Cai Haoxiang

29/7/2013

LAST week, a complicated but rigorous way to value a business called the discounted cash flow (DCF) model was discussed.

This method says a business is worth the sum of all its future cash flows, discounted to their present day value.

I showed how an investor can try to price a real company using its free cash flows. However, many assumptions have to be made.

This week, we continue the discussion of how to price businesses using the DCF model. There is plenty of financial jargon for the uninitiated, but not to worry - the underlying ideas are not as difficult as they seem.

The DCF model equation has two major inputs. The first, cash flow, goes into the numerator. The higher the cash flow, the higher the valuation of the company. This makes intuitive sense. If a company is generating more cash every year, investors will want to pay more for it.

The second input, the cost of capital, goes into the denominator. How people calculate this number is the topic for today.

The cost of capital is the interest rate which investors can be persuaded to invest in the company you are valuing. It is also a measure of risk. The higher the risk, the higher the interest rate an investor will demand to take on the risk.

Investors would not want to pay the same amount of money for a company that suddenly became more risky due to, say, a strike by unhappy workers. They will pay less.

Similarly, if you want to persuade me to invest in a country that is currently torn apart by civil war, the returns had better be really, really good.

For example, if I invest $1 million in a company in Singapore and can get a 5 per cent annual return, or $50,000 a year, I would not want to invest in a company in war-torn Syria and only get $50,000 a year. Maybe I need to get $200,000 a year - a 20 per cent return - before I can be convinced to part with my $1 million.

After all, the company's factories might get bombed. It might not be able to expand anywhere due to the huge uncertainty caused by the civil war. I could lose my entire investment.

If investors now demand a cost of capital of 20 per cent, and the company's cash flows remain at $50,000 a year, its valuation will be just $250,000.

So if a company becomes riskier, its cost of capital will go up. Because the cost of capital is in the denominator, a higher cost of capital would result in a lower overall valuation.

Conversely, if a company is less risky, a lower cost of capital results in a higher valuation.

A large telco with a monopoly over its customer base will have a much lower cost of capital than a small biotechnology startup. Banks, for example, are willing to lend money at a lower cost to the telco. Investors, too, do not require a high return for the telco, because there is relatively little risk taken to get a steady return.

Calculating the cost of capital

How is the cost of capital calculated? This is when we take a deep dive into some financial theory.

In a DCF valuation model for a business, cash flows are discounted by the weighted average cost of capital (WACC) of the business.

As the words "weighted average" implies, there is more than one component to a company's cost of capital. A company's capital often comprises two parts: debt, or how much it owes others, and equity, what is due to its owners.

To calculate WACC, you need to answer these questions:

* How much debt does the company have as a proportion of its total debt and equity? In other words, what is the company's debt weight?

* What is the company's after-tax cost of debt?

* How much equity does the company have as a proportion of its total debt and equity? In other words, what is the company's equity weight?

* What is the company's cost of equity?

Once you have the answers to these questions, you get WACC by this equation that adds the two costs together after adjusting for their weights in a company's capital structure: (debt weight)(after-tax cost of debt) + (equity weight)(cost of equity).

Debt and equity weights

Let's start with the easy part and calculate the respective weights to be assigned to the cost of debt and the cost of equity.

To do that, you need to know the total capital the company is using to finance its business. You use debt valued at market prices, and equity valued at market prices.

If a company's debt is not traded, as is often the case, the book value of debt is used.

To calculate equity valued at market prices, take the company's share price and multiply it by the number of shares it has outstanding.

For example, if a company has $1 million of debt and $3 million of equity, its debt weight is 25 per cent and equity weight is 75 per cent.

Preferred shares have to be separately weighted along with the cost of preferred equity.

Sometimes, the company you are trying to evaluate is not listed or does not trade often. You can't determine the market values of its debt and equity. In that case, it might be better to find a comparable company and use that company's debt and equity weights instead.

Cost of debt

Now, you have two "weights", 25 per cent and 75 per cent. You need to attach an interest rate to each of the weights, and you will have your weighted average cost of capital.

The cost of debt can be seen in the financial markets. It is the interest rate a company would pay to borrow money.

Riskier companies pay a higher interest rate. The larger and more stable the company, the lower the interest it pays.

If the company's debt is rated by a credit rating agency and traded on the bond markets, it is easier to get the exact interest rate its debt is trading at through a search of market data providers like Bloomberg.

Another way to estimate the cost of debt is to use a company's interest expense, how long more before the debt matures and its book value. One can use a financial calculator or a spreadsheet to work out the yield to maturity.

Otherwise, an estimate has to be made from a comparable company.

Interest payments on debt that is used to finance income-producing assets are tax-deductible in Singapore. To account for the tax deductions and get the true cost of debt, you multiply the cost of debt by (1 - tax rate).

Cost of equity

Figuring the cost of equity is the subject of numerous finance textbooks. A popular model to determine the cost of equity is called the Capital Asset Pricing Model, or CAPM.

Essentially, you get a company's cost of equity by adding the risk-free interest rate - the minimum rate investors demand - to the product of the company's beta and the equity risk premium.

The risk-free rate is usually the yield on a 10-year government bond.

Beta is a measure of risk. The riskier the company, the higher the beta and thus the higher the cost of equity.

Risk is measured by volatility, or how much a stock price change differs from a change in the benchmark.

Mathematically, beta is measured by the covariance between the percentage return of the stock and the benchmark return, divided by the variance of the benchmark return. You can get a list of prices from sites like Yahoo Finance, and use an Excel spreadsheet to do this.

A beta of one means price movements are perfectly correlated with the STI. A beta higher than one means the stock is riskier than the benchmark, and a beta lower than one means the stock is less risky compared to the benchmark.

Websites like Reuters, Financial Times and Yahoo Finance will also have the beta of listed companies available. Cyclical companies such as airlines will have higher betas compared to companies selling essential goods.

The equity risk premium, meanwhile, measures how much investors are compensated by buying riskier stocks compared to risk-free government bonds.

Studies have been done showing historical equity risk premiums of around 4 to 7 per cent. There is no consensus on what this figure should be.

If the company you are looking at has a beta of 1.5 and an equity risk premium of 6 per cent, and the risk-free rate is 3 per cent, the CAPM model says its cost of equity would be (0.03) + (1.5)(0.06) = 12 per cent.

With an after-tax cost of debt of 4 per cent, and with the two different weights, we are now ready to calculate the company's weighted average cost of capital.

The equation for its WACC is: (0.25)(0.04) + (0.75)(0.12) = 10 per cent.

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