# Cost of Capital

After you are finished with university, it is very doubtful that you keep much interest in issues related to the cost of capital. Your boss may give you a required IRR. Your investment bank may have standard WACC that they apply. You may be given a CAPM framework to plug in. You may get some country risk premiums from a horrible horrible website that lists them. This is how I my life worked after university a very long time ago and I doubt things have changed much. But the older I get the more I keep coming back to nagging cost of capital issues. That is why have spent time creating this page and documenting different alternatives to the cost of capital.

## Alternatives to Computing the Cost of Capital Using the CAPM

I believe that cost of capital and the CAPM is a lot like the phenomen of “fake news.” Somebody writes something in a fake newspaper that is not really true. But it conforms to what people want to believe. Then it gets millions of hits on facebook and it becomes generally accepted by a segment of the population. In this way the CAPM is a lot like the story of people buying marijauana with food stamps. Estimation of the cost of capital cannot be avoided in valuation (directly or indirectly) and many people are still proud of themselves by applying the CAPM where comparison companies unlevered Beta is computed and then translated into the weighted average cost of capital. These days, cost of capital estimation is debated and people seem to apply the CAPM without really believing it. One of the quotes from Taleb that I like a lot is when he compares believing the CAPM to believing that a magic potion sold on the internet will cure your sickness. Many analysts know that the CAPM model has never been confirmed from an empirical standpoint and the model requires many subjective inputs including the equity risk premium and ridiculous adjustments to beta for mean reversion that came from poor analysis in a paper written in the 1970’s. In the video lessons below I demonstrate that you can use creative alternatives to the CAPM through making a regression analysis of market to book ratios and deriving the cost of capital from P/E ratios or EV/NOPAT ratios. The set of videos is supposed to suggest practical alternatives even though regression analysis of price to book ratios is presented and statistical analysis of beta is discussed. The videos and files generally demonstrate that CAPM overstates the cost of capital. In addition, the corrected value driver formula is used to evaluate the cost of capital. The lesson includes two files that illustrate the theory of coming up with cost of capital from the P/E formula and the P/B formula and also a database to compute the cost of capital using a lot of different methods. Both the data analysis and the theory are quite advanced and not consistent with traditional methods to evaluate the cost of capital.

### Videos Associated with Valuation Concepts Lesson Set 1: Using Methods other than CAPM to Estimate the Cost of Capital

The set of videos for the cost of capital begins with an introduction to an approach that collects data from finance.yahoo.com and from marketwatch.com on stock prices, historic financial information, interest rates, earnings rates and growth rates. The database evaluates historic market to book ratios relative to projected return on equity to evaluate cost of capital. In addition PE ratios and published growth estimates are used along with assumed transition rates to back into the cost of capital. The CAPM is also computed along with the dividend discount model. The next set of videos explain the theory behind using the market to book ratio and the P/E ratio using simulation and sensitivity analysis. The final set of videos in the set explain details of how to build the data base.

Files Used in Advanced Valuation Concepts Lesson Set 1: Using Methods other than CAPM to Estimate the Cost of Capital

There are two general sets of files associated with the cost of capital analysis. The first set of files in the cost of capital set work through the theory of valuation and alternatives to the CAPM. The second set of files show how the models work with real market data. The set of files and videos below include both development of spreadsheets that measure the theory and explanation of how to construct comprehensive financial ratio databases that can be automatically uploaded to evaluate cost of capital. Deriving the cost of capital from the P/E ratio requires a lot of assumptions about long-term ROE versus cost of capital, long-term growth, inflation rates and transition periods. The P/E ratio files and videos use alternative scenario analyses to demonstrate the difficulty. The P/E Analysis file below evaluates the cost of capital with sensitivity and scenario analysis. It demonstrates how to correct the value driver formula P/E = (1-g/ROE)/(k-g) for inflation and changing returns.

This files below evaluates the price to book ratio analysis with regression analysis and shows how to develop the formula: PB = (ROE-g)/(k-g). It shows how you can use the market to book ratio to compute cost of capital and it demonstrates how a regression equation for the market to book ratio can be used to evaluate the cost of capital. If the CAPM is a biased and flawed model, bizarre attempts to adjust the cost of capital for country risk resulting in premiums as much as 11% for some countries. These CAPM derived premiums published by a man named Mr. Damoradan and frequently used have to imply that the real cost of all sorts of products ranging from houses to electricity can be as much as double for so-called risky countries.

If you want to earn a badge for the cost of capital course, you first pick an industry, then you put your own ticker symbols into one of the three above files. Next, clear the existing sheets and re-run the macro to compute the cost of capital. Finally, send me the file with your industry and go through the various different methods to remove companies (with the TRUE/FALSE switch). Even though you will be doing me a favour by doing the painful job of finding the ticker symbols and entering them in a file, I will still charge 40 Euros for putting your name on the website. I will also post your file on this page and give you credit. According to modern marketing theory, you will feel much better about this process when you have to pay me money than if you did not have to pay. That is why I must charge a fee.

### Lesson Set 2: WACC, Tax Shields, Debt Beta, Target Capital Structure and Circularity

If you are like me, when you study how to apply the WACC in a DCF model you can be frustrated. When you read about applying the WACC in financial articles written by academics with dense equations and esoteric theory your confusion will without question increase. Some articles suggest that you must use APV and discounting tax shields at the all-equity cost of capital. Most write down a seemingly sophisticated formula for Be and Bu as a function of Bd and the tax rate. This lesson set addresses many of the issues including application of a target capital structure, un-levering and re-levering beta, resolving an apparent circularity problem and valuing the tax shields created by interest. The video below introduces some of the issues.

