# Capital Asset Pricing Model

Weighted Average Cost of Capital depicts the overall combined cost of equity and debts to finance the business operations or acquisitions. It is calculated as follows

WACC=E/V * Ke + D/V * Kd (1-t)

Where E is Equity

D is total Debts

V is total of Equity and Debts used for financing

Ke is the cost of Equity

Kd is the cost of Debts

t is the ratio corporate tax

In case of goodway plc holding company, we have relevant figures for the calculation of the weighted average cost of capital.

 Market price per share £ 1.10 Dividend 11.4p MV of Irredeemable loan stock £ 31.60 MV of Redeemable loan stock £ 103.26 MV of Unsecured loan £ 75.42

And the figures from the balance sheet

 Accounts £ MV of irredeemable debt 442400 MV of redeemable debt 1548900 MV unsecured Loan 1500000 Bank loan 1540000 MV of Equity 2200000 V (equity + debts) 7231300

The cost of equity is calculated on the basis of a formula

Kd = Do/MV

Do is the dividend paid

MV is the market value of a share

 cost of equity Ke 10.36

Cost of debts for irredeemable loan stock is calculated by

Kd = I/MV

I is the rate of return

MV is the market value of per stock

 cost of irredeemable debt Kd 9.49

The cost for redeemable loan stock is calculated by the internal rate of return Method

 time Cash flows DF @ 15% PV DF @ 5% PV 0 -1548900 1 -1548900 1 -1548900 1 to 10 Interest payment (9*(1-0.35)) 87750 5.02 440396.9469 7.72 677582.2 Capital Repayment 1500000 0.25 370777.0592 0.61 920869.9 NPV -737725.994 49552.12

IRR = 5% + (49552.12 / (49552.12+737726) × (0.15-0.05)

 IRR of redeemable loan 5.63

The unsecured loans cost is also calculated by the IRR

IRR = 0.04+ (483778.2 / (249637+483778.2)) × (0.1-0.04)

 time Cash flows DF @ 10% PV DF @ 4% PV 0 -1500000 1 -1500000 1 -1500000 1 to 10 Interest payment (6*(1-0.35)) 78000 6.14 479276.2342 8.11 632649.9 Capital Repayment 2000000 0.39 771086.5789 0.68 1351128 NPV -249637.187 483778.2
 IRR of unsecured loan 7.96

By using all these calculations the weighted average cost of capital is calculated.

 Types Of Capital Amount £ % of total the cost Cost pre-tax Cost After-tax Weighted cost MV of Equity 2200000 30% 10% 10% 3% MV of irredeemable debt 442400 6% 9% 6% 0.3% MV of redeemable debt 1548900 21% 8% 5% 1% MV unsecured Loan 1500000 21% 12% 8% 2% Bank loan 1540000 21% 13% 8% 2%
 Weighted Average Cost Of capital 8.11%

According to the shilpa Gohal’s opinion for different projects, the only cost of capital is inappropriate because the weighted average cost of capital is calculated on the base of debt financing for a particular project. So for every project the cost of capital should be calculated separately.

Keeping in mind the above-mentioned statement it is true because WACC is calculated for particular debts and issued capital. Modigliani and Miller (1958) in corporate finance theory contributed by saying this only WACC is inappropriate for calculating the cost of capital because for different risks the required rate is different.

Moreover, figures of goodway plc show information related to the particular projects. So the WACC calculated could not be used for the evaluation of all the different projects. Similarly, the debts used for financing have a different required rate of return. And the maturity time is also different. So, for example, the goodway plc invests in long-term projects then the debt value to finance those projects will also be dissimilar, because the long-term projects need major investment and financing but a company cannot meet all projects with the only cost of capital.

Another side of using WACC for all projects and keeping the point of view of Lord Hariss tweed, it can be used for projects with the same level of risk as well as a same amount of investment. To support of this argument Grinblatt and Titman (2002) note that “the WACC of a firm is only relevant to the one of its projects only when these projects has same risk profile as the entire firm”. Similarly, Brealey, Myers, and Allen (2005) particularize that “the weighted average cost of capital formula works only for carbon copies of projects which firm already hold”.

Finally, shilpa Gohal’s is right in her opinion that for all projects the discount rate must be calculated separately. Single WACC is purely unable to describe the cost of capital for all other projects.

## 3.1.1. Capital Asset Pricing Model:

CAPM is used for the risk-adjusted required rate of return or the cost of capital. It is calculated on the basis of β which the relative measure of risk. β shows how much riskier is the investment for a particular firm. The firms paying more than the average required rate of return are considered having more risk than the market.

