Net Present Value (NPV) is a financial technique used in capital budgeting to evaluate the profitability of a project. To determine the viability of investment, it is critical to invest when NPV is positive or greater than zero. Organizations face option to move forward with the investment or to abandon an investment. When an NPV is greater than zero, the investment should be accepted. The decision tree is very critical in the investment analysis. Using NPV could assist in making right investment decision. From fig 1, John could only accept the investment since it is revealed that NPV of an investment is more than 1 which is profitable. However, when the profit is $0. It will not be possible for John to pursue the investment
Fig 1: Decision Tree
In the contemporary business environment, investor should consider volatility of stock before making an investment decision. Typically, the variable behind calculating fair value of stock option is the volatility, and volatility has largest effect on stock price. Typically, the percentage change in stock price is normally being affected by the volatility of the stock price. Volatility of stock measures the uncertainty about the return that stocks will yield. Although, it is essential to pursue with the investment decision when NPV is positive, however, when there is high degree of volatility in the economy, it is better to wait before implementing an investment even when NPV is positive. It should be noted that volatility of the stock is out of control of decision maker. However, using Black-Scholes Model, it is advisable to implement short-term investment under volatility period when NPV is positive.
Moreover, "in the absence of dividends, it is not to exercise call earlier. In the real option context, it is always better to wait unless there is a cost of doing so. The greater the costs, the less attractive, the less attractive the options to delay become." (Hillier, Ross. Westerfield, and Jaffe, 2005). However, the interest rate is the critical factor that determines call premiums. The increase in the interest rates will increase the call premiums which will make the premium to decrease. To understand the effect of interest rates, it needs to compare option position to owing a stock. On the other hand, cash dividends option prices have significant effect on the underlying stock price. The stock price is expected to drop by the amount of dividends at ex-dividend rate. Dividends are very critical when exercise a stock call option. The call options are very critical when determining the cash dividend. Investment decision is based on the whether an investment stands to yield positive NPV. (Brealey, Myers, and Allen 2008).
To value a project; it is necessary to estimate the discount cash flow to determine the opportunity of highest value of a project as being measured by NPV. Given uncertainty inherent in the investment due to volatility, it is essential to assess the sensitivity of an investment using NPV. (Hillier, Ross, Westerfield, and Jaffe, (2005)
Using the Black-Scholes Model it is appropriate to start the project today and not to wait for one year before starting the project. To invest today or wait for one year before starting the project, it is essential to invest when NPV is substantially greater than zero. It is critical to invest today if the NPV of today is greater than NPV of waiting. For example, an investment that currently has negative NPV should wait until the NPV is positive. If the NPV is positive today it is better to invest today rather than wait till next year because an investment with positive NPV today is likely to generate positive free cash flow. In the real world, there is always a price to pay by delaying an investment decision. Thus, it is better to invest today if the NPV is positive and exceed the option of waiting. When there is high degree of uncertainty due to volatility, it is better to wait before implementing an investment.
Based on the application of the Black-Scholes model in the present day financial analysis, short-term investment analysis could only be valued using Black-Scholes model because volatility could change at very rapid rate within few days. Typically, Black-Scholes model is not too applicable for medium term or long-term option. As being argued by the Black-Scholes model, hedge is the key behind the derivation where option of buying and selling the underlying asset right away is very critical to eliminate the investment risks. The model calls the hedge the delta hedging which is the basis of complicated hedging strategies. Typically, Black-Scholes require an investor to make investment decision right away to eliminate investment risks in order reduce the risks of price volatility. Black-Scholes Model reveals a mathematical model in the capital market, which reveals the derivative investment instrument. Black-Scholes deduces the formula that gives the price the European-style option. The model is widely used by option market participants.
The assumptions of Black-Scholes Model are as follows:
There is no way an investor can make riskless profits because there is no arbitrage opportunity.
It is possible to lend and borrow cash at constant risk-interest rate
It is possible to buy and sell any amount of stock and this includes the short selling.
The above transaction is frictionless market where transactions do not incur paying fees.
The stock price follows constant volatility with geometric Brownian motion
It is not necessary to pay dividends in the underlying security.
Hedging position is possible with the assumption of Black-Scholes Model.
Although, the model could be applicable in the real world situation however volatility is not constant in real world situation.
The Black-Scholes is a mathematical model that follows the stochastic process to calculate the value of stock option and pricing equity option. The basic principle behind the model is that the price of an option is being determined by the price of the underlying stock. According to Black-Scholes model, the price of a stock is t-1 and is independent of price in time t, which is referred to random walk.
The Black-Scholes formula consist of three parts:
The above formula is used to calculate the option values. The part tells the price of European-style call option. The T. And S. are equal to the price of the stock that could be adjusted to interest rates, volatility, and spread.
In this option, Black-Scholes model is very similar to European-style put option, and could be calculated by subtracting the price of the stock from the present value of the stock delivery, and used to adjust for interest rates, volatility and spread.
For several years, the Black-Scholes model governs the price option because the model is a key idea behind the derivatives to perfectly hedge an option. While Black-Scholes model is widely applicable during in the past and the present capital market, the Black-Scholes model disagrees with reality in number of ways. There are limitations identified in the application of the Black-Scholes model in the modern practice.
First, the Black.Scholes model underestimate yielding trail risks that can be hedge by using out-of -- the money option. Moreover, the assumption of the model which refers to yielding liquidity risks and cost-less trading are difficult to hedge.
Typically, the simplicity assumption of the model reveals that the model does not follow the real world price. Typically, the significant imitation of the model is that it does not follow a strict stationary lognormal process. The capital market moves in a way that is not consistence with the random walk hypothesis. It'd essential to realize that volatility is constant in a real world practice, and Black-Scholes model could only be applied to very-short-term options This indicates that the model can only be applied to the short tem investment. This reveals the limitation of the Black-Scholes model because it could not be applied to the medium term investment or long-term investment.
Despite the limitation of Black-Scholes model, the model is useful in number of ways. First, the Black-Scholes could be used to analyze the direction of movement of price when crossing critical point in the financial market. While volatility is not constant, the model is a useful tool to minimize investment risks. Typically, the model is used to hedge an option in a correct proportion to minimize the risks. One of the best usefulness of Black-Scholes model is that it can be adjusted to address some of its limitation. Rather than assuming that interest rates or volatility is constant, it is possible to assume them as variables and is added as source of risks. In addition, the model could be used to solve volatility over given set of duration to construct implied volatility surface. This could be used by quoting price in term of implied volatility leading to trading of volatility of option markets. (Donald and Millo 2003).
Adjusted Present Value (APV) is a financial instrument to determine the worth of an investment.…