Chapter 25
Weighted average cost of capital
A firm’s ‘weighted average cost of capital’ (or WACC) is a financial metric used to measure the cost of capital to a firm. It is a weighted average of the firm’s cost of debt and its cost of equity.
When to use it
- To decide what discount rate to use in capital budgeting decisions.
- To evaluate potential investments.
Origins
The term ‘cost of capital’ was first used in an academic study by Ferry Allen in 1954: he discussed how different proportions of equity and debt would result in higher or lower costs of capital, so it was important for managers to find the right balance.
However, this informal analysis was eclipsed by Modigliani and Miller’s seminal paper, ‘The cost of capital, corporation finance and the theory of investment’, published in 1958. This paper provided a strong theoretical foundation to discussions about the right capital structure in firms. Building on this theory, the WACC formula is a straightforward way of calculating the approximate overall cost of capital for a specific firm.
What it is
Firms are generally financed through two methods – through debt, which means borrowing money from lenders, and through equity, which means selling a stake in the firm to investors. There is a cost to both these financing methods. Holders of debt expect to receive interest on their loan. Holders of equity expect their share in the firm to go up in value, and may receive an annual dividend payment.
The weighted average cost of capital for a firm is calculated by working out the cost of debt (which is simply a function of the interest rate it pays) and the cost of its equity (a more complicated formula, as described below), and then coming up with a weighted average of the two depending on its proportions of debt and equity.
In more technical terms, the WACC equation is the cost of each capital component multiplied by its proportional weight and then summing:
Where:
- Re = the cost of equity.
- Rd = the cost of debt.
- E = the market value of the firm’s equity.
- D = the market value of the firm’s debt.
- V = E + D = the total market value of all sources of financing (both equity and debt) in the firm.
percentage of total financing that is equity.
percentage of total financing that is debt.- Tc = the corporate tax rate.
In summary, WACC is an aggregate measure of the cost the firm incurs in using funds of creditors and shareholders. This measure has implications for those running the firm and for potential investors. For those running the firm, creating value requires investing in capital projects that provide a return greater than the WACC, so knowing what the number is helps the firm’s managers decide which projects to invest in. For potential investors, the firm’s WACC tells you how much of a return the current investors are getting – and whether the firm might ultimately be worth more or less than that.
How to use it
Here is an example of a WACC calculation. Gryphon Conglomerate is a mid-sized firm assessing a few initiatives. To determine if any of these initiatives will deliver value to the firm, Gryphon is looking to calculate its WACC. Its shareholders, principally its founder and his family, started the company and continue to provide 80 per cent of its equity capital. They are looking for a 25 per cent rate of return on their money. The other 20 per cent consists of long-term debt, with an interest rate of 6 per cent.
Let’s assume the marginal tax rate is 30 per cent. If it were 100 per cent equity-financed, its weighted average cost of capital would be 25 per cent. With debt, its WACC (using the formula shown above) is as follows:
With this WACC in mind, each initiative has to have the potential to achieve an average annual return greater than 20.84 per cent for Gryphon to consider it. This is, in reality, a pretty high number. Even initiatives with a target return of 15–18 per cent per year would not be viable for Gryphon, although they would be for many other firms.
Since other firms in its industry use a greater proportion of debt in their capital structure (50 per cent on average), Gryphon decides to take on more debt, until it reaches the industry average. Its new WACC is shown here:
With its new capital structure, Gryphon can take on initiatives that have the potential to earn 15–18 per cent per annum because the potential returns are higher than its WACC.
What if Gryphon takes it one step further and attempts to finance itself with 80 per cent debt? Here is its revised, hypothetical, WACC:
One can see that as the proportion of debt (which carries a lower cost) increases, the WACC goes down. But this new WACC is hypothetical because as Gryphon takes on more debt, it takes on more risk for its equity holders, who will be worried about the company’s ability to service the debt. The equity holders may, as a result of the increased risk of bankruptcy, demand a higher return on their investment. The impact of a higher cost of equity will then increase the WACC.
In calculating the WACC for a firm, investors generally want to know what the firm’s target capital structure will look like, and this target is usually based on what is typical in the industry. For example, one might expect to see a higher proportion of debt used in real-estate investment trusts compared to firms in the high-tech sector.
How do you calculate the cost of debt and the cost of equity? The cost of debt is easy to estimate – you can simply look at the average interest paid on its existing long-term debt (or you can use the numbers from comparable firms). To calculate the cost of equity, one option is to use the ‘capital asset pricing model’ (CAPM), which provides an estimate based on the risk-free rate, the market return and how volatile the share price has been in the recent past. The second option is to use the dividend discount model, which provides an estimate based on dividend pay-outs. The third option is to estimate a risk premium on top of the current risk-free bond yield. For example, if the current 10-year US government bond is yielding 4 per cent and the market risk premium is 5 per cent, then the cost of equity for the firm would be 9 per cent.
Top practical tip
Estimating the WACC for a firm is a relatively straightforward calculation, because it is based on assumptions that make intuitive sense, and it does not involve difficult calculations. However, it is worth bearing in mind that, for many uses, a ‘back-of-the-envelope’ calculation is actually all that is required. For example, if you are trying to decide whether a significant capital investment is worth pursuing, you need to know roughly what the firm’s WACC is (i.e. within 1–2 per cent), because the margin of error around the investment’s returns is likely to be far greater than 1–2 per cent.
Top pitfall
Calculating the cost of equity requires estimates to be made. For example, if CAPM is used, one has to determine whether the current risk-free rate is an anomaly, whether the stock’s past performance (in comparison to the market’s performance) is likely to continue, and what the current market risk premium should be. Using different estimates will yield different results for the cost of equity.
Further reading
Allen, F.B. (1954) ‘Does going into debt lower the “cost of capital”?’ The Analysts Journal, 10(4): 57–61.
Miles, J.A. and Ezzell, J.R. (1980) ‘The weighted average cost of capital, perfect capital markets, and project life: A clarification’, Journal of Financial and Quantitative Analysis, 15(3): 719–730.
Modigliani, F. and Miller, M. (1958) ‘The cost of capital, corporation finance and the theory of investment’, American Economic Review, 48(3): 261–297.