I have tried to demonstrate that these WACC issues are really not very difficult and do not require a whole bunch of seemingly complex formulas that seem to come from nowhere. Instead I use a couple of simple and hopefully clear-headed ideas along with simple excel models to prove the ideas. Rather than working through the technical formulas without much real explanation, the files and videos in this section demonstrate how to prove a few key concepts. The models are simple financial models. Construction of the models is demonstrated in videos. Key conclusions of the financial model proofs and the theory that I hope is explained in simple terms include:

1. Tax Shields from Interest Deductibility in WACC Can Be Resolved with Gross and Net Capital Structures. The excessive discussion about how to value tax shields associated with debt is a colossal waste of time. When you recognize that the tax shield is equivalent to a reduction in the coupon rate on debt, the proof of how to treat the tax shield becomes clear. The market value of debt to the corporation is reduced to when the coupon rate falls and the equity value increases. For example if debt was 1,000 at with an interest rate of 10% and the coupon rate is reduced to 6%, the market value of debt decreases form 1,000 to 600. If the opportunity cost of debt for providers of funds is 10% both before and after the coupon rate decrease, the value of the debt declines to 60 of interest/10% or 600. This example is just the same as the tax effects of the interest shield at a 40% tax rate. Using the simple an basic principles that the fixed cost to the corporation is reduced from the tax shield and that the opportunity cost to providers of debt does not change from the corporate tax rate, the following equations quantify the tax shield. The second method is equivalent to the traditional WACC implementation.

Tax Shield Percent = Gross Observed Market Debt to Capital * tNet Equity Percent = Gross Equity Observed/(1-Tax Shield Percent)
Net Debt Percent = 1- Net Debt Percent
Ku = Kd * Net Debt Percent + Ke * Net Equity PercentKe = [Ku – Kd * Net Debt Percent]/Net Equity Percent
Bu = Bd * Net Debt Percent + Be * Net Equity PercentBe = [Bu – Bd * Net Debt Percent]/Net Equity Percent

2. Beta on Debt Should be Derived from Bond Yields: The beta on debt is generally assumed away in considering the WACC. But the debt beta can be derived from the credit spread on debt given the EMRP and Rf. For example, the historic spread on BBB bonds is about 2% and the gearing of BBB companies is about 55%. This implies the beta on debt or Bd is given by the equation Cd = Rf + EMRP x Bd. Restating the equation implies that CSd = EMRP x Bd and Bd = CSd/EMRP. If the credit spread is 2% and the EMRP is 4%, the the Bd is .5. Data on the relationship between debt to capital and credit ratings can be used to derive the beta on debt as a function of the market capital structure

Total Interest Rate = Rf + Credit Spread
Total Interest Rate = Rf + EMRP * Debt Beta
Credit Spread = EMRP * Debt Beta
Net Debt Percent = 1- Net Debt Percent

3. Bd Should Vary with the Capital Structure in Computing Be and Bu. Even though this is obvious, it is virtually never done in practice. S&P standards for the leverage and credit rating and published credit spreads can be used to establish Bd that varies with capital structure. When the varying credit spreads are applied, the effects on the relationship between Be and Ke and the capital structure are dramatic. The cost of equity at high leverage is dramatically reduced which reflects the call option premium that is inherent in the Ke and the put option cost that is part of the Kd.

Bu = Bd * Net Debt Percent + Be * Net Equity Percent, where Bd is a function of Gross Debt/Capital
Be = [Bu – Bd * Net Debt Percent]/Net Equity Percent, where Bd is a function of Gross Debt/Capital

4. Circularity in WACC and Valuation from Tax Shield can Easily be Avoided. As the equity to capital ratio is computed using the market value of equity and, in turn, the market value of equity requires a value of WACC that is in turn driven in part by the equity to capital ratio. This implies a circular reference seems to exist. This is not much of a problem when the Bu and Ku is established from a comparison set of companies. The remaining circular reference from re-levering the beta can be easily resolved.

5. Target versus Actual Capital Structure Does Not Matter With No Interest Tax Shield. If there is no tax shield, the WACC should not change if you use different capital structure assumptions because the cost of equity changes to compensate for risk created by gearing. This means that without taxes, use of a target capital structure in the context of DCF is not beneficial, necessary or relevant in terms of accuracy or theory. Without the interest tax shield, when the cost of equity is derived from re-levering the unlevered beta using the market value of debt at the valuation date, the result is exactly the same as if the company moves to a target capital structure.

6. APV does not add anything new to valuation. Correct application of the WACC accounts for all items in the bridge between equity value and enterprise value in the WACC calculation. Investment bankers typically do this with using net debt rather than gross debt in computing WACC. Similar adjustments to the WACC should be made for associated investments not included in EBITDA, the fair value of derivatives, discounted operations and any other items.

## Application of WACC in the DCF

Video explanations include theory and some background APV does not add anything new to valuation. Correct application of the WACC accounts for all items in the bridge between equity value and enterprise value in the WACC calculation. Investment bankers typically do this with using net debt rather than gross debt in computing WACC. Similar adjustments to the WACC should be made for associated investments not included in EBITDA, the fair value of derivatives, discounted operations and any other items.