# WACC & Beta

Description: Explains WACC and how to calculate it

## WACC & Leverage

Cost of capital is a concept that we introduced with opportunity cost in our last post. From the discussion so far, we know that that are two ways to raise capital. We can either invest on our own account, which we call equity investment. Or we can go out and borrow money from friends, family & the neighborhood bank. We call this debt.

Leverage is the proportion of debt to equity. If a business raises 100 dollars in capital, out of which 70 dollars is an equity investment and 30 dollars is debt, then what is the leverage ratio? If we divide 30 dollars of debt by the 70 dollars of equity we find, that for every dollar of equity there are 42 cents of debt available. Or the leverage for this business is 42%. An alternate definition takes the opposite view and divides the 70 dollars of equity by the 30 dollars of debt to determine that for every dollar of debt there are 2.33 dollars of equity available.

What about cost of capital, or WACC, for this combination of funds? How much return should a business generate on this hundred-dollar investment to break even?

To discuss these issues lets take step-by-step approach. This way we’ll be able to build on concepts explained earlier in the session.

## Step A – WACC – Simple Weighted Average Calculation

One way is to just do simple averaging. Let’s assume that you have to pay 10% interest on the 30 dollars you have borrowed; this is the cost of debt. The risk of taking on equity is a little higher than average, which is why it costs more; as such, the cost of equity is 20%. Both are required returns. What is the correct required average return? In other words what is the weighted average cost of capital or WACC?

WACC = (30 * 10%) divided by (30 + 70) + (70 * 20%) divided by (30 + 70)

This expression can be simplified to

WACC = (30* 10% + 70 * 20%) / (100)

if we solve it we get

WACC = (3 + 14 ) / (100) = 17%

Using this approach the venture should earn 17% on every hundred dollars invested to satisfy the required needs of its debt and equity holders. As this is the cost at which capital is available, any return less than the WACC means that investors actually loose money.

## Step B – Issues affecting interest rate on debt

The example above is interesting. However, the question for a practitioner is how to calculate the required rates of return for debt and equity. The required return for debt is dependent on two factors:

### A) Government Debt Rate

The first factor is the rate that the government is offering on its debt. Accepted wisdom is that since the government has the power to print currency, any amount loaned to the government will definitely be paid. In fact, the government is the ideal borrower every banker and investor would like to have since its almost certain that it will repay such a loan.

The government is not dumb. In return for being such a high profile borrower, it also ensures and requires that it pays the lowest possible rate on traditional debt.  US government issues debt as treasury bills, bonds and notes. We use the rate on treasury bonds (bills and notes) as a proxy for the true risk free rate.  The risk-free rate is the rate of interest that would exist on a riskless security. As we have stated above, government securities and bonds are a classic case of these kind of securities, which is why the rate the government expects itself to pay on debt is generally taken to be the risk free rate of return.

### B) Credit Risk

The second factor is credit risk. Credit risk is an assessment of the chance that the borrower will default on his loan and will not be able to pay the interest due (in a best case scenario) or would not be able to repay the original principal or both (in a worst case scenario).

Assessing credit risk is a major industry with firms like Moody’s, Standard & Poor, etc. acting as guardians over public issues of debt. They generally rate debt within a range of alphabets indicating how strongly they feel about the chances of the borrower honoring his obligations. AAA are great, anything beyond Ds means you are in trouble and should have paid more attention in your credit assessment classes. The ratings can change quite dramatically over a short period. An event, or change in direction, or market sentiment places an issuer of bonds (debt) in a situation where he may not be able to meet his commitments.

The higher your credit rate (AAA’s and above) the lower the interest rate you have to pay on your debt. The lower your credit (B’s, C’s, D’s), the higher the rate people will expect your bonds to pay.

But it is not likely that you’re listed on Moody’s or Standard and Poor if you’re borrowing for the first time. The person or institution offering you the debt may evaluate your credit rating by looking at the mortgage payments on your house, the lease payments on your cars and payment of your other obligations like utility bills etc.

In short, the required rate of return on a bond comprises of two factors. The first is the rate on government bond referred to as the risk free rate. The second is dependent on how high your credit rating is.

### Example

KnowItAll, Inc., your new startup currently has equity worth \$20 million, and no debt on its books. You need money for your company’s immaculate growth, and decide to issue debt worth \$10 million. What is the new leverage of your company?

Leverage is the debt to equity ratio. Hence in this case:

Debt = \$ 10.0

Equity = \$ 20.00

Leverage = 10/20 = 50%

## Step C – Issues affecting required rate of return on equity

The required rate of return on an equity investment also follows the same intuitive reasoning above. But this time there are three components.

i. Risk Free rate of Interest

The first is our old friend “the risk free rate of interest”

ii. Market rate of return

The second is the market rate of return. This is the average return the total market of equity securities earns. As calculating, updating and reviewing this calculation is a tough job we use proxies. For example, we can use the return on the S&P 500 Index to track the market rate of return. The Standard and Poor Index of 500 companies is the index that tracks the performance of these 500 companies.

iii. Beta

The third component is Beta. Beta for any equity security is a factor that indicates how that security will react when the market moves in a certain direction. A Beta of 1 for Avicena’s shares means that if the market increases by 50%, Avicena’s share price will increase by 50%. While, a Beta of –1 means that if the market increases by 50% Avicena’s shares will fall by 50%. A Beta of 2 means that a 50% move in the market will result in a 100% increase in Avicena’s share price.

### Putting it together

We now want to pull these three components together to get an idea of how to calculate the required rate of return for an equity investment. But first we need to define one more term

We calculate it as follows:

Risk Premium = ( Market rate of return – Risk free rate of return)

In simpler terms this is the difference between the returns on the total market of equity securities and the returns on treasury bonds. It’s called the risk premium because it is an indicator of the compensation provided to an investor as he takes on incremental risk in equity securities. It is the price charged for the risk that the investor is taking by investing in a certain equity security. Historically this “Risk Premium” has ranged between 5% – 8 % depending on who you speak to. Another simple way to remember – it is the difference between the return on equity securities and the return on bonds.

The Required Return on an equity investment can be written as

Required Return on Equity = Risk free rate of interest + Beta * (Risk Premium)

### 6 thoughts on “WACC & Beta”

1. Hello ,
How to solve the Wacc if the prportion of the debt is 0.10and the costof the debt is 3.7% ,lastly, the cost of the equity is 11.1%
Thanks

2. Also,
The actuel for 2008 net sale is \$1,400,000
Gross profits =\$390,000
Projects for 2009
Net sale = grow by 15%
Cost of Goods sold is 1,135,050
Lastly, beginning inventory =100,000
Ending inventory =150,000
Calculate the Gross profits for 2009
Thanks again

3. @Alfas:
The answer to the WACC question is as follows:
Weightage of debt wd=0.10 so weightage of equity,we, will be 1-weightage of debt =1-.10=0.90

cost of debt, rd =3.7%
cost of equity,re =11.1%

WACC =wd*rd+we*re=0.1*3.7%+0.9*11.1%=10.36%

4. @Alfas: