The Importance of Cost of Capital in Financial Management

The Importance of cost of capital in Financial Management
The concept of cost of capital is crucial in financial management. Like any other source of finance has a cost and cannot, therefore, be used in the most effective manner unless that cost can be accurately determined and taken into account.
There are many misconceptions about the cost of capital which must be carefully avoided. If, for example, a business has large amount of cash which it proposes to invest in a project, it might appear that the finance in this case is free of charge because no payment has to be made for its use to outside suppliers. It should be remembered, however, it does have an opportunity cost, ie the cost of foregoing which the cash might have earned in some other use even if this only be the placing of it on deposit at a bank.
Another cause of difficulty is the notion of the weighted average cost of capital. The fact that debenture is issued in order to raise the cash for a project does not mean that the cost of that debenture is the cost of capital for that project. Finance is not normally project-specific and must be regarded as being drawn from a common pool containing all sources in a desired mix. Many questions will require the calculation of weighted average cost of capital.
In this paper, I will try to illustrate the main variations on the theme of the cost of capital which are likely to be encountered and the main difficulties associated with these. They are:
The cost of individual components of capital, that is equity and debt.
The calculation of the weighted average cost of capital
The concept of marginal cost of capital
The implications of expected growth to the cost of equity.
It should be notices that other topics can creep unto question on the cost of capital. Examples are the calculation of the market prices of securities, ratios and investment appraisal.
Cost of individual components of cost of capital
To illustrate the implications of calculating individual components of cost of capital, I will use an example to explore the issues related to evaluate how debt affects the cost of capital and the concept of marginal cost of capital, to decide what form of finance best suite for a project.
Example:
Company X has the following balance sheet as follows:
000's
Share capital (1.00 per share) 5000
Reserves 2000
Trade creditors 3000
overdraft 1000
Total 11000
000's
Fixed assets 6000
Stock 3000
Debtors 2000
Total 11000
It intends to invest in a major project, which will increase earnings by 30%. The project will require the purchase of fixed assets totaling 2 million and stocks, debtors and creditors will increase by 25%.
At present the annual profits of the company are 2 million and dividends of 1.5 million are paid. Assume these figures are expected to to persist indefinitely ignoring the new project. The ordinary shares have a stock exchange value of 2.00 each.
The directors are considering alternative methods of raising the 2.5 million required for the project and have identified the following alternatives:
An issue of 2.5 million 15% debentures. This would have the effect of increasing to 25% the earnings yield required by the stock market on the ordinary shares of the company.
A rights issue on the basis of one new shares at par for each two shares already owned.
Say the directors want to calculate the cost of capital of the proposed debenture issue. As well, they want to calculate the value of the ordinary shares after making the proposed rights issue. Above all, they want to evaluate the relative merits of the proposed financing methods and any other alternatives to the proposed financing methods applicable for this project.
In order to address all issues relevant to this problem the directors must have a step by step method to address all the issues. My guide to this problem is as follows:
Step 1: calculate the marginal cost of capital in respect of the debenture issue.
In this example, this is complicated by the fact that the change in the capital structure has an effect on the cost of equity and that the calculation of the marginal cost of debenture issue must take into account.
Total cost of debenture issue:
Interest at 15% of 2.5 million 375000
Required increase in earnings
of equity 500000*
Total cost of Debenture issue 875000
*Current yield is earnings/ Value of equity = 2/10=20%
This has increased to 25%. That is it has to increase by 5% of 10 million. This is 500000.
There fore the actual marginal cost of debenture = 875000/2500000= 35%
Step 2: Calculate the probable value of the ordinary shares if the proposed rights issue is made.
In this instant, it can be presumed that the value or market value of the shares after rights issue is equal to the current market value of the existing shares plus the cash raised by the rights issue.
Value now is 5000000*2 10000000
Cash raised by rights issue 2500000
Value after rights issue 12500000
Number of shares after rights issue is 7500000
Value of each share = 12500000/7500000= 1.67
Step 3: Determine the rate of return offered by the major project under consideration.
Increase in earnings is 30% of 2 million. That is the expected earnings of the project is 600000.
Investment required
Fixed assets 2000000
stock 3000000
Debtors 2000000
Total 5000000
