So if you are here without first reading this, you are going to be confused.
This is step 2 in evaluating a firm that
- Is considering only the effects by tax shields and other benefits from financing
- Does not have a constant proportion of debt to equity financing
- Has equity that depends on financial risk and business risk
The first bullet is important because it is the reason we are using NPV to calculate the companies value rather than APV.
The second and third bullet are important because those are the reasons we are calculating NPV in the 3-step approach with levered and un-levered WACC; instead of using the flow-to-equity method, which is much more “simple” — I guess.
Ok so, let us begin.
Remember in step one when I kept inserting “levered” and “un-levered” everywhere, asking you to remember it, but never explaining? Well, now I will.
Basically what is happening is that since we know the debt ratios will differ and the business risks will differ, we need to account for those changes WHILE we are calculating the WACC, which is the rate we used in the previous entry to calculate the NPV.
The reason for all of this is complicated. There are these two guys, Modigliani and Miller who proposed that changes in debt and equity do not change the assets (or value of a company). If the company were a pie and the pie was made up of two things: flour and sugar, the pie would not get bigger if you increased either of those two things. It would just get grosser. If you added more flour there would be less room for sugar, and vice verse, but the pie would be the same size.
That is how Debt and Equity work. The assets (or value) would stay the same, you just change up how much of debt or equity it is composed of.
BUT there is a trick. (The whole reason for this long, complicated approach)
Financing with debt or equity give you different benefits and different risks and can even make the pie larger (if the above assumptions hold true).
Debt is cheaper for a company. They can get money from a bank at a lower rate than say if they raised money by selling shares. Not only that, when they have debt they can deduct it as an expense! This is not something that happens internally in accounting books, but on income statements. Meaning the money they save is real and does add value to the company.
The trick is, if you start borrowing so much that your firm is more risky than the industry, then the banks will charge you a higher rate to borrow. If that rate gets too higher, you might as well not even have a tax shield.
Also, if you do add on debt, it could look risky to the shareholders. If they think you are more risky by playing around with the amount of debt or equity in order to raise money to invest with, they will, like the banks above, start to ask for more money (or a higher return on equity). Why do they do that? Because investing in a company is already dangerous for them. If they think you are going to make it MORE dangerous, they want MORE reason to keep their money in, i.e., a higher return on equity. So again, is it worth it to add on “cheap” financing (debt) if in the end you look more risky and all your rates go up?
All this can be accounted for by doing 3 things (the 3 things this whole post is about and we have yet to see) un-levering, levering, and re-levering.
First, we need to find the un-levered WACC. Another way to call it is “opportunity cost of capital” or “r” or “WACC without accounting for taxes”. What we are basically saying is that the debt is not effecting the WACC or the “price” of the cost of equity (Re).
Opportunity cost of capital = r = Rd D/V + Re E/V
Now, we have to see what the new rate of return of equity (Re) is going to be if we use a new debt ratio (D/E) or if we add more or less debt as compared to equity.
Re = r + (r – Rd) D/E
And by the way, (r – Rd) I learned in a very difficult way, can also be expressed as the market risk premium (MRP). It does not sound more simple this way, but after incorrectly trying to find the listed Rd over and over and over again, I realized the figure was GIVEN to me as the market risk rate for that particular company. So now I am telling you, you’re welcome.
Note: sometimes, you will have to make an important assumption about the cost of debt (Rd). If not otherwise stated, you will have to decide of the cost of debt changes when you add more debt or not, and you will have to do it at this step. If you do not think it will change, just use the same Rd. If you think it will change, come up with another Rd. If you are solving a case study, there will most likely be a clue. Usually if the company is stepping into a different risk index or the rates of treasury bonds are changing then the Rd will also have to change with the new debt amount being considered. Be careful — like I said, “over and over and over again.”
Ok, now last step (in calculating the WACC). We are going to find the “levered” WACC using the new Re we found based on the new debt-equity ratio we found and possibly the new added risk (Rd or MRP). So again, a levered WACC is just a WACC that takes into consideration of a tax shield.
Therefore the equation you should use is the following:
WACC = Rd D/V (1 – Tc) + Re E/V
Now, you take this (adjusted, levered discount rate) WