Executive Summary
The current paper is devoted to studying of two financial valuation approaches and consists of two parts. The first part contains a description of Adjusted Present Value (APV) as valuation method and its advantages over other valuation methods. Computation of APV of the Top Plc Company was provided.
The second part of the paper is devoted to the description of Black-Scholes Model, its practical application and limitations on the example of House4You Company.
Introduction
There are many valuation methods in financial analysis. The first part of the paper is devoted to the description, analysis and application of Adjusted Present Value method (APV). APV method is gaining more popularity nowadays as using WACC method is sometimes dangerous for an analyst. The advantages of application of APV method over WACC and CCF methods are described and a practical application of APV method is given on the example of Top Plc Company.
Black-Scholes Model is often used for the valuation of the value of an option. Its practical implication is given in the current paper with the detailed description of the limitations of the model are described. The value of an option is shown on the example of House4You Company.
1. Part A
1.1 Advantages of APV as Evaluation Method
APV method of assets in-place operations valuation appeared as an alternative to WACC method. One of the reasons why analytics choose APV is that APV requires fewer limitative assumptions. Another advantage is that APV is less inclinable to significant errors. But the most important advantage of APV is that together with assets worth it helps determine the source of value (Leuhrman, 2003).
Most of the discounted-cash-flow methods forecast cash flows discounted at a riskless rate (Harris and Pringle, 1985). Compared to discounted-cash-flow methodologies, APV analyses financial operations separately and then adding their value to business, while discounted-cash-flow methods differ in details of their realization, in particular, the way how value is created and destroyed (Leuhrman, 2003).
WACC approach is in adjusting the discount rate or the cost of capital aiming to show financial improvement. The serious disadvantage of this method failed to reflect financial side effects (Modigliani and Miller, 1958). Besides, it addresses tax effect and uses only one discounting operation, thus representing a simplified calculation which advantage is irrelevant nowadays (Leuhrman, 2003).
APV appears to be more flexible method in comparison to discounted-cash-flow method or WACC and it can be adjusted to particular circumstances as well. Thus, APV is more convenient than WACC methods because:
Utilization of fixed debt ratio is not necessary. The value of unlevered firm is calculated separately from debt calculation with no relation to the firm value (Sabal, 2005).
The formula for the present value of the tax shield computation considers tax legislation for each computed period what helps avoid approximate assumptions (Sabal, 2005).
APV model provides the debt value in absolute value while using debt ratio I n WACC model is not sufficient (Miller, 1977).
Capital Cash Flow (CCF) method as an example of discounted-cash-flow method can be treated as one of the versions of APV. It can be described as an incomplete capital structure model, implying 100% of debt, thus APV represents better method since it reflects wider information compared to CCF (Booth, 2007).
Interest is assumed that the risk free rate is the cost of debt.
To conclude, APV took positive value, it means that the project should be accepted. Analysis of Equity and Debt financing showed that PV of Debt is greater, thus, Debt financing of the project is more preferable.
2. Part B
2.1 Limitations of Black-Scholes Model
Black-Scholes Model is considered one of the best approaches in financial theory being widely used. It gains more popularity nowadays gradually replacing other valuation models, such as WACC and CCF approaches (Rubash, n.d.). The Black-Scholes Model is used for the calculation of a theoretical call price of an option using main variables: stock and strike prices, time to expiration, risk free interest rate and volatility (Hoadley, 2011).
One of the biggest advantages of this model is the possibility of estimating market volatility of underlying assets as a function of price and time without referencing to particular investors’ characteristics (Renico, 2011).
The second advantage of using this model is hedging, a kind of self replicating strategy which provides insurance against loss, due to which an investor can trade derivatives in accordance with this strategy not incurring loss (Hoadley, 2011).
However, Black-Scholes Model also has certain limitations of its application. The limitations are mainly linked to assumptions regarding the market used in the model. The limitations are as follows:
Volatility (a measure of a stock fluctuating) is expected to be constant over time which is not possible. While volatility can be constant in a short term period, it cannot be constant over the long term (Teneng, 2011).
The direction of the market or a stock is unpredictable. The assumption is that the price of underlying stock goes up and down with an equal probability which is not actually true (Teneng, 2011).
The assumption of normal distribution of log returns and underlying stock prices are appropriate though contradict observed financial data.
