5 2016-11-11 Febmat.com

# All about cost of capital

## Cost of capital

## Systematic risk

## Unsystematic risk

## Hurdle rate

## Sources of finance

## Cost of equity

## Capital Asset Pricing Model (CAPM)

*CAPM formula:*

## Security market line (SML)

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## Gordon growth model (Dividend discount model)

*Example***:**

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## Growth rate

## Cost of debt

**Cost of irredeemable (perpetual) debt**** – debt without any fixed date of repayment**

## Example no.1

## Example no.2

**Cost of redeemable debt**** – debt that will be repaid during specific period of time**

## Cost of retained earnings

## Formula

## Weighted average cost of capital (WACC)

## Formula

## The main problem with WACC used in investment projects appraisals is that it assumes that:

## Marginal cost of capital (MCC)

## Therefore, there are two adjustments to traditional WACC to obtain MCC

## Coefficient beta

## Unlevered beta

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## Risk adjusted WACC

##

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Last updated: 11.11.2016

This series contains articles relating to a way of determining the cost of capital, usually WACC, and its basic components (costs of debt and cost of equity or risk-free rate and surcharges for risk).

It contains description of basic methods for determining WACC (CAPM and Gordon Growth Model), description of the marginal cost of capital and how to evaluate projects exposed to other business risk than the risk of existing business.

**Cost of capital is the cost rate of the funds that the company uses as its capital, therefore the rate that mixes costs of various sources of finance. It usually has the form of Weighted Average Cost of Capital (WACC), but all the components mentioned below can be also called with the broader term “cost of capital”. **

**Cost of capital is used to:**

- evaluate investment projects – cost of capital serves as the minimum return that the investment projects shall achieve and as such it is often used as a hurdle rate
- evaluate the company performance – WACC is a component used in calculation of EVA
- design optimal capital structure – it is the structure that keeps the cost of capital to minimum and maximizes the value of the company (37)
- set up dividend payment policy – if the company is able to undertake investments with rate of return exceeding cost of capital, the equity holders may decide to retain the earnings in the company and not pay it out as a dividend (37)

**Components of cost of capital from the viewpoint of various sources of finance:**

- cost of debt
- cost of equity
- cost of preference shares
- cost of retained earnings and other internal sources of finance

**Components of cost of capital from the risk point of view:**

- risk-free rate – yield on government bonds are often used
- risk premium – the higher is the risk, the higher is the premium. Risk premium is included for:
- systematic business /market risk (there should be no premium for nonsystematic risk!)
- financial risk – the risk of high gearing

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*Used sources:*

*37. Significance And Components Of Cost of Capital (online). Citation date: 29.1.2016. Available from www: http://accountlearning.blogspot.cz/2011/07/significance-and-components-of-cost-of.html*

**Systematic risk is the undiversifiable risk to which are exposed all companies in the market. An example can be the risk of changes of most macroeconomic factors. **(43) The fact that systematic risk cannot be diversified does not mean that it cannot be dealt with – it can be for example insured.

**Investors should obtain a compensation for the systematic risk in the form of a premium over the risk-free rate of return (this excess is called market risk premium). **(43)

The opposite of systematic risk is unsystematic risk.

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**Used sources:**

*43. Systematic risk (online). Citation date: 2.2.2016. Available from www: https://en.wikipedia.org/wiki/Systematic_risk*

**Unsystematic risk is the diversifiable risk specific to the considered company, e.g. risk resulting from geographic location. Since unsystematic risk is diversifiable risk, the risk can be eliminated by holding a well-balanced portfolio and the total risk is equal just to the level of systematic risk (undiversifiable). **

Therefore, investors shall not be compensated for the unsystematic risk in the form of an excess over the risk-free rate of return. They shall only be compensated for the systematic risk.

**Hurdle rate is the minimum return rate that the company wants to exceed when it undertakes an investment project. It is often (but not always) the company´s cost of capital (WACC). Hurdle rate is therefore often used as a discount rate in DCF calculations and the project´s IRR % shall exceed it.**

**In general, sources of corporate finance can be summarized into the following groups:**

**internal sources of finance**– mainly retained earnings**external sources of finance**:**debt**– bank loans, issue of debentures, lease**equity**- issue of shares

Each source of finance bears its own cost of finance, also known as cost of capital.

