## Saturday, 9 January 2016

### Business Valuation and the Risk Free Rate

Government bond yields are at historic low levels in Canada and across the developed world (see the table below that charts the yield of the 10-year Government of Canada bond, over a 5 year period). This has very important implications on the values of businesses (and other assets too, but this post will stick to commenting on business equity values). This blog post will examine the impact that historically low risk free rates have on the cost of equity in a business valuation. What’s the risk free rate?

Simply stated, the risk free rate is the theoretical return that would be earned on a theoretical investment that has no risk of loss. In other words if you invested money into a risk free investment there would be zero risk of loss to you. Government bond yields (in rich, developed countries) are usually used as a proxy for the risk free rate as these bonds are thought to be without risk to investors. Some people may dispute this notion, especially after listening to the congressional debate about the debt ceiling in the United States. As an aside, the real risk free rate is probably even lower than government bond yields since sovereign risk has likely
gone up since the Great Recession relative to times before then.  But for our purposes let's assume that the risk free rate does equal government bond yields.

The risk free rate is an important number. It is a foundational rate used to calculate the cost of capital for a business. More on that later…

First, a brief tutorial on some basic business valuation principals

In order to value a business the basic approach is to determine the “cashflow” of a business and then to discount or capitalize that cashflow by a cost of capital. The result would be the value of the business.

Simple example: suppose the business cashflow is \$100 and the cost of capital is 14%. The value would be calculated as follows: \$100 / 0.14 = \$714.28 value.

In finance, the cost of capital often refers to the weighted average cost of capital (“WACC”) which consists of two elements:

• the cost of equity for the business, and
• the after-tax cost of debt for the business.

As you can see, the business’ cost of equity is an important overall component of its overall cost of capital, the WACC.

The risk free rate also influences the cost of debt for business, but this blog post will only take a closer look at the cost of equity.

How the risk free rate impacts the cost of equity

There are a few methods that can be used to calculate the cost of equity for a business but the “build-up method” is an intuitive one to explain. Essentially the build-up method calculates the cost of equity for a business by building up to it from its component pieces, which are:

• the risk free rate +
• the equity risk premium +
• industry risk adjustment +
• size premium +
• company specific adjustment
= the cost of equity for the business

From the above, the risk free rate is the starting point as it refers to the risk-free return available in the market to investors. From here we layer on more risk/return based on the characteristics of the specific investment.

The equity risk premium from the above equation refers to the premium that investors expect to earn on investments in equities as a class, over and above the risk free rate.

The industry, size and company factors in the above equation are other case specific adjustments made to the cost of equity but we won’t focus on them in this post.

Conventional thinking holds that as the risk free rate goes down then so should the overall cost of equity, since the risk free rate is part of the overall cost of equity. And therefore if the cost of equity goes down then the overall value of the equity should then go up, right?? Not necessarily.

A simple example using conventional thinking

Assume a business earns \$100 in equity cashflow and the business’s cost of equity is 10%. Assume that the 10% cost of equity is comprised of a 3% risk free rate plus a 7% equity risk premium (for simplicity, assume no growth or other variables like industry, size or company adjustment). The value of the \$100 would therefore be \$1,000 (\$100 / 0.10).

Now assume that the risk free rate goes down by 2% to 1%. Conventional wisdom holds that the new cost of equity would be 8% (1% risk free rate + 7% equity risk premium). Therefore the \$100 in equity cashflow would now be valued at \$1,250 (\$100 / 0.08).  The value goes up by \$250. The trouble with this approach is that it ignores much of the nuance going on in the background.

It’s important to peel back the layers of the onion

An often made mistake is that the risk free rate and the equity risk premium are viewed in isolation. The fact of the matter is that they are very much inter-related for a few important reasons, such as:

•  A low risk free rate is a reflection of what investors see happening in the overall growth and health of the economy. A theory used in corporate finance is that in the long term the risk free rate and growth rate of the economy do correlate. In other words, there is a positive relationship between the risk free rate and economic growth. So, from the simple example above, if the risk free rate is at historic lows it is not enough to simply reduce the cost of equity. A lower risk free rate may also suggest lower cashflow and sluggish growth which would have downward pressure on the valuation.  Careful analysis is needed to determine what is actually going on.
• In times of economic uncertainty investors tend to flock to safe(er) government bonds (the so-called flight to safety). This has the impact of lowering the yields on government bonds and increasing the spreads on equities (therefore the equity risk premium should increase). Referring to the example above, the risk free rate may drop by 2% but the equity risk premium spread may widen too, thereby potentially reversing the impact of the drop in the risk free rate.

So what does all of this mean for the values of businesses?

The point to the above is that in this environment of low government bond yields, it is important to understand the component variables of a business valuation and how they relate to one another.  Although this blog post focused on the cost of equity, the similar principles hold true with the cost of debt, which is also influenced by fluctuations in the risk free rate.

The key to remember is that the risk free rate, the equity risk premium, the cost of capital, cashflow and growth are all inter-related variables and should not be viewed in isolation.  A low risk free rate does not necessarily mean a higher equity valuation.  Plug and play valuation models which simply update the cost of equity but don’t take a closer look at all of the other drivers in the valuation are dangerous in that they may be incomplete, incorrect and may misstate value.

Please contact Steve Skrlac, MBA, CFA, CBV at 905-592-1525 or steve@keystonebv.ca to discuss business valuation issues. www.keystonebv.ca