option on a corporation that faces both taxes and bankruptcy costs. According to Geske, Subrahmanyam, and Zhou (2016), taking into account the influence of leverage helps reduce pricing errors in contrast to the traditional Black-Scholes model (1973). Leverage can have an impact on option pricing, and much like in the case of the compound option model, skewness in the risk-neutral distribution can be generated by a dynamic model of the firm (e.g., implied volatility surface sloping down). Even if the company's endogenous investment program offers a limited number of growth possibilities, there is still a significant interaction between the effect of leverage and the economic force of the options. The equilibrium implied volatility surface is therefore reliant on the current condition and can take any form, including an upward slope, a downward slope, a u-shaped shape, or even an inverted u-shaped shape. The accumulation of growth options is caused by the model's future investment possibilities as well as the presence of capital adjustment costs, which make the investment process to be lumpy. Both of these factors contribute to the model's overall flexibility. Because the model's primary source of economic uncertainty (i.e., productivity shock) is characterized as a persistent stochastic process, it is possible to anticipate future investment possibilities. When productivity shocks continue for an extended period of time, an option's implied volatility will decrease with time.

Black-Scholes makes the assumption that stock prices follow a lognormal distribution due to the fact that asset values cannot be negative (they are bounded by zero). Today's financial markets frequently display instances of right skewness and kurtosis of asset prices (fat tails). Significantly more frequently than would be predicted by a normal distribution, the market experiences downturns associated with high levels of risk.

If the values of assets are assumed to follow a lognormal distribution, the Black-Scholes model predicts that the implied volatilities will be the same for each of the strike prices. Since the market crash of 1987, the implied volatility of options that are either at or out of the money has been lower than the volatility of options that are either in or out of the money. This is happening more often as a result of the market pricing in a greater probability of a dramatic move in the markets in a negative direction. The skew in volatility that we see results from the occurrence of this phenomena. When charting the implied volatilities of options that have the same expiration date, it is feasible to produce a "grin" or "skew" form on a graph by combining the two sets of implied volatilities. When it comes to determining the implied volatility of an option, the Black-Scholes model is an abject failure.

## Valuing options using Black-Scholes model

When calculating option values in Europe, the Black-Scholes model, on the other hand, does not take into account the fact that American options may be exercised before the date on which they are set to expire. Despite this, the model contains assumptions about risk-free rates and payouts that may not be correct when applied to real-world situations. The assumption made by the model is not compatible with the fact that volatility shifts in response to variations in supply and demand levels.

In addition to this, other assumptions, such as the absence of transaction costs or taxes, the consistency of the risk-free interest rate across maturities, the permissibility of shorting securities with the proceeds, and the absence of risk-free arbitrage opportunities, can lead to prices that are different from those that can be found in the real world. In the real world, prices can be found to be as follows:

If taxes, commissions, and many other trading costs and taxes are not taken into account, it is likely that values will diverge from real results. This is another scenario in which the divergence might occur.

Fundamental analysis can be used to value the enterprise. The fundamental analysis method uses the financial statement data in determination of the value of the firm. The analyst will be required to determine the cashflow of the firm and since they will be forecasted cash flows, the analyst will be required to determine their present value through the process of discounting. The present value of the firm’s cash flows will be equal to the present value of the annual cash flow plus the present value of the terminal cash flow.

Fundamental analysis is one method that may be utilized to ascertain a stock's intrinsic value. It does this by combining information from many sources, such as market movements and news headlines, with the financial data that is available. It is essential to bear in mind that the "intrinsic worth" of a stock, often known as its "fair value," does not change overnight. You may make use of this kind of analysis to establish the most essential aspects of the firm and to assess its worth by taking into account both macroeconomic and microeconomic factors (Wafi, Hassan & Mabrouk, 2015). Because of fundamental analysis, it is possible that the share price of a firm does not necessarily reflect the stock's true value. It is frequently overpriced or sold at a low price.

Fundamental analysis enables one to forecast the patterns that the market will exhibit over the long run. Investors who hold stocks for the long haul favor it since it provides them with an indication of what the stock's predicted value will be. In addition to this, it helps you to recognize potentially lucrative businesses in which to invest, such as those that provide a high rate of return.

An additional advantage of the analysis is that it helps with one of the most important yet intangible variables, which is business acumen. This component, when investigated as part of an investment inquiry, may tell you a lot about the future of a certain firm.

The overall cost of capital which is known as the WACC will be computed using the CAPM. The cost of capital is computed as follows;

Cost of capital (WACC) =

Based on this information, the cost of capital to be used as the discounting rate in the valuation will computed as shown below;

Cost of capital =  = 0.0555

Cost of capital (r) = 5.55%

Terminal cash flow is assumed as the cash flow the firm will generate at the termination of the project. In this analysis it is very important to determine the value at the end of 2032. The determined value the firm is expected to earn will be the terminal value. The terminal value is computed using the following formula

Terminal value =

Where g is the cash flow growth rate. It is assumed to be the growth rate of the sales and r is the cost of capital of the firm.

Terminal value

Cash flow on 10th year

3153.06

growth (assumed growth of sales at last period)

4.6%

 r =

5.55%

Terminal value =

Terminal value

352307

 Computation of Annual cash flows Year (n) 0 1 2 3 4 5 6 7 8 9 10 Sales 4885 3940 4297 5567 6194 6678 7495 8440 8940 9320 9750 Sales with synergies 4885 4137 4511.85 5845.35 6503.7 7011.9 7869.75 8862 9387 9786 10237.5 Variable costs -3527.2 -3311 -3443.4 -3581.2 -3924.4 -4081.4 -4244.7 -4714.4 -4903 -5099.1 -5303.1 Fixed costs -880 -892.32 -904.81 -917.48 -930.32 -943.35 -956.56 -969.95 -983.53 -997.3 -1011.3 EBITDA 477.8 -66.32 163.598 1346.69 1648.95 1987.15 2668.54 3177.61 3500.45 3689.56 3923.13 Depreciation -162 -71.58 -69.433 282.65 -75.829 -73.554 278.652 -79.707 -77.316 -74.997 -72.747 EBIT 315.8 -137.9 94.1649 1629.34 1573.12 1913.59 2947.19 3097.9 3423.14 3614.56 3850.39 Less tax -63.16 27.58 -18.833 -325.87 -314.62 -382.72 -589.44 -619.58 -684.63 -722.91 -770.08 EAT 252.64 -110.32 75.3319 1303.47 1258.5 1530.88 2357.75 2478.32 2738.51 2891.65 3080.31 Add back Depreciation 162 71.58 69.4326 -282.65 75.8291 73.5543 -278.65 79.7072 77.316 74.9965 72.7466 Operating cash flow 414.64 -38.74 144.765 1020.82 1334.33 1604.43 2079.1 2558.03 2815.82 2966.65 3153.06 r (computed) 5.55% Discounted cash flow (OCF*(1+r) ^-n 414.64 -36.703 129.941 868.113 1075.05 1224.7 1503.58 1752.66 1827.85 1824.49 1837.17 Total discounted annual operating cash flow 12006.8 Present value of Terminal cashflow 205276

The value of the firm is equal to the present value of cash flow plus the present value of the terminal value. This computed in the table below;

 Total discounted annual operating cash flow 12006.8 Present value of Terminal cashflow 205276 Value of the firm 217283

The first step in defining the investment in the bonds or management of the bonds is the measurement of the probability of default for the corporate exposure over a give investment period. Many analysts will base their parameter estimates through comparing the results from the reported values of the rating agencies.

The calculation of the default rate will be computed using different methods. One of the methods will deal with the computation of the withdrawals. The method will ignore withdrawals and there are no adjustments for the withdrawals.

The default risk probabilities are defined differently by different rating companies. The default risk probability to be used for this analysis is the average default risk probabilities of the companies provided. This means that the average default risk probabilities are equal to 5%.

The preceding diagram illustrates that there is a substantial chance, often referred to as default risk or default probability, that a debtor would fail to fulfill the terms of the debt security that they have agreed to. The other part of credit risk is the amount of the loss, and default risk is one of the two dimensions of credit risk (Antunes, Gonçalves & Prego, 2016). Credit default swaps and other derivatives, including government and corporate bonds, need to have their values determined taking default risk into account (CDS). Assessing the default risk of these instruments is more important than calculating the quantity of the possible loss that may be incurred in the case of failure. This is because of the lower default rates that are associated with high-quality bonds (Giglio, 2016).

To phrase it another way, the price of financial instruments and the return they provide are mainly influenced by the default risk associated with such assets. Because of the correlation between higher default risk and higher interest rates, bonds that carry a higher default risk typically have a more difficult time accessing the capital markets. This is because higher interest rates tend to go hand in hand with higher default risk (which may affect funding potential).

References

Ammar, S. B. (2020). Catastrophe risk and the implied volatility smile. Journal of Risk and Insurance, 87(2), 381-405.

Antunes, A., Gonçalves, H., & Prego, P. (2016). Firm default probabilities revisited. Economic Bulletin and Financial Stability Report Articles.

Geske, R., Subrahmanyam, A., & Zhou, Y. (2016). Capital structure effects on the prices of equity call options. Journal of Financial Economics, 121(2), 231-253.

Giglio, S. (2016). Credit default swap spreads and systemic financial risk (No. 15). ESRB Working Paper Series.

Wafi, A. S., Hassan, H., & Mabrouk, A. (2015). Fundamental analysis models in financial markets–review study. Procedia economics and finance, 30, 939-947.

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