**Cost of equity (COE) is:**

**the return required by the shareholders****the component of cost of capital (WACC)**

**Cost of equity can be calculated by using several methods, each of which may result in different cost of equity rates: **

**Capital Asset Pricing Model (CAPM) is used to calculate the expected rate of return on particular security. As such, it is used to estimate the cost of equity. The variables of CAPM can be drawn by Security market line (SML).**

**risk-free rate + β * market risk premium**

*where**:*

*market risk premium* (P) = (expected market return – risk-free rate) → excess return of the entire market or market segment over risk-free rate

*risk-free rate*: often the yield on government bonds

*coefficient β*: a ratio of systematic risk attached to the company equity shares compared to risk present in the market:

- β > 1 → the particular share is more risky (volatile) than shares in the market (38) (e.g. company share price will rise more quickly than average share in the market segment)
- β < 1 → the particular share is less risky (volatile) than shares in the market (38)

**Disadvantages of CAPM**

- CAPM assumes that there is linear relationship between the systematic risk and expected return
- risk-free rate also varies with the length of maturity
- all the CAPM formula components becomes out-of-date over time

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**Used sources:**

*38. Definition of „Systematic Risk“ (online). Citation date: 29.1.2016. Available from www: http://www.investopedia.com/terms/s/systematicrisk.asp*

**Security market line (SML) reveals the relationship between the level of systematic risk and the expected return and as such presents the outputs of Capital Asset Pricing Model (CAPM). The slope of the curve represents coefficient β. **(42)

**SML line is used to derive expected (= well priced) return for the considered level of systematic risk. However, the return increases with the level of risk.**

(42)

The shares above SML are undervalued as they bring higher return than would be expected for the level of systematic risk. (42)

The shares below SML are overvalued as they bring lower return than would be expected for the level of systematic risk. (42)

**Used sources:**

*42. Security market line (online). Citation date: 2.2.2016. Available from www: https://en.wikipedia.org/wiki/Security_market_line*

**Gordon growth model (Dividend discount model) uses the assumed relationship of the constantly growing dividend amount received in perpetuity and the share price and is used to **(39)**:**

**calculate market value of share (equity) = present value of future dividends**

P_{0 }= D_{1} / (K_{e} – g)

**calculate cost of equity (or required rate of return)**

K_{e }= (D_{1}/P_{0}) + g

* where*:

K_{e }= cost of equity

D_{1} = expected annual dividend per share in year 1 (D_{1} = D_{0} * (1 + g))

P_{0 }= ex-dividend share price = market value

g = constant annual growth rate (39)

*The last dividend per share was € 0,15; current share price is € 0,89; annual growth rate is 3%. *

*D _{1} = 0,15 * (1 + 0,03) = 0,1545*

*K _{e }= (0,1545 / 0,89) + 0,03 = 0,204 (= 20,4%)*

**Used sources:**

*39. Dividend growth model (online). Citation date: 30.1.2016. Available from www: https://wiki.treasurers.org/wiki/Dividend_growth_model*

**Growth rate is the rate by which the considered variable (revenues, expenses, dividends, investment, GDP etc.) increase either annually or over the considered period of time. It is usually derived from past data and can be calculated by a number of methods. None of the calculation methods is correct or incorrect, but it is important to know that a presented growth rates does not necessarily need to be fully comparable as the result of using different methods. The calculation models can include:**

- average annual growth rate (AAGR)
- straight-line growth rate (i.e. % change of final and beginning figure)
- compound annual growth rate (CAGR)
- Gordon growth model

**Cost of debt is:**

**the return required by the debtholders****the component of cost of capital (WACC)**

**Cost of debt is the interest paid reduced by the tax deduction on the interest. **

**Cost of debt is calculated separately for each type of debt: **

- irredeemable debt
- redeemable debt

**K _{d} = (annual interest / debt value) * (1 – tax rate)**

If the debt is issued **at** **discount or premium **(i.e. not at par value), the denominator is reduced / increased by the amount of the discount/premium (not the basis for calculation of annual interest!).

*The company issues 8% irredeemable debentures to raise € 10 000. The rate of taxation is 15%. *

*K _{d} = ((8% * 10 000) / 10 000)) * (1 – 0,15) = 0,08 * 0,85 = 0,068 (6,8%)*

*The company issues 8% irredeemable debentures to raise € 10 000 at 5% premium. The rate of taxation is 15%. *

*K _{d} = ((8% * 10 000) / (10 000*1,05)) * (1 – 0,15) = 0,07619 * 0,85 = 0,065 (6,5%)*

Cost of redeemable debt is calculated the same way as internal rate of return (IRR). Therefore, relevant cash-flows for each year (or other period) must be prepared and these cash-flows are discounted to present value.

