## Cost of Equity

okay excellent in this lesson we’ll talk

about discount rates we said that to perform a capital budgeting exercise we

must discount future cash flows and obtain their present value however we

still must cover a subtle topic which is the discount rate that should be used

for this calculation well that’s up to the person carrying out the analysis but

a few alternatives are typically used in different scenarios depending on the

project we are valuing and the way it will be financed our discount rate could

be the firm’s cost of debt the firm’s cost of equity its weighted average cost

of capital or a hurdle rate chosen by management cost of debt this is the

average interest rate the company pays on its borrowings it makes sense to use

the cost of debt as a discounting rate if the entire project is financed with

debt in this case this is the cost the company sustains to finance the project

hence when we use the cost of debt as a discounting rate we’ll be able to

compare the investment required now and the present value of the cash flows the

project will generate an alternative discount rate is the company’s cost of

equity there are many ways to calculate a company’s cost of equity in this

course we’ll apply the one used by investment bankers it is called the

capital asset pricing model also known as cap M the model was introduced in the

1960s but remains relevant to this day and age the capital asset pricing model

suggests a company’s cost of equity is equal to the risk-free rate plus beta

multiplied by the market risk premium the risk-free rate in an economy is the

rate of return that an investor would expect from a financial security that

contains zero default risk the investor buys the security man can be certain he

will be repaid on time and in full in the complicated world of today very few

securities can be considered risk-free but most practitioners use the yield of

a ten-year government bond to approximate this measure the governments

of developed countries have a saw reputation and can be trusted in a

10-year time frame the rationale behind using a 10 year and not a three month

bond is that the valuation of the firm is a multi-year exercise

hence the risk-free rate used shouldn’t reflect a period as short as three

months the next component in the calculation is beta this is a

statistical measure for those of you who love statistics and quantify Nantz beta

can be calculated with the following formula and it is basically used to show

how a financial security behaves regarding the rest of the market that is

why we are dividing its covariance with the rest of the market by the markets

variance if this is confusing don’t worry

many financial providers calculate a company’s beta for you let’s open P and

G’s Yahoo Finance profile as promised you can’t immediately see the company’s

beta here it is almost 0.5 which usually is considered a conservative stock a

beta that is less than 1 indicates the stock is less volatile than the market a

beta of 1 shows the stock is as volatile as the market if the market gains 1% it

will also gain 1% if the market loses 5% it will lose 5% stocks that have a beta

higher than 1 are considered aggressive and are more volatile than the market if

the market grows 2% the respective stock will probably earn 2 point 5 or 3% and

so on you get it right a company’s beta will typically have a

value ranging between 0 and 2 the next component in cap M is market risk

premium theoretically it is given by the average expected return of the market

minus the risk-free rate academic research has shown the average market

risk premium rate varies between 4.5% and 5.5% and most practitioners use 5%

in their cost of equity calculations so we will have the following the cost of

equity in a company is given by the risk-free rate in the economy where it

operates plus the company’s beta multiplied

by 5% cost of equity is not that difficult to calculate right you can

find the yield of a 10-year US bond in Google then we saw that accompanies beta

is available in platforms like yahoo finance and Bloomberg and finally we

multiply by a constant 5% easy right if we take a careful look at Cap M it makes

sense a financial securities return should be composed of two parts first

the risk free rate of return has a minimum compensating the investor for

the time value of money and a second component compensating the investor for

the additional risk for holding a security that is not risk-free the risk

is measured by comparing the stock to the rest of the market and the result is

that the riskier the stock the higher its expected return should be brilliant

isn’t it so this is how we can calculate a company’s cost of equity the cap M

model is one of the most widely accepted academic papers on this topic we can use

the cost of equity as a discounting factor for projects financed entirely

with our own funds with equity this is an assumption that no debt will be used

to finance the project I’m sure you’ll agree that in practice projects are not

financed with just equity or debt in 90% of the cases we’ll use a mixture of both

stay tuned and we’ll discuss what to do in these situations in our next lesson