less creditors 3000000
Working capital 2000000
25% increase 500000
Total Investment 2500000
Yield = 600000/2500000=24% per year.
Step 4: Based on the above calculations, evaluate the merits of the proposed financing methods.
Step 1 shows that the marginal cost of debenture issue is 35% per year. If this form of finance is to be used the project is not worthwhile as it yields only 24%. This proposal therefore should be rejected.
The current cost of equity is 20%. It may be assumed that an increased yield is required only if gearing is introduced and that therefore the marginal cost of the rights issue is 20% per year. This same for the existing equity. This would make the proposal acceptable and this is the form of finance which should be used.
Step 5: Draw attention to alternative sources of finance.
The alternatives are:
Leasing of fixed assets. This is what is known as off balance sheet financing and means that the initial investment by the company is reduced to that required by the increase in working capital.
Consider Bank overdraft. The cash flow from the proposed project of 600000 would make it possible to pay back the initial investment of 2500000 in a little over four years. The bank may be willing to increase the overdraft facility for such a short time.
Retained profits. If dividends were curtailed and the project postponed for a period sufficient funds could be raised to finance the new project within a year or two.
The models used to calculate the expected return on equity and their advantages and disadvantages
The dividend growth model approach
The easiest way to estimate the expected cost of equity is to use the dividend growth model. Under this model it is assumed that the dividends will grow at a constant growth rate.
If the constant growth rate= g
The price per share = P0 then
P0 = D0* (1+g)/(Re -g) where D0 is the dividend paid now and Re is the rate of return on equity. That is Re = D1/P0 + g.
In this model to estimate Re one must know D0, P0 and g. For publicly traded shares D0 and P0 are readily observable. However g has to be estimated from past dividend data. The growth rate can be calculated on the basis of historical data or use the forecasts from different sources and average them because all the forecasts will vary considerably. It is obvious from this model that the accuracy of the Re depends on the accuracy of the dividend growth rate “g”. If the growth rate is not accurate then the expected return on equity also will be inaccurate more than the growth rate changes.
For example, suppose a company paid a dividend of 20 cents per share last year. The share is currently sell for 2.60. If one estimates dividend will grow steadily at 4 per cent per year into the indefinite period in the future. What is the expected return on equity?
In this example D0 = 0.2 there fore d1 = 0.20*(1+0.04) = 0.208
Using the dividend growth model Re = D1/P0 + g, Re = 0.206/2.60 + 0.04 = 0.12 or 12%.
That is, the expected return on equity or cost of equity is 12%.
In the above example, if say the growth rate is 2% instead of 4% what will be the effect on the expected rate of return? Applying the the model using 2% as growth rate the expected rate of return on equity is 0.0985 or 9.85%. That is the expected rate of return has changed by 2.15% if the the growth rate has changed by 2%. That is the expected rate of return on equity in the dividend growth model is very sensitive to the changes in the growth rate other things are being equal.
Advantages and disadvantages of the dividend growth model
The main advantage is the simplicity of the model. That is, it is easy to understand and easy to use. However, it has a number of practical problems in application and disadvantages.
First if companies do not pay dividends then the model is not applicable. Even they pay dividends this model assumes the dividends will grow at a constant rate. This is not the case for most of the companies. There fore, it is only applicable to companies where there is reasonable grounds to assume the dividends will grow steadily.
Secondly as demonstrated above the model is sensitive to changes to the growth in dividends. That is, if there is an error in the estimate of dividend growth rate the the expected return on equity will change more than the error in the estimate of dividend growth rate. As well, the dividends are estimated from past dividend records. The future dividends may considerably change because of future conditions may be quite different to the past.
Finally, the dividend growth model does not take in to account explicitly the riskiness of the investment like the Security Market Line approach. That is it does not take in to account the certainty or uncertainty of dividend growth rate. As a result, it is difficult to say the return on equity is commensurate with the level of risk. However, there is an implicit adjustment for risk using the current market price of shares. All other things being equal, the higher the risk lower the share price. Further, lower the risk higher the share price. However it has to assume all the other information is the same. This is not the case in reality.
The Security Market Line approach
According to Security Market approach expected return on a risky asset such as equity depends on three things. They are as follows:

