Throughout this case, extensive use will be made of the Capital Asset Pricing Model (CAMP). In order for the conclusions made in the case to be Justified, three assumptions underlying the CAMP have to be satisfied: 1) Investors can buy and sell all securities at competitive market prices (without incurring taxes or transaction costs) and can borrow and lend at the risk-free rate. 2) Investors hold only efficient portfolios of traded securities, yielding the maximum expected return for a given level of volatility.
) All investors have homogeneous expectations regarding the littleness, correlations and expected returns of securities. We realize that some, if not all of the assumptions are not realized in practice, but they are reckoned as reasonable approximations of reality. As a result, the CAMP is relatively straightforward and easy to apply. Question 1 a) In order to estimate the equity beta’s for INS, ASSAM and Old, linear regression has to be applied. More in particular, ordinary least squares (LOS).
The dataset consists of monthly stock quotes for all firms, dividend included .
The linear relation that has to be estimated is: (Ri-Ref)=a+ џ(Arm-Ref). Here, Ri is the return of the individual share, Ref is the risk-free return and Arm is the return of the market. The parameters a and represent respectively the constant and the slope of the regression line. In order to estimate the equity beta according to the LOS principles, the beta is given by Cove(Ri,Arm)Nary(Arm).
With Cove and Vary representing respectively the covariance and the variance. Fortunately, using the Slope function, Excel can calculate these values for us, Yielding: 1,972874041, 1,002967073, 0,395735831 b) The more stocks comprise an index, the less influence individual stocks have on the returns and volatility of the entire index. In larger portfolios, like the S;P 500 and the FIFTIES, more independent risk is averaged out through diversification, so they more realistically symbolize the market.
In the small AXE index, movements in just one share will have a relatively large influence on both return and volatility of the entire portfolio, so their beta’s, because not all the independent risk is properly averaged out, should be higher than were the company included in a larger index. This is the case intuitively because the index does not only include common, but also idiosyncratic risk, with the result that the correlation of the individual stock is higher, o the return reacts stronger to the index than to the market as a whole.
Question 2 Computing the asset beta for a company requires information on the capital structure of the company. More specifically, the amount of equity and net debt needs to be known. Net debt is determined by: Interest Bearing Debt – Cash and Cash Equivalents, and the beta of debt zero. Armed with these assumptions, the equation becomes ) Where pa, pee and represent the beta’s of respectively assets, equity and debt. And E, D and ND respectively equity, debt and net debt.
In millions and using most recent data, ignoring taxes: E(long)= 47284, ND(ins)=752754-64900=687854, assuming that interest is bayed on the deposits, and non of the financial assets are liquid enough to be counted as cash equivalents. 2773. 91 , 1851-2600=749 Based on and the equity beta’s calculated under question 1, the assets beta’s are. џa(ASSAM)=1. 81, Question 3 The asset beta’s for both ASSAM and Old are higher than their equity counterparts. This is the case because the net debt of both firms is negative, resulting from relatively large cash balances as compared to outstanding interest-bearing debt.
Both asset beta’s, however, differ significantly in value. Asset beta shows the market risk of a firm’s projects, while ignoring risk due to leverage. The asset beta makes it possible to compare the ‘base’ level of risk with the market’s level of risk (which is 1). Old has a low asset beta (0,45), which meaner they react weak on market risk, whereas ASSAM moves stronger than the market with a high asset beta (1. 81). B) Ins, however, has very high debt relative to equity, especially when deposits are accounted for as debt, resulting in an asset beta of 0. 3, or 0. 42 when deposits are excluded. So, when the effect of debt is excluded, Inn’s risk is low compared to the arrest. But, when the risk caused by debt is taken into account, Inn’s level of risk becomes much higher, resulting in an equity beta of 1. 93. Question 4 The debt beta measures the risk of a firm’s defaulting on it’s debt. CALM and Old both have a negative net debt, which meaner they can repay their (interest-bearing) debts immediately from their cash supplies.
So their risk of defaulting on debt is low, but Inn’s net debt is higher than its equity, which meaner that most of their capital is provided by loans, for which they don’t have the liquid assets to repay them. This earns that for CALM and Old it is reasonable to assume that their beta of debt is zero, while for INS it is not. B) Assuming the debt beta for all three firms is 0. 1, the asset betas is calculated according to the equation: џd*D/(E+D). With the results established under question 2, the asset betas become: Baa(long)=O. 22, џa(ASSAM)=1. 3, Equity beta = unleavened beta + (DIE) * (unleavened beta – beta of debt) When the debt to value ratio increases, (DIE) will be higher and the equity beta increases as well, which is explained by the bigger proportion of debt that causes a higher risk. So the new equity beta becomes: 0. 44+0. *(0. 44-01)=0. 61. Asset beta does not change when there is an increase in the debt to value ratio, because the asset beta only measures the rockiness to assets Witt respect to the market and is not changed by a different distribution of debt and equity (I. E. , a change in the capital structure).
Question 5 To determine the risk-free rate on December 31, 2010 by considering a maturity of 10 years, a benchmark is needed, for which the probability that the issuer defaults on his payments is zero. In reality, the assets that approximate this condition are government bonds, or more specifically, AAA-rated government bonds. On this date, and still in 2012, Dutch treasury bonds fulfill this requirement. The yield on December 31, 2010 was: 3. 154%. This data is taken from: http://www. Bloomberg. Com/ Question 6 The Market risk premium is assumed to be 4%.
The equity beta’s correspond to the ones calculated under question 1 . Ri=Ref+ џ(Arm-Ref): 54+1. 973*4=11. 046% Question 7 The Weighted average cost of capital (WAC) is determined by: Re*E/(E+ND)+ Rd*ND/ (E+ND)*(1-Etc). Where Re and Rd represent the return on equity and debt respectively, and Etc is the corporate tax rate. In this calculation, however, taxes are ignored, so the equation becomes: Re*E/(E+ND)+ Rd*ND/(E+ND). The return on equity for all firm’s correspond to the calculations under question 6, and the return on debt is calculated below: -; -; 4. 1% These calculations were done using the formula: WAC= Re*E/(E+D)+ Rd*D/(E *D). When taxes are not in consideration, the WAC corresponds to the return using the asset beta: Ra=Ref+ џa(Arm-Ref). With pa representing the unleavened return. The solutions are identical, with deviations resulting from rounding errors: Ra(Old)=3. 1 % Note: These calculations, however, depend crucially on assumption that opposites at INS earn interest, so the amount deposited is part of the interest- bearing liabilities. In reality however, little interest is earned on sight deposits, so the calculations may not be entirely accurate.
When deposits are not included , using the same tools as above, the equity beta equals 0. 42, and the asset beta equals 0. 496. The corresponding unleavened return is 3. 1 54+0. 22*4=5. 2, which is significantly higher than the result calculated above. Question 8 The WAC in the case where there are no taxes is independent to the relative proportions of debt and equity, because in a perfect capital marker, the total value of firm is equal to the market value of the cash flows generated by its assets, and the capital structure does not affect these.
Formally, no taxes are only one underlying assumption of perfect capital markets, but when perfect capital markets are assumed, the law of one price dictates that because total cash flows paid to all security holders of a firm, are equal to the cash flows generated by the assets, the securities and assets will have the same market value. As long as the capital structure does not influence the cash flows generated by the firm’s assets, the market value of the firm will not be affected. In reality, corporations pay taxes.
The amount of interest they pay on debt reduces their earnings, so reduces the corporate taxes they have to pay. In fact, tax deductibility of interest payments, as opposed to dividend payments in the case of common stock, is the most important incentive for firms to use debt as a form of financing. The important disadvantage of using debt to raise funds is that it increases risk. Interest payments cannot be postponed, so can create a significant amount of fixed costs. When times are bad, firms could run into problems as we have seen in the financial crisis for instance.
Just a small reduction in the value of a banks assets could leave it insolvent, this would not be the cause would their equity as a percentage of total assets have been greater, creating a cushion to fall back on. C) After taxes come into consideration, perfect capital market are no longer assumed and the WAC differs from the unleavened return. The WAC = Re*E/(E+ND)+ Rd*ND/(E+ND)*(1-Etc). The return on equity and debt, as well as the equity and net debt are based on the computations in previous questions. With a corporate tax rate of 40%, the calculations are as follows: 1 1. 24% 5. 12%
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