# How to calculate weighted average shares outstanding

Weighted Average Cost of Capital (WACC)

for a Company

For use in Conjunction with the Firm Valuation Project

First ensure that you have read relevant pages in the text.   Some important sections would include the following, but you may also double-check the references in the text by using the index [see:   Cost of Capital and Target (optimal) Capital Structure, etc.]:

The important Chapter in the text is the one entitled "The Cost of Capital ," – with a particular focus on the section entitled “The Weighted Average Cost of Capital” and the section “Four Mistakes to Avoid” at the end of the chapter.

The WACC formula discussed below does not include Preferred Stock.   Should your company use PS, be sure to adjust the equation for it, and see the section in the chapter on the Cost of Preferred Stock.

The WACC formula that we use is:

We need to know how to calculate:

1. r s the cost of common equity.   Use the Security Market Line (SML) – this is why you learn how to calculate a company’s beta and also why you learn how to find the appropriate risk-free rate and market-risk premium.   For a review, see the section the text, The CAPM Approach.

2. The weights (wd and ws – note that:   wd + ws = 1; so you only have to calculate one of them).     We need to calculate the weight of debt and the weight of equity (for the cost of debt, this simply means:   what proportion of the firm’s financing is by debt?).   There is a lot to say here, simplified as Theory 1, Theory 2 and Practice:

a. Theory 1 .   Theory says that we should use the target weights along with the market values of both debt and equity (see the Four Mistakes to Avoid ).   But the market value of debt is typically difficult to calculate, because we need to know the YTM (which is rd ) for all of the company’s debt, but we cannot calculate the YTM without having the current prices of the company’s outstanding bonds, and most company’s bonds do not trade (i.e. they will not have up-to-date or current prices – remember how to calculate the price (value) of a bond on your calculators?!).   As a result, at least for the group project, we go to Theory 2.

b. Theory 2 .   Theory also says that we should use the TARGET weights, but this is a management decision, and as “outsiders” we do not have access to the thoughts of the CFO or CEO.   So we should look instead to the historical pattern of the use of debt (mix of debt and equity), and this is one reason that you should have about 10 years of financial data.

c. Practice :   Since we cannot “work” according to the strict theory of finance, we have to estimate the relevant weights.   As a result, we will use the formula:

wd = Book Value of Debt / [Market Value of Equity + Book Value of Debt]

The book value of debt is calculated by adding up ALL of the debt on the balance sheet.   This will typically be the sum of Notes Payable, Current Portion of LT Debt and Long-Term Debt.

The market value of equity is the “Market Cap,” and equals the number of (common) shares outstanding multiplied by the price/share.   Note that the “timing” of this value should coincide with the book value of debt.   For example, if you calculate the book value of debt as of 12/31/03, then the market cap should also be calculated for that date.   Be very careful about using the reported Market Cap on Yahoo.finance – it may not have the same

“timing.”

By using this formula, you should be able to track the company’s use of debt over many years.   Finally here, you may also calculate the “straightforward” Debt Ratio (as defined in the text in the chapter on the analysis of financial statements), which would use the book value of common equity instead of the market value.   This is not a recommendation to use that ratio for the WACC, but the Debt Ratio may be useful for comparison.

3. r d ; the cost of debt.   There may be more than one acceptable approach to calculate or estimate a company’s cost of debt (be sure to read the text!).   One relatively straightforward method is to discover the company’s debt rating (e.g. by Moodys).   This can usually be found on the company’s 10K (see the link on my homepage) and doing a word search for ‘rating’ or ‘debt rating.’   For a discussion of bond ratings, see the text (look in the index).   If you can find the debt rating for your company then you can carry out the following steps (if you cannot find a bond rating for your company, you might try to estimate/guess what it is by considering your company’s beta and comparing the bond ratings for companies with similar betas). If you are not able to find a bond rating readily, you can register (for free ) at Standard & Poor's and at Moody's to find company ratings. You may also find other interesting and useful information there. For a general discussion of what the ratings mean, see the information from these rating agencies on my homepage at the Bond Rating link.

Once you have the actual bond rating or an estimate you can then find or estimate your company’s cost of debt by going to Yahoo.finance and clicking on the Bonds/Rates link (http://bonds.yahoo.com/rates.html).   Look at the yields for the 20 year Corporate Bonds by rating.   If your company’s bond rating is listed, you’re in luck.   If it is not listed then you can estimate the cost of debt.   For example, if the AAA yield is 6.50%, the AA yield is 6.75% and the A yield is 7.00%, you can see a pattern (equation).   For every increase in risk (from AAA to AA), there is a 0.25% increase in the yield.   If your company has a BB rating, then it is two steps “below” the A rating, so you should add approximately 0.50% more to the 7.00% for the A rating, giving you a cost of debt for your company of about 7.50%.   Note that this approach assumes a linear equation for the cost of debt (which may not be strictly true).

4. The corporate tax rate ( T ).   Be sure to read the section in the text on Corporate Income Taxes (Chapter 2).   The correct tax rate for a company is the marginal tax rate for the future.   If you expect your company to be very profitable for a long time into the future, then the tax rate ( T ) for your company should probably be the highest marginal tax rate applicable for corporations.   But there are times when companies can obtain long-term tax breaks so that their tax rates may be lower than the stated (regulated) tax rate.   Consequently you may want to calculate several/many historical effective tax rates for you company.   The effective tax rate is the actual taxes paid divided by earnings before taxes (on the income statement).   You can calculate/consider these rates for the past 5-10 years and then compare this effective tax rate to the legally mandated highest marginal corporate tax rate.   If the past historical effective rate is lower than the marginal tax rate, there may be a good reason for using that lower rate in your pro formas.

Source: mihaylofaculty.fullerton.edu

Category: Forex