1. The risk free rate “ r f “
   
2. The market risk premium, “E(rm)- r f”.
   
3. The systematic risk of the asset relative to average, which is the beta co-efficient, “b”.
   

That is applying the SML model Re = Rf + b:* (Rm – Rf).
Implementing the SML approach
To use one must estimate Rf the risk-free rate, market risk premium (Rm -Rf) and the beta co-efficient.
In a study it has been found the behavior of returns for shares and government bonds from 1882 to 1989 the risk premium over the period was 7.94%. Over the same period the risk free rate was found to be 5.21%. Studies in US, UK and Canada revealed the long-term premium to be around 7%. For large company shares from 1923 to 2003 it has been found that the risk premium in USA to be 8.6%, while for the 1901 to 2006 in Australia the risk premium was 7.6%. That is one can use 8% as risk premium and 5% as risk free rate in the SML model as an estimate. However, one must beware the SML model uses future reurns not past returns. The past returns can be used as future return assuming the economic conditions are not very different. If say for a company the beta of the shares is 0.875 then applying the risk-free rate of return and market premium rate the return on equity can be cal calculated as below:
Re = Rf + b*(Rm – Rf)
Re = 5% + 0.675*8% = 12%.
Advantages and disadvantages of SML approach in estimating the return on equity
The SML approach has two primary advantages. First, it explicitly adjust for risk. Second, it is applicable to companies other than with steady dividend growth. Thus it may be useful in a wide variety of circumstances.
There are disadvantages in SML approach. This approach is based on estimating the risk-free rate and the market risk premium and beta co-efficient. To the extent the estimates are poor, the resulting cost of equity will be inaccurate. For example using different time periods may estimate quite different risk premium and risk free rate. Finally, like the dividend growth model SML approach also uses historical data to estimate the inputs of the model even though the figures are for the future. That is the future is estimated on the past.
The future mat be quite different to the past and the estimation based on the past may not be relevant and it may be quite inaccurate. However, in a perfect world, the dividend and SML approach are both applicable and both result in similar answers. If this happens, one can have confidence in the estimation of the inputs in to these models. It advisable to compare the results of the calculation with other similar companies as a reality check.
The expected return on debt and preference shares
The expected return on debt
The cost of debt can be calculated using the coupon rate of say a debenture and using an approximate equation as follows:
Say the Interest = I, par value of debenture = PV, Net proceeds of issue = market price -cost = NP, number of years to maturity = n then expected return on debt “Rd' can be approximately expressed in the variables as mentioned above. The equation for the Rd is as follows:
Rd = [I + (PV – NP)/n] / (PV + NP)/2
If the rate of corporate tax is say = t%
Then the after tax expected return or the cost of debt = Rd* (1-t)
Say a company issued an eight year debenture at 7% interest on par vale of 100. Say it has been issued 2years ago.. The debenture is currently selling at 95.38. The expected after tax return calculation is as follows:
Rd = [7 + (100 – 95.38)/6] / (100 + 95.38)/2 = 7.95%
This rate of return for debentures is before tax. As tax is deductible for a company the interest cost the after tax return on debentures must be less by the tax percentage.
There fore, the Rd after tax = 7.95%* (1-0.30) = 5.565% approximately.
Expected return on preference shares
As preference shares have a fixed dividend rate, the value of preference shares is the perpetuity of the dividend amount discounted by the rate of dividend. That is, if the preference shares market price is “ P0” and the dividend amount is “D” then the the expected rate of return on preference shares “R p” can be expressed as follows:
R p = D/P0.
Say a company is trading preference shares in the stock exchange. Its current price is 2.11 and the par value of preference shares is 2. Its expected rate is 0.14/2.11. That is, the expected rate of return on preference shares is 6.64%.
The weighted average cost of capital(WACC)
Say the market value of debt = D
Market value of stock or shares = E
Then the total value V = D + E. therre fore the weights of equity is E/V and the weight of debt is D/V.
There fore like the portfolio average return, the weighted average cost of capital is as follows:
WACC(unadjusted) = E/V* Re + D/V*Rd.
If taxes are incorporated then the WACC equation will be as follows:
WACC = E/V*Re + D/V* Rd* (1- t), where t is the rate corporate tax.
Approximate and explicit after-tax expected return on debt
The equation above for the expected return on debt is an approximate equation, for the after tax expected return. The other concept is the approximate after-tax cost of debt and actual or explicit after-tax cost of debt or expected after-tax return on debt. In approximate after tax cost of debt one calculates the yield and then adjust for the tax on interest. However, in the explicit cost of debt calculation the tax is discounted and included in the original equation in one step.
If the current yield = Rd
Debt nominal interest rate = C
Par value = F
period to maturity = t
Current market price = P then
P = C* [1- 1/(1+ Rd)t ] /Rd + F/(1+Rd)t
Approximate after-tax cost of debt = Rd* ( 1- T) where T = corporate tax rate
If one wants to calculate the explicit cost of debt incorporating the tax effect in one step then the equation for explicit cost of debt is as follows:
Say the explicit after-tax cost of debt = R d(t)
Then market value P = C*(1-T)* [1 – 1/(1+R d(t))t ]/ R d(t) + F/(1+R d(t))t
say P = 94.75, C = 5, t= 3, F =100, T = 30%, then applying the approximate equation Rd or yield is as follows:

1.  
   1. = 5*[ 1- 1(1+ Rd)3] /Rd + 100/ (1+Rd)3
      

By trial and error the yield is 7%. Then applying the corporate tax equation the approximate cost of debt = 7%* (1-0.30) = 4.9%
If one calculates the explicit cost incorporating the corporate tax in one step, then Explicit after-tax cost of debt for the above inputs is as follows:

1.  
   1. = 5*(1-0.30)*[1 -1/ (1+ R d(t)3] / R d(t) + 100/ (1+ R d(t) )3
      

By trial and error the after tax explicit cost of debt = 5.443%. One can see the approximate after-tax cost of debt varies from explicit after-tax cost of debt. However, the approximate equation is a good estimate for the explicit after-tax cost of debt. There fore one can use the approximate equation as a proxy for the explicit after tax cost of debt.
Example - Calculation of WACC
Company A has 1.4 million shares outstanding. The share price of the company is currently is 20.00. The publicly quoted price of debt currently is 93 cents of par value. It has total book value of 5 million. The current yield is 11%. The risk-free rate is *5, and the market risk premium is 7%. The beta estimated for company A is 0.74. The corporate tax is 30%. Calculate the WACC of company A?
Solution
From using the SML model approach, cost of equity = 8% + 0.74* 7% = 13.18%. Total value of equity is equal to 1.4 million* 20 = 28 million. The pre- tax cost of debt is 11% as given. The market value of debt = 0.93* 5 million = 4.65 million. The total value = 2* + 4.65 = 32.65. The percentage of equity to total value = 28/32.65.= 0.8576. There fore debt to total value = 1-0.8576 = 0.142. There fore, the WACC for company A is as follows:
WACC = 0.8576* 13.18% + 0.1424*11% 8 (1-0.30) = 12.4%.
Divisional and project cost of capital
In a company the overall company risk may vary from that of divisional risks depending on the different risk profile of project they undertake compared to the overall risks of the company as whole. If projects are evaluated on the basis of the cost of capital compared with rate of return of individual projects of divisional performances, then based on the SML Line analysis, company may accept high risk projects, which tends to have higher returns as opposed to lower risk projects. This may lead to inaccurate project evaluation process and may cost the company and may loose shareholders wealth by investing in high risk projects.
That is, if projects are perceived to have high risk profile compared to ovral company activities then they must calculate divisional cost of capital compared with similar companies rather than using cost of capital for a company to evaluate the projects or divisional performances. In effect they must adjust the companies weighted average cost of capital so that it reflects the risk profile of those projects. In addition, if there exists financing cost to issue additional capital for a specific project, then this fact must be taken in to account in the weighted avarage cost of capital when evaluating competing projects before accepting or rejecting such projects.
Conclusion
As mentioned above the concept of cost of capital is an important concept in financial management as this can be used as a tool to compare different projects and to enable to use appropriate long -term finances and investing in projects which earns more than the risks involved in those projects. That is cost of capital acts as a bench mark if it is estimated properly and used wisely as discussed above. It is also essential to know the limitations of the models to estimate equity rate of return in particular and use appropriate models depending on the nature of their dividends, whether they are private or public companies and whether their operations differ substantially between different divisions. In addition, the cost of capital also is an important concept to be used in the proper capital structure of a company, particularly in real world cost of capital vary with different gearing ratios because of tax, cost of finances, risk of insolvency using debt and cost of bankruptcy.