Required rate = risk-free rate + β( average return on market – risk-free rate)

### 3.1.2. Risk:

The risk is a most probable loss of Investment. There are two types of risk systematic or symmetric risk, and other is the unsystematic or asymmetric risk.

1. Symmetric Risk, this risk is known as a market risk which almost same for all. This risk is the non-diversifiable risk for investors.

2. Asymmetric risk, this risk is known as a firm risk which varies for firms. This is the diversifiable risk by creating a portfolio.

Mostly the Investors demand for the asymmetric risk form the firm so on average the required rate of return meets their demands.

### 3.1.3. Beta understanding:

Beta is known as the relative measure of risk, which determines the actual risk associated with the firms. It is calculated statistically by using the variance and covariance. Once β is calculated it shows the riskiness of firms as follows.

If the value of β >1 it shows that Investment is more risky than average.

If the value of β<1 it shows that investment is less risky than average.

If β =0 it shows investment is risk-free.

### 3.1.4 Beta for project appraisal:

For a firm, it is difficult to take decision while investing in another company. Because which β should be used for calculating the cost of capital. So the β for a geared company is calculated by this formula.

β a= {Ve/( Ve+Vd(1-t))* βe} + {Vd(1-t)/(Ve+Vd(1-t))* βd}

βa = assets beta

Ve = market value of equity

Vd = market value of debt

βe= equity beta

βd = debt beta

t = corporate tax

This beta is used for calculating the cost of equity by CAPM, and also useful for the calculation of the weighted average cost of capital.

CAPM is useful for both Investors and equity issuer. Firstly, according to the Investors point of view, it provides the accuracy in required rate of return. Return calculation is accurate because it provides the extra return for taking the asymmetric risk. Secondly, it is important for equity issuer because the cost of equity is calculated by adjusting the riskiness of the firms.

## 3.2. (b):

### 3.2.1. Cost of Equity by CAPM:

Firstly the asset beta of the company is calculated by de-gearing where goodway plc want to invest.

The formula is

β a = {Ve/( Ve+Vd(1-t))* βe} + {Vd(1-t)/(Ve+Vd(1-t))* βd}

In this company β assumed is equal to zero so the formula is

βa = Ve/( Ve+Vd(1-t))* βe

Market value of noggin plc is,

 Equity beta 1.51 Vd long term debt value 2600000 Ve equity value 2106000 T 35%

βa = 0.837

Now by using this assets beta, goodway plc’s beta would be found by re-gearing.

 debt beta 0.2 MV of Equity 2.2e+06 MV of irredeemable debt 442400 MV of redeemable debt 1.5489e+06 MV unsecured Loan 1.5e+06 Bank loan 1.54e+06 V (equity+debts) 7.2313e+06

β a= {Ve/( Ve+Vd(1-t))* βe} + {Vd(1-t)/(Ve+Vd(1-t))* βd}

Where βa = 0.837

0.837= {2200000/2200000+5031300(1-0.35)}* βe + {5031300(1-0.35)/ 2200000+5031300(1-0.35)* 0.2}

βe = 1.784

This is beta for goodway plc, and this will also be used for calculating the cost of equity by using standard CAPM formula.

Ke = Rf+ β( Rm- Rf)

Ke is cost of equity

Rf is risk free rate

Rm is market risk return

Ke = 0.05+ 1.784(0.14-0.05)

Ke= 0.2105 = 21.05%

Now the risk adjusted cost of capital is.

 Types Of Capital Amount £ % of total the cost Cost pre-tax Cost After-tax Weighted cost MV of Equity 2200000 30% 21% 21% 6% MV of irredeemable debt 442400 6% 9% 6% 0% MV of redeemable debt 1548900 21% 8% 5% 1% MV unsecured Loan 1500000 21% 12% 8% 2% Bank loan 1540000 21% 13% 8% 2% Weighted Average Cost Of capital 11%

The Risk-adjusted cost of capital is 11% while the weighted average cost of capital for goodway is 8.11%. Goodway plc will face 2.89% extra cost of capital if they invest in Noggin plc because the beta for noggin plc is higher than 1 so the investors will demand a higher rate of return. Finally, the higher demand will result into an increase of Ke, so the Risk-adjusted cost of capital would be higher.

### 4.1. Critical Analysis:

According to Mark Darcy’s comment, if the Goodway plc issues more debt rather than the equity, it will lower the weighted average cost of capital. To some extent issuing more debt will result in the decrease in weighted average cost of capital because it will provide the tax relief to the company. Similarly, the values of cash flows and discount rates are opposite for the company. The cash flows can be maximized when the WACC is minimized. So the problem is how to minimize the weighted average cost of capital?

