P = D / [r - g]

Where:

- P - Current price of equity
- D - Dividends expected in next period
- r - Required rate of return on the market
- g - Divided growth rate

PE multiplier = P / EPS

P = EPS / PE multiplier

P = EPS / PE multiplier

Does something look familiar? Well, substitute dividends for earnings and the PE multiplier for [r - g] and you have the same formula. This should come as no surprise as the underlying math and assumptions are virtually identical for these valuation techniques (infinite geometric series - the discount and growth being the geometric term and earnings being the base case).

What I would like to focus on, is r - the required rate of return. Right away, it should be obvious that this is somehow related to WACC. As r goes up, the divisor goes up and the price goes down. This is a similar relationship with what we should expect from WACC, as the cost of raising capital for a company goes up, on some level its margins on return must also drop.

Looking strictly from a capital markets perspective, it should be clear that if a company were given capital at WACC, it would have to generate returns in excess of WACC (at r) in order to justify the additional risk of the venture. Using a modified version of the Sharpe ratio to decompose what's happening here:

What I would like to focus on, is r - the required rate of return. Right away, it should be obvious that this is somehow related to WACC. As r goes up, the divisor goes up and the price goes down. This is a similar relationship with what we should expect from WACC, as the cost of raising capital for a company goes up, on some level its margins on return must also drop.

Looking strictly from a capital markets perspective, it should be clear that if a company were given capital at WACC, it would have to generate returns in excess of WACC (at r) in order to justify the additional risk of the venture. Using a modified version of the Sharpe ratio to decompose what's happening here:

S = [Rp - Rf] / sp

Where

- S - Sharpe ratio
- Rp - Return on portfolio
- Rf - Return on risk free asset
- sp - standard deviation of return (risk)

S = [Rr - Rwacc] / sp'

Where

Another thought: What is the relationship between required rate of return on the market (r above) and cost of equity component in WACC? Isn't it the same? Isn't the difference in cost of equity and WACC the use of leverage such as debt to provide amplified returns (which also explains why WACC < r)?

- Rr - Required rate of return on company's stock
- Rwacc - Weighted average cost of capital
- sp' - change in standard deviation

Another thought: What is the relationship between required rate of return on the market (r above) and cost of equity component in WACC? Isn't it the same? Isn't the difference in cost of equity and WACC the use of leverage such as debt to provide amplified returns (which also explains why WACC < r)?

## 2 comments:

r (cost of equity) in the Gordon Growth Model (first equation you mentioned) is the same as the one used in computing WACC.

WACC = wd * d * (1-t) + we * r

wd and we are debt and equity ratios to total capital, and (1-t) is when interest is tax deductible.

Debt is used because it is cheaper than equity (which is also why WACC < r). But since it is a fixed cost companies can't just use debt as 100% of their capital structure. They need to find an optimal mix where the total cost of capital is minimum considering other risks.

Thanks for the clarification! That's a perfect explanation.

Post a Comment