Using the rates yield curve rates as at 11 / 7/08.
The bond yield to maturity will
Year/bond
1
2
3
5
10
-1000
-1000
-1000
-1000
-1000
Year 1
1023
25.9
28.8
32.7
39.6
Year 2
1025.9
28.8
32.7
39.6
Year 3
1028.8
32.7
39.6
Year 4
32.7
39.6
Year 5
1032.7
39.6
Year6
39.6
Year7
39.6
Year8
39.6
Year9
39.6
Year10
1039.6
Yield to maturity
2%
2.59%
3%
3.27%
3.96%
The yield to maturity calculated above the 1 year rate of 2% is taken for this assignment.
The company beta as at the same date was 0.92 .this means that the risk free rate is 2% and market rate will be therefore, 2% + 7% = 10%.
Rs = Rf + Bs (Rm – Rf)
Where:
Rs – cost of equity capital
Rf– the return that can be earned on a risk – free investment = 2%
Rm – the average return on all securities (e.
g , S & P 500 stock index)= 9%
Bs – the securities beta (systematic) risk. =0.92
It is easy to see that the required return for a given security increases with increases in it’s a beta.
Substitute this data into the CAPM equation, we get.
Rs = 2% + {0.92 (7%)
= 2% + 6.44%
=8.44%
In estimating the cost of capital using CAPM a number of steps are followed. The model is important applications that field of capital budgeting and is known as the capital asset pricing model.
It is operated by determining for each project an appropriate discount rate for use in calculating its net present value. This rate is the risk free cost of capital plus a risk premium where the premium is determined according to the degree of risk attaching to the project in the content of its addition to an existing portfolio. The existing portfolio has a rate of return which is regarded as being a risk reel rate of return plus a risk premium appropriate to that portfolio.
It could write this as Rf + Rp. The risk premium appropriate to anew project to be evaluated is determined by the application of a factor known as the ?(beta) factor. Thus the rate of discount for the individual project is Rf + ? Rp. The ? factor is (in theory) very easily determined and is given by:
? = covar. Pi
Var p
Where covar. Pi is covariance of expected returns of the existing portfolio and those of the new project. Var p is the variance of the returns of the existing portfolio. Another way of expressing ? which might seem more meaningful is:
? = Corr pi x ?i
?p
When corr pi is the correlation coefficient between portfolio returns and individual investment returns and ?p is the standard deviation of portfolio returns
?i is the standard deviation of the individual of the individual investment returns
Thus ? depends on the correlation coefficient between the portfolio returns and the investment returns and the respective risks attaching to the portfolio and to the investment.
CAPM represented diagrammatically. Here risk is measured by ?. The risk/return profile of all assets should lie somewhere along the line rfT, which is known as the security market line (SML). It is important to recognize the difference between the capital market line and the security risk is measured in terms of standard deviation of returns. This is appropriate because the CML represents the risk/return trade-off for efficient portfolios, i.e. the risk is measured by ? i.e. only by the systematic risk elements the individual security. No individual security’s risk/return profile is shown by the CML because all individual securities have an element of specific risk, i.e. they are inefficient. Thus all individual securities (and indeed all inefficient portfolios) lie to the bottom-right of the efficient frontier
Expected return (%)
0
Risk (?)
Using book values of 31st December, 2007 and market capitalization date of 11th July, 2008.
Source (a)
Book Value (b)
(In thousands)
Market Value (c) (In thousands)
Proportions (d)
Equity
6,866,000
42,750,000
0.9388
Long term debt
2,627,000
2,627,000
0.0577
Short term debt
159,000
159,000
0.0035
Total
45,536,000
1.0000
Using the above details the asset beta will be as
Equity beta = asset beta ( 1+ (1-T)(D/E))
Whereas T is tax rate = 34%
D is market value of debt= 2,786,000,000
E is market value of Equity = 42,750,000,000
Equity beta = 0.92
Therefore,
0.92 = Asset beta(1+ (1-0.34)(2,786,000,000)
42,750,000,000
0.92 =asset beta (1+0.043)
Asset beta = 0.92
1.043
= 0.88
The asset beta is 0.88
The beta of the asset seems to lower the company’s beta. This can be explained that the overall performance of the company is due to assets that are mostly financed by the equity.
REFERENCES
Biger, N., (2007), The Cost of Capital and Capital Budgeting Decision – PP presentation
Ghetti A. (2008); Terrific introduction to financial management; Amazon
Winger and Frasca Personal Finance An Integrated Planning Approach, Pearson
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