One of the most important keys to both intelligent investing and raising capital for a business is understanding the cost of equity. This is another way of describing the rate of return a shareholder will require in order to invest in a business. It’s fairly simple to calculate post-tax, as it simply uses post-tax figures. But what if you want to work out a pre-tax option?
There’s an easy method: post-tax cost of equity ÷ (1 – tax rate). You might have used this before, or at least heard of it. The only problem is that it’s quite inaccurate. All pre-tax cost of equity calculations are estimates, but this one is particularly rough as it doesn’t take a wide range of factors into account.
So, how do you calculate the pre-tax cost of equity? Here are our five steps for doing so as easily as possible:
1. Work out your post-tax cost of equity
This is the easier figure to calculate. The formula for what is known as the Capital Asset Pricing Model (CAPM) is as follows:
Cost of Equity = Risk-Free Rate of Return + Beta x (Market Rate of Return - Risk-Free Rate of Return)
You can usually find the risk-free rate of return by looking at your government’s figures. In the US, for example, a ten-year Treasury note can be used, which will provide you with the yield over a decade.
Beta is a measure of the risk of the investment, which will depend on the company being invested in. Anything above one means the asset is more volatile than the overall market, while a figure below one means it’s less volatile.
Finally, you need the expected market return, which is simply the average return of investments across the market, usually over the last ten years. Again, you can use figures from your country, such as the S&P 500 in the US.
2. Make some base calculations/assumptions
Now we need some more figures. Your pre-tax cost of debt is basically the interest rate paid on your debts; you can average this if you have taken out multiple loans. Then you need your post-tax cost of equity, which we calculated above, and the tax rate.
Finally, work out your proportion of debt, which is determined by dividing the value of all your debts by the value of all your assets, and turning the results into a percentage. Then put all that data into the following formula:
Pre-tax cost of debt x (1 - tax rate) x proportion of debt) + (post-tax cost of equity x (1 - proportion of debt)
The resulting percentage is your post-tax weighted average cost of capital (WACC); the rate your company is expected to pay on average to all security holders, in order to finance your assets.
3. Work out your DCFs
The next stage is to determine your discounted cash flows (DCFs), which use a discount rate to determine the present value of future flows. You’ll probably be doing this over multiple periods, so decide what these will be. Then, you can use the formula:
Cash flow ÷ (1 + WACC)
This will give you your DCF. You can perform this multiple times across different periods to get more DCFs, which will be useful for the next step. This is explained in further detail by the Corporate Finance Institute.
4. Calculate your NPV
Your net present value is the difference between the value of the money you’re investing, and the value of the cash flows you’ll get from said investment over a period of time. There are complicated methods of working this out, but for our purposes we can use an extremely simple one at the expense of a little accuracy:
DCF - today’s value of investment
For example, if you invested $100 and your DCFs over a period of a year equated to $550, your NPV would be $450. For multiple time periods there’s a slightly more complicated formula, which you can find over at Investopedia.
5. Putting this all together
Now we’ve got all these numbers, we can plug them into a formula that will give us the pre-tax cost. Unfortunately, this is much harder than you might expect. Dealing with this many complicated formulas is next to impossible, especially when working it out using multiple DCFs. That’s not hyperbole, either; Galois Theory makes it literally impossible to solve if there are more than four DCFs.
Luckily, you can get a downloadable excel file that will do the work for you. To get around Galois Theory, the creator has instructions showing you how to use Excel’s ‘goal seek’ function to get an accurate result.
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