Session 8: Cost of Capital

• Guiding the learner how to estimate the cost of equity
• Guiding the learner how to estimate the cost of equity
• Explaining to the learners the relevance of cost of capital

• Weighted average cost of capital( WACC)
• Financial risk premium
• Business risk premium
• Risk free rate of return

• The cost of funds that a company raises and uses, and the return that investors expect to be paid for putting funds into the company.
• It is therefore the minimum return that a company should make on its own investments, to earn the cash flow out of which investors can be paid their return.

1. Risk free rate of return
   Return required from a completely risk free investment. E.g. yield on government securities.
2. Business risk premium
   Increase in required rate of return due to uncertainty about future and business prospects.
3. Financial risk premium
   Dangers of high debt levels, variability in equity earnings after payments to debt capital holders.

• New issues of shares.
• Cash derived from retained earnings.

• Dividend valuation model
  Ignoring share issue costs, the cost of equity for both new issue and retained earnings, could be estimated by means of a dividend valuation model. The assumption that the market of shares is directly related to expected future dividends on the shares.
  a) Constant dividend
  Where is it assumed that dividend will remain constant through out the years the cost of equity is calculated as follows:
  

Ke is the shareholders’ cost of capital.
D1 is the annual dividend per share, starting at year 1 and then continuing annually in perpetuity.
From the formula above the market value of shares can be calculated as:

b) The dividend growth model

• Capital Asset Pricing Model
  The required return on ordinary shares can also be calculated by an alternative approach called the capital asset pricing model. This topic is covered much in next chapter. It is a model based on the proposition that the return on any shares equals to the risk – free rate of return plus a risk premium on risk which cannot be diversified.
  systematic risk - the risk which can be minimised through diversification.
  unsystematic risk -the risk which remains even after diversification (or market risk)
  Under the capital asset pricing model (CAPM), the required rate of return for ordinary shares can be described by the formula:
  

  Ke	= 10% + 0.6 (15% - 10%)
  	= 10% +0.6(5%)
  	= 10% + 3%
  	= 13%

  If the risk of the shares was a little bit high say 1.6 then the cost of shares will also be high to compensate for the increased risk levels.

  Ke	= 10% + 1.6 (15% - 10%)
  	= 10% +1.6(5%)
  	= 10% + 8%
  	= 18%

2. Cost of preference shares

The preference shareholder is entitled to a fixed rate of dividend which is quoted together with the shares. i.e 12% K4 Preference shares means the shares have a nominal value of 12% and are entitled to an annual dividend of 12% per the nominal value.
So the cost of preferred shares is the rate which is given.

3. Cost of debt

The cost of debt capital which has already been issued is the rate of interest (the internal rate of return) which equates the current market price with the discounted future cash flow from the security.

• Irredeemable debt
  For redeemable debt the cost is calculated as the interest payable over the market value of debt.
  
  The tax is included because interest on loan is allowable for tax purposes so if a company use borrowed capital there is always a saving due to tax relief on interest paid.
  For example, if the tax rate was raised from 30% to 40% the cost of debenture would be:
  Insert insert bleh
• Cost of redeemable debt
  These are debts with a defined period or date of repayment. The cost of these debts will be found by using the internal rate of return.
  Example:
  Peet Ltd has 7% debentures in issue. The market price is K95.75 ex interest. Ignoring taxation, calculate the cost of this capital if the denture is:
  (a) Irredeemable.
  (b) Redeemable at par after 5 years.
  Solution
  (a) The cost of irredeemable debt capital is:
  
  (b) The cost of debt capital is 7.3% if irredeemable. The capital profit that will be made from now to the date of redemption is K4.25 ( K100 – K95.75). This profit will be made over five years which gives an annualised profit of K0.85.(4.25/5) which is about 0.9% of current market value. The best trial and error figure to try first is, therefore, 7.3% + 0.9% = 8.2% say 8% to the nearest.

  Year	Cash flow		discount	PV	Discount	PV
  			8%		10%
  				K		K
  0	Mkt value ( 95.75)		1.000	(95.75)	1.000	(95.75)
  1 – 5	Interest	7	3.993	27.95	3.791	26.54
  5	Repayment	100.00	0.681	68.10	0.621	62.10
  					0.30	(7.11)

  
  The approximate cost of debt capital is therefore:
  
  The cost of debt capital estimated above represents the cost of continuing to use the finance rather than redeeming the debt securities at their current market price. It would also represent the cost of raising additional finance if we assume that the cost of additional capital would be equal to the cost of that already issued. A company with no debt capital can make the calculations using the information of another company which is judged to be similar as regards to risk.
• The weighted average cost of capital (WACC)
  As stated above the structure of a company consists of equity capital and various forms of debt capital, and each capital item has its own cost. The weighted average cost of capital is the average cost of a company’s different sources of finance.
  The WACC is calculated on the assumption that the company will maintain the same level of debt equity ratio. The WACC calculated is used as the discount rate for capital project appraisals. This is will be ideal where:
  • In projects of a standard level of business risk, and
  • By raising funds in the same equity/ debt proportions as its existing capital structure.
  The general formula for WACC is:

  

  if you need to calculate the WACC where debt is redeemable, you should calculate the after-tax cost of debt using the techniques set out earlier and substitute this into the formula in place of Kd ( 1 – t).
  Example:
  Kwacha transport LTD is financed partly by bonds. The equity proportion is always kept at two-thirds of the total. The cost of equity 14% and that of debt is 8%. A new project is under consideration that will cost K200,000 and yield a return before interest of K75,000 a year for four years. Should the project be accepted? Ignore taxation.
  Solution:
  The WACC is the best rate to be used in appraising the project.

  	Proportional	Cost		Cost x Proportion
  Equity	2/3	14%		9.33%
  Debt	1/3	8%		2.67%
  			WACC	12.00%

  
  

  Year	Cash flow	Discount factor	P.V.
  		12%
  0	(200,000)	1.000	(200,000)
  1	75,000	0.893	66,975
  2	75,000	0.797	59,775
  3	75,000	0.712	53,400
  4	75,000	0.636	47,700
  Net present value			27,850

  The NPV of the investment is K27,850 and the project appears financial viable.

• Weighting
  In the example the weighting for debt and equity was simplified, but in real environment the can be determined by using
  • Weights could be based on the market values of debt and equity.
  • Weights could be based on balance sheet values( book value)
• Arguments for using the WACC as a discounting rate
  WACC is relevant if the following assumptions hold;
  1. The project is small relative to the overall size of the company.
  2. The weighted average cost of capital reflects the company’s long-term future capital structure and capital costs.
  3. The project has the same degree of business risk as the company has now. When the new project has a different business risk the WACC can not be used.
  4. New investments must be financed by new sources of funds, retained earnings, share issue, new loans and so on.
  5. The cost of capital to be applied to project evaluation reflects the marginal cost of new capital.