**The calculation formula is the same as with IRR and the relevant cash-flows include:**

- market value of the debt instrument issued
- repayments of principal and interest payments
- possibly also transaction costs

**Retained earnings are the profit that has not been distributed to shareholders and it is certainly not for free. It is the money that could have been paid out as dividend, but was not – probably due to the fact that the stockholder was not able to achieve better return on investments than the considered company. Therefore, cost of equity represents the opportunity costs and retained earnings shall be valued at least with this rate (or little lower, due to income tax paid by shareholders on dividends and transaction fees related with dividend payment).**

cost of equity * (1 – tax rate) * (1 – transaction costs rate)

**WACC is the mixed cost rate of all possible sources of finance that the company uses (equity, debt, preference shares, retained earnings…). It is calculated as the sum of the rates for each capital type that are weighted by the proportion of each capital type on the total capital amount.**

**WACC represents the minimum return that is required from an investment project. It is often used as a discount rate in DCF calculations and as a hurdle rate.**

*K _{e} = cost of equity*

*K _{d} = cost of debt*

*MV = market value*

**Market value in the WACC formula can be replaced by book value (value from balance sheet). Naturally, market values are preferred as they better reflect reality. But these values are of course more difficult to obtain.**

- the investment is exposed the same risk profile as the entire company – if the business risk is different, it can be resolved by calculating risk adjusted WACC
- and existing mix of funding sources (debt, equity) will remain unchanged – this can be resolved by using Marginal cost of capital (MCC) instead or Adjusted present value for investment appraisal

**Marginal cost of capital (MCC) is the rate calculated based on the same formula as WACC, but compared to WACC considers both the existing capital finance as well as all the effects of undertaking the project.**

- recalculate the cost of equity using new parameters
- use the new market (or book) values of equity that includes both the original new funds
- include to calculation formula new debts and their cost of debt

**Coefficient beta (β) is a measure of systematic risk of the company and its shares compared to systematic risk present in the market. In other words, it measures the proportion of undiversifiable risk present within the company capital that is compared to the overall market (systematic) risk. Beta is used in CAPM model to calculate the expected rate of return (cost of equity) and can be derived by the slope of Security market line (SML). **

Company capital comprises of equity and debt capital. As the debt beta is assumed to be zero (it is in fact very low, but not zero), coefficient β is related just to the cost of equity. Therefore, if:

- β > 1 → the particular share is more risky (volatile) than shares in the market (38) (e.g. company share price will rise more quickly than average share in the market segment)
- β < 1 → the particular share is less risky (volatile) than shares in the market (38)

**Unlevered beta is beta of the traded company exposed to the similar business risk as our company or our new investment which has been adjusted (unlevered or ungeared) for the effect of financial risk by using a formula **(41)**:**

*β _{u} – unlevered beta*

*β _{i} – beta of the comparable company*

As the result, unlevered β (βu) does not contain the effect of the specific capital structure of similar company and shows only the systematic business risk present in the market (industry).

**This unlevered beta can be then, by using another formula shown below, transferred (relevered or regeared) to the specific capital structure of the considered company (to reflect the financial risk of the considered company) **(41)**. **

**By using this beta in WACC formula we obtain risk adjusted WACC which is used to evaluate projects exposed to different systematic business risk than other activities currently undertaken by the company.**

**This procedure is often used to ascertain beta of:**

- the entire considered untraded company
- investment projects that have different business risk than other activities currently undertaken by the company

**Used sources:**

*41. Unlevered beta (online). Citation date: 1.2.2016. Available from www: https://www.educba.com/unlevered-beta/*

**Risk adjusted WACC is the adjusted WACC which is used to evaluate projects exposed to different systematic business risk than other activities currently undertaken by the company. **

**The steps used in calculation are **(41)**:**

**1. Find beta of traded company with similar business characteristics **(and therefore similar systematic business risk) in the industry where the company intends to diversify.

**2. Use formula below to calculate unlevered beta** to remove the effect of financial risk (resulting from specific capital structure) of the compared company. β_{u }will then show only the systematic risk present in the market (industry).

*β _{u} – unlevered beta*

*β _{i} – beta of the comparable company*

**3. Relever the beta to the existing (or expected) capital structure using the formula below** to reflect the financial risk of the considered company:

(41)

**4. Calculate WACC using new parameters.**

The biggest problem results from the fact that it is difficult to find companies with similar operating characteristics.

**Used sources:**

*41. Unlevered beta (online). Citation date: 1.2.2016. Available from www: https://www.educba.com/unlevered-beta/*