The assumption of constant interest rates is not applicable to the real world. A notion of risk free rate is conventional (Teneng, 2011).
Dividends are not paid during the options life while most companies actually pay dividends. The assumption is applied with regard to the basic Black-Scholes formula since later versions of the model were adjusted to dividends (Radhakrishan, 2004).
The model does not consider any trading expenses, such as, commissions and transaction costs. It is not usually true because brokers charge rates (Teneng, 2011).
The model assumes European-style options which are exercised on the expiration date while American-style options can be exercised at any time during the option life (Coelen, 2002).
The model assumes that markets are perfectly liquid and any amount of stock is available any time. This appears not to be a plausible assumption since investors possess limited amount of money to invest, depend on policies of the companies and the willingness of sellers to sell (Teneng, 2011).
The limitations listed above related basic Black-Scholes Model mainly because there was other advancing of the model. It is impossible to capture all the aspects of the market while Black-Scholes Model advancing attempted to do so (Boehme, n.d.).
2.2 Practical Application and Analysis of Black-Scholes Model
2.2.1. Estimation of the Value of an Option Using Black-Scholes Model
For estimation of the value of a given option (C) the following formula should be used:
C = SN(d1) – X*e˄(-rt)*N(d2),
where S – current stock price, e – Euler’s constant (2.718…), t – time remained till expiration (percent), X – exercise (strike) price, r – riskless rate.
d1 = ln(S/X) + [r+(0.5*σ²]T/σ√T,
d2 = d1 - σ√T, where σ - market volatility.
S - current price, S = 36+6=£42m (NPV= PV of inflow – PV of outflow; 6 = x – 36; x = £42m).
House4You is a company paying dividends with cost of capital 10%. Let us compute minimum value with dividends using current stock price of £42m at risk free level of grow stock equal 6%:
d1 = [ln(42/36)+(0.06+0.5*0.2²)]*3/0.2√3= (0.15+13+0.24)/0.3464 = 0.39415/0.3464 = 1.1378 ≈ 1.14.
d2 = d1 - σ√T = 1.1378 – 0.7914 = 0.79.
Thus, N(d1) = 0.8729, N(d2) = 0.7852.
C = (42*0.8729) – (30.069*0.1852) = £13.05m.
As it can be seen from the calculations provided, the actual present value of the project could be significantly larger than estimated if House4You Company will not exercise the option to build. The additional value obtained shows that the risk was partially eliminated by the ability to delay the construction of the housing complex at Smalltown. A decision based on the evaluation is as follows: the investment should be delayed until the Government announcement regarding transport link construction. The Company should place a value of £13.05 million on the project including option delay.
2.2.2. Estimation of Overall Price of the Project
For the estimation of the overall price of the project, method of discounted cash flow was used. Let us calculate discounted cash value using the following formula (Fernandez, 2005):
DPV = FV/(1+r) ͭ ,
where FV - the nominal value of a cash flow amount in a future period; r – cost of capital, t – time when future cash flows occurs (in years).
DPV = 42/(1+0.1)³ = 42/1.331 = £31.5552m ≈ £ 31.56m.
Thus, the present value of future cash inflows at the end of the third year is 31.56m. Since discounted cash flow method is widely used in real estate development, it is applicable for the estimation of the present value of the project.
2.2.3. Limitation of Valuation Method
In this example Black-Scholes model of the option delay evaluation was used. There is a difference between European and American options: American options can be exercised at any time up to the expiration date. Thus, a potential investor should take into account that only American options can be exercised at any time.
To answer the question if the government will announce the beginning of the construction of the new transport link at any time over next three years, the Table 3 was developed.
As it can be seen from the Table 3, the most unsuccessful time for the option call will be if the government will announce the development of a new transport link during the first year.
The second year is not as bad as the first one. The third year is the best time to the project commencement.
Conclusion
The APV method and the Black-Scholes model were described in the current paper. APV method is often used for advanced computation of the net present value (NPV) which takes into account financial effect of the NPV.
The Black-Scholes model is often used for the computation of the value of the options. However, this method has limitations in its implication which were described in detail in the second part of the paper. The value of the Black-Scholes model is that it takes into account volatility of the market to some extent which is considered unpredictable.
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