In support of the Mark Darcy’s comment, when a company uses more debts than the equity this terminology is known as the financial leverage. If it is assumed that the corporate tax is zero then the levered company will increase the shareholder’s wealth. Issuing more debt will increase the earning per share and the return on equity which will describe the better performance of the company. If goodway plc’s operating activities are good enough to generate the higher earnings before interest and taxes then issuing more debt than equity will be beneficial for the company. Moreover, it depends upon the other factors faced by the company. It should select the optimal point of equity and debts to maintain or minimize the weighted average cost of capital.

For optimal debt, to equity ratio two noble Laureates Modigliani and Miller gave their point of view, which is known as “Modigliani and Miller preposition”. They noted that corporate borrowings are less significant when it comes to corporate structure because investors can borrow or lend on their own. So the value of stock remains same whatever the cost structure is chosen. According to their first preposition, it is totally irrelevant how a firm chooses to arrange its finances, but when the firm issue more debts than the equity it takes to the firm’s credibility to pay its debts. On another hand, if issues more equity than its debts the cost of capital increases because the investors demand more for the compensation of risk. In their second preposition, they explained that if firms issue more debts then equity the financial risk increases and shareholders demand more return for financial risk. The business risk which is associated with operational activities is already compensated in their return Modigliani and Miller (1958). Finally, Modigliani and Miller suggested that firm should select the optimal point where the tax benefits from debts are equal to the direct bankruptcy and indirect bankruptcy cost resulted from the increased probability of financial distress.

Finally, keeping in mind the existing literature Mark Darcy’s comment should not be considered in case of goodway investment. The contradiction to the Mark Darcy’s comment is due to the current financial situation of the company. In current scenario the goodway capital structure is already divided into 30% of equity and 70% of debts, so increasing more debts will result into an increase of cost of equity. If a company increases the debts the shareholders and bondholders will demand more return to compensate their financial risk, as well as the weighted cost of capital, will increase. So the company should issue some equity to finance the upcoming projects to lower the weighted average cost of capital.

## 5.1. Critical Analysis:

Organic growth is the growth rate that a company can achieve by enhancing its output and sale other than merging or acquiring the subsidiary companies. To some extent, organic growth is better for the companies because when the company sets a goal and does its best to achieve that goal without involving and dividing its efforts to other tasks. Companies following the organic growth can easily meet their liabilities and increase the wealth of shareholders.

For more understanding, if there are two companies A and B. Company A is growing at a constant rate of 8% but the company B’s growing rate after a decision is 20%. The investors would probably want to invest in company B because of its growth rate. But actually, Company B purchased its competitors due to the decrease in their sale of 5%. By acquiring its competitors the risk of company B increases as well, But company A’s risk is same. So the better option for investment is A.

The acquisition is basically the inorganic growth of a company. It is done when a company wants to minimize the threats of competitors. In acquisition, a company buys not all but 50% of the stake to control it. Acquiring company take all the decisions related to production, financing, and operating.

In case of goodway plc if company focus on the organic growth rate it is beneficial for the company because the current financial position is in favor of organic growth. If the company invests in other projects related to their production their risk will remain constant. The bondholders and shareholder will not put extra pressure on the financial disasters. With constant growth goodway plc will be able to meet all its liabilities.

If the company invests in the Noggins plc this would be a riskier investment. The target company has beta more than 1 which is much risky. By acquiring Noggins plc the weighted average cost of capital will increase because equity holders and bondholder will ask for more return. The overall liabilities will also increase which is a negative sign for goodway because they already have high debt to equity ratio. So goodway should focus on the organic growth.

## References:

Brealey, Richard A., Stewart C.Myers, and Franklin Allen, 2005, Principles of Corporate (McGraw-Hill: New-York, NY).

Graham, John R., and Campbell R. Harvey, 2001, The theory and practice of corporate
finance: evidence from the field, Journal of Financial Economics 60, 187-243.

Grinblatt, Mark, and Sheridan Titman, 2002, Financial Markets and Corporate Strategy (McGraw-Hill: New-York, NY).

Modigliani, Franco, and Merton H. Miller, 1958, The Cost of Capital, Corporation Finance and the Theory of Investment, The American Economic Review 48, 261-297.

Shin, Hyun-Han, and Ren´e M. Stulz, 1998, Are Internal Capital Markets Efficient?,
Quarterly Journal of Economics 113, 531-552.

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