Financial Management
Answer on Question 1
a) There are many methods in measuring the risk of the single asset. The sensitivity analysis is one of the common methods for the analyzation of risk. The three levels of the estimates are one of the forms of sensitivity analysis. This also involves the changing of the different variables in testing the sensitivity of its variables (Ibid). Taking the example of the case of Carolina Freight Company, it used the sensitivity analysis in considering the expansion for its truck fleet. From the data of the company, it recorded the use of the sensitivity analysis (Carrey and Essayvad, 1990, p. 41).
The table below shows the sensitivity analysis that had done.
This implies that if the graph of the sensitivity analysis will be drawn, then the steeper the slope will have the greater sensitivity. This method of measuring the risk helps to identify the input of the variables that can affect the asset, it can provide the useful insight regarding the risk, and it can conduct the results as well as it is easy to interpret (Baker and Powell, 2005, p. 291).
The other way in measuring the risk is the calculation its standard deviation from the expected return or to the mean. The table below shows the expected values for assigning the probabilities on the projected return.
It had determined that the expected returns of the both projects are similar, but implies that B was riskier than A. Using the standard deviation, the calculation for the project A had been done. The standard deviation for the project A will be the square root of variance or the square rot of 16,261 = 128 and the same method had been, the standard deviation for the project B will be 85. The probability distribution for both project are normal but B has the wide dispersion from the expected value. Nevertheless, the distribution for the project B will consider being riskier as compared to the project A. Both the probability distribution have the same expected value yet the project A had narrower distribution and indicates the less volatility which are relative in the expected value and less risky (Gropelli and Nickbakht, 2001, p. 86)
b) The use of correlation on the expected return is also important for the assessment of portfolio. The risk of the portfolio is always dependent on the correlation coefficient in its assets and it can be measured to the degree of moving of the two variables which the numerical value of -1.0 to 1.0. This can be defined as:
σp = √ w2A σ2A + w2β σ2 β + 2wA wβ • ρAB σA σB
Where σA and σ β = standard deviation for the asset A and B respectively
wA and wβ = weights or the fraction of the total funds that are invested in the asset A and B
ρAB = correlation coefficient between the assets A and B
The portfolio risk can also be minimized through diversification or the combination of the assets in the appropriate manner. This is also the degree wherein the risk can be minimized and depends on the correlation of the assets that are being combined. As an example, the combination of the two perfectly correlated assets and the portfolio risk can be eliminated. This means there is no reduction of risk if there is combination of the two perfectly positive correlated asset (Shim, J et. el, 1998, p. 176). The example can be done in the ownership of the two housing or automobile stocks.
Asset σ w
A 20% 1/3
B 10% 2/3
The portfolio risk will be:
σp = √ w2A σ2A + w2β σ2 β + 2wA wβ • ρAB σA σB
σp = √ (1/3)2 (0.2)2 + (2/3)2(0.1)2 + 2 ρ AB (1/3)(2/3)(0.2)(0.1)
σp = √ 0.0089+0.0089ρAB
a). It had been assumed that the correlation between the stocks A and B is +1 which has the positive correlation. This only signifies that the value of asset A increase has the response on the market conditions and to the value of the asset B which has the same rate A. This means that the portfolio risk for ρ = +1 which can becomes:
σp = √ 0.0089+0.0089ρAB = √ 0.0089+0.0089 (1) = √0.0178 = 0.1334 = 13.34%
b.) If the value of ρ = 0, its assets lack the correlation and the portfolio risk which is simply the risk of the expected return for the assets. Example is the weighted average of the standard deviation of individual assets of the portfolio. This means that when ρ AB = 0, the portfolio risk in this example will be:
σp = √ 0.0089+0.0089ρAB = √ 0.0089+0.0089 (0) = √0.0089 = 0.0943 = 9.43%
c) If ρ = -1, then it means that they are perfectly negative correlation which also signifies that the price of A rises the price of B declines at the same time and rate. In this case, the risk is eliminated completely. Therefore, when ρ AB = -1, the portfolio risk will be:
σp = √ 0.0089+0.0089ρAB = √ 0.0089+0.0089 (-1) = √0.0089 – 0.0089 = 0 .
Comparing the results of a, b, and c. It had been seen that the positive correlation assets will increase the risk of portfolio and above the zero level of correlation while eliminates the risk for the perfectly negative correlation.
Answer on Question 2
The investors that currently holding the common stock in 1 year, the stock value can be the present value for both the dividends that needs to be received in the a year while at the end of the year for the expected market price per share. If the common stock has no definite maturity value and can be held in many years, then it is important that multi period model is needed. The general stick valuation is defined in the following form:
P0 = ∑ Dt / (1+r)t
There are four ways in valuing the common stock for the cases of dividend growth. This includes the use zero growth, the constant growth in Dividend, the non-payment of the dividends at the first few years, and the irregular dividend during the first few years and needs to follow the constant growth rate which is in dividend.
Zero Growth
For the case of the zero growth, if
D0 = D1 = ….= Dn
The valuation model therefore is:
P0 = ∑D/(1+r)t
The formula can also reduce by:
P0 = Dj / r
In accordance to the fundamental theory of the value, the financial asset value at any point in the time equals to the present value of the entire dividends. The future dividends also can be the same and the present value of the dividend stream will constitute the perpetuity. This implies that the present value of the perpetuity is simply equal to:
C/r or, in this case, D1 / r
In the case of the Superland, Inc. it has the common stock that is paying for .00 dividend and is expected to remain the constant forever. The required return will be 10%. This means that the stock which needs to be selling today will be /0.10 or it is . The stock for 1 year therefore is equal to value of the stock P1 which must be equal to the present value of the remaining future dividends. The dividend is known to be constant and D2 = D1 , and the value of P1 is given below:
P1 = D2 / r = /0.10 =
In general, the absence of the changes in the expected cash flows and to the given constant rate discount is the price of the no-growth stock which can never be change. In other aspects, there are no reasons in expecting the capital gains income taken which taken from the stock (Georgia State University, 2008).
Constant Growth
In the year 1973, Jonh Burr Williams, developed the discount dividend model which can be used by investors in forecasting the dividends which can pay by the company and can also discount them from the confidence forecast. Therefore, if the dividends will grow at the constant rate, the Gordon and Shapiro can produced to be one of the most commonly used formulas in the valuation of the stock (Wake Forest University, 2008).
In the real world, the investors are expected generally in the firm as well as the dividend it pays which can grow over time. The constant growth stocks can then be use which is the stock whose dividends are all expected to have the growth at the constant rate in the foreseeable future. This also fits to the some of the established firms and tends to have the growth for the long run for the same rate as in the economy. In this case, the constant growth can be assumed that the dividends can grow at the constant rate for g and every year Dt = D0 (1+g)t, then the above model can be simplified as:
Pa = D1 / r – g
Take the example of the D1 = .00, r = 10%, and the dividends are all expected to increase by 5% every year. The stock can have the price today and the equilibrium value for the constant-growth which is D1 / r – g = .00/0.10 – 0.05 =
On the other hand, the value of the stock can be also being computed with the given rate of 3% and that is:
D1 / r – g = .00/0.10 – 0.03 = .29
The used model can make the assumption regarding the flat of the continuity growth, the stock’s risk which reflects the single discount rate, and the extrapolation from the past dividends can reflect the future earnings (Shim, J et. al., 1998, p.179).
Non Payment Dividend During the first few years
This the supernormal growth of the DDM that states that the value of the common stock of the firm is equal to the present value of the expected dividends and during the above normal growth period added and added to the present value of the terminal price which is the entire value of the remaining dividends up to infinity and begins at the start of the constant growth.
Vn = ∑ Do (1+g)t / (1+ks)t + Pn / (1+ks)n
The investors can have the multiple-year holding period that can be given in the investors can be hold by the common stock for greater than a year and it can be useful in valuing the stock for over the expected holding period of the investors. The example of this is the plan of the investor in holding the stock of RF for 2 years. RF Expects to pay in the common equity of the shareholders of .25 per share for the two years. It has also been anticipated that the stock will close at the end of time at per share. At the given rate of 10%, the value of the firm in the common stock has two-year time period. Therefore, computing the value of RF will be .24/(1+10)1 + .25/(1+10)2 + /(1.10)2 = .49.
Irregular Payment of Dividend and Constant growth rate of dividend
The above equation can also apply to the two stage of DDM to the delayed dividend stream. Take the example of the company which can pay no dividends during the first stages though they have to pay the other dividends at the constant rate. Since the company can have the possibility to experience the different growth levels in the dividends and earnings for the time, the variable growth can be use in this change of dividend growth rate. This can be considered as the multi-stage growth pattern which can involve the high growth for the certain period and followed by the stable growth due to the fact that the company cannot maintain the high growth in the entire period. The model is suited for the companies which cannot sustain the high dividend payments. As an example, the expected dividend of the analysts at the certain corporation is growing at the rate of 20 percent for the next four year with the 5 percent at the year thereafter. The firm paid the dividend of per share whereas the investors are requiring having the 12 percent return. There are steps to follow in valuing the firm as finding the present value at the supernormal growth model and that is .54. The second step is the present value of the terminal price at the end of the supernormal growth which is .25. Lastly is the present value for the dividends in the 4-year supernormal growth at the terminal price of the year 4 which is .10.
Answer on Question 3
The first justification in the high dividends is that the stockholders want the current time. This means that they have the ability in selling the portion of the shares every year in getting the income but need to incur the cost of transaction and the possibility of the capital gains taxes. This also implies that the stockholders are said to prefer the dividends in retaining the earnings due to the fact that the dollars of the dividends in the hand is much better as compared to the of the hoped for capital gains n the bush. In summary, these are less risky and more valuable to the investors as compared to the retained earnings. For the second theory, the investors maintain the group care for only the total returns and not about the receiving of the form of dividends or the appreciation of the prices. The said “dividend irrelevance” tells that it is merely the financing decisions which is the way of dividing the pie of the corporate earnings. This implies that the only important determinant of the company’s value is the power of its future earnings, as well as paying the high dividend while retrieving the capital in the new debts or stocks and matter for the investors. For the third theory, it implies that the company is caring for the total returns and are divided at the mid of the price and the dividends appreciation and commonly due to the tax code. In this extent, the dividends are taxed at the higher rates as compared to the capital gains whereas the investors will collectively prefer to have the lower rates regarding the payout policy (Stern and Chew, 2003, p.196).
Regarding these policies and theories, there are statistical problems that arise in making the results inconclusive. In this manner, none of this theories can provide the exact answer to the way the companies can choose to pay out the higher proportions of the earnings which are dividends and end up producing the higher total returns for the stockholders. In general, I think, the most advisable to use is the signaling effect of the dividend which had been said to arise in the information of the asymmetries at the mid of the managers and the investors. This signifies that the managers are reluctant in cutting the dividend and they increase the dividends if they are optimistic in the future earnings while the cash flow enable them to maintain the higher payout and the earnings. The investor is aware in the said issues due to the reason that the managers are likely to have the clear view of the prospects companies.
Bibliography
Stern, J and Chew, D 2003, The Revolution in Corporate Finance, Blackwell Publishing, United States.
Shim, J et. al., 1998, Schaum’s Outline of Financial Management, McGraw-Hill Professional, United States.
Groppelli, A and Nikbakht, E 2001, Finance, Barron’s Educational Series, United States.
Baker, K and Powell, G 2005, Understanding Financial Management: A Practical Guide, Blackwell Publishing, United States.
Carey, O and Essayvad, M 1990, Essentials of Financial Management, Research & Education Association. New Jersey.
Basic Stock Valuation 2008, Wake Forest University, viewed 28 July, 2008, http://www.wfu.edu/~palmitar/Law&Valuation/chapter%204/4-3-2.htm#constantgrowth
Common Stock Valuation – The Nonconstant Growth Case 2008, Georgia State University, viewed 28 July, 2008, http://www2.gsu.edu/~wwwms1/8622summer03/files/StockValue.ppt#264,9,T9
Credit:ivythesis.typepad.com
0 comments:
Post a Comment