1. Workshop 6 Dr Francesca Gagliardi
7BSP0379 – Financial Management
Cost of Capital
Workshop 6
Dr Francesca Gagliardi

2. Learning outcomes
By the end of the session students should be able to:
Calculate the costs of different sources of finance used by a company
Calculate the weighted average cost of capital
Appreciate the reasons for preferring market values to book values
Understand how to apply the (weighted average) cost of capital in investment appraisal

3. Knowledge development
In previous weeks:
We looked at the sources of finance that are available to companies
We analysed how investment appraisal methods can be applied to make capital investment decisions
We also discussed the risk-return trade-off faced by investors
Today we go a step further and discuss how the level of risk of different financing sources affects their required rate of return, hence a company’s cost of capital

4. Why focus on cost of capital?
The cost of capital is the rate of return required on invested funds
Companies should seek to raise capital by the cheapest and most efficient methods
Minimisation of the average cost of capital will increase the net present value of a company’s projects, hence its market value
To minimise the cost of capital:
Information on the cost of available financing sources is needed
Knowledge of how to combine different sources of finance to reach an optimal capital structure is required

5. Calculating the cost of capital
A company’s cost of capital can be used as:
Discount rate in investment appraisals
Benchmark for company performance
Calculating a company’s cost of capital can be difficult and time consuming
To calculate the weighted average cost of capital, need first to find the cost of capital of each source of long-term finance used by a company

6. Ordinary shares
Equity finance can be raised either by issuing new ordinary shares or by using retained earnings
The cost of equity can be calculated using the dividend growth model as:
where:
Ke = cost of equity
D0 = current dividend
g = the expected growth rate of dividends
P0 = the current ex-dividend share price
Example: If D0 = 12p per share, g = 5%, and the current share price is 120p, the cost of ordinary share is calculates as:
Ke = [12p * ( ) / 120p] = 15.5%

7. Ordinary shares Rj = Rf + βj (Rm - Rf)
The cost of equity can also be found from the CAPM:
Rj = Rf + βj (Rm - Rf)
where:
Rm = return of the market
Rf = risk-free rate of return
(Rm – Rf) = equity risk premium
βj = beta value of ordinary share
CAPM allows shareholders to determine their required rate of return, based on the risk-free rate of return plus an equity risk premium

8. Preference shares
Dividend paid on preference shares is usually constant
The cost of preference shares is found by dividing the preference dividend by the ex dividend market price:
where:
Kps = cost of preference shares
P0 = current ex-dividend preference share price
Dp = preference dividend

9. Kid(after-tax) = Kid(1 – CT)
Irredeemable bonds
Like preference shares, bonds involve a constant annual payment in perpetuity
Kid = cost of irredeemable bonds
I = annual interest payment
P0 = current ex-interest market price
Interest is tax-deductible. The after-tax cost of debt is:
Kid(after-tax) = Kid(1 – CT)
CT = corporation taxation rate

10. Example 10% irredeemable bonds Ex-interest market price: £72
Corporation tax: 30%
Kid (before tax) = £10 / £72 = 13.9%
Kid (after tax) = 13.9 x ( ) = 9.7%

11. Redeemable bonds
Redeemable bonds involve several fixed interest payments plus redemption value. The after-tax cost of debt is:
I = interest payment
RV = redemption value
Kd = cost of debt capital
n = number of years to maturity
CT = corporation tax rate
Note: The before-tax cost of debt is found by using I instead of I(1-CT)

12. Convertible bonds
To calculate cost of debt need first to determine whether conversion is likely to occur
Conversion not expected: bond treated as redeemable debt
Conversion expected: cost of capital found by a modified version on the redeemable bond valuation model
Use number of years to conversion (not to redemption)
Use future conversion value (CV) instead of redemption value

13. The relationship between the costs of different sources of finance
The cost of each financing source is linked to the risk faced by each supplier of finance
Equity finance: highest level of risk faced by investors, hence most expensive source of finance
Cost of preference shares less than cost of ordinary shares as the former are less risky and rank higher in the creditor hierarchy
Debt finance: generally no uncertainty on interest payments. Debt further up the creditor hierarchy. Hence, cost of debt less than cost equity
Whether bank debt is cheaper than bonds depends on the relative costs of obtaining a bank loan and issuing bonds, the amount of debt and the length of period over which debt is raised

14. Calculating the weighted average cost of capital (WACC)
The costs of individual sources of finance are weighted according to their relative importance as sources of finance
E = value of equity D = value of debt
Ke = cost of equity Kd = cost of debt
E/(E+D) is the proportion of equity
D/(E+D) is the proportion of debt
CT = taxation rate
The equation will expand in proportion to the number of different sources of finance used by a company

15. Market value or book value weighting?
Book values are historical and are obtained from a company’s accounts
Book values rarely reflect the current required rate of return of providers of finance
Example: an ordinary share with a nominal value of 25p has a market value of £1.76
Book values will underestimate the impact of the cost of equity on the average cost of capital, hence unprofitable projects will be accepted
Market values reflect current requirements and can be obtained from financial press and databases

16. Class activity Source of finance Cost Market value (£000)
Equity Ke = 16.9%
Preference shares Kp = 13.4%
Irredeemable debt Kid = 9.7%
Redeemable debt Krd = 8.7%
Bank loans Kbl = 8.8%
871.5
Required: calculate the WACC

17. Solution

18. Practical problems with WACC
Calculating the cost of particular sources of finance may not be straightforward
Ordinary shares of private companies
Solution: use the cost of equity for a listed company, with similar characteristics and add a premium to reflect the higher risk of the private company
Market value of bonds
Solution: find the market value of a bond issued by another company, with similar maturity, risk and interest rate, and use this market value as a proxy
The accuracy of the calculated cost of capital depends on the reliability of the models used

19. Practical problems with WACC
Which sources of finance should be included in the WACC calculation?
The difficulty of finding the market value of securities impacts on the weightings applied
Debt finance raised in foreign currencies needs to be converted
WACC is not constant
Changes in the market value of securities and in macroeconomic conditions affect a company’s average cost of capital
Which sources of finance should be included in the WACC calculation? Finance sources used to fund the long-term investments of a company should be included in the calculation of WACC. What about a bank overdraft used on an ongoing basis?
The difficulty of finding the market value of securities impacts on the weightings applied. Both market and book values are used in practice

20. WACC in the real world Companies pay attention to the value of WACC
A company’s WACC is of interest to national regulatory bodies to determine what is considered to be a ‘fair’ level of profit
A company’s WACC is of interest to national regulatory bodies to determine what is considered to be a ‘fair’ level of profit
Several companies claimed that the cost of capital calculated by the regulatory body underestimated their true cost of capital

21. WACC and investment appraisal
WACC is often used by companies as a discount rate for new projects
However, companies should use their current WACC as a discount rate when appraising a future investment only when:
The company intends to maintain the same long-term capital structure
Any new project has the same systematic risk as the existing company

22. Summary Today we looked at:
How to calculate the cost of different sources of finance
How to calculate the WACC
Main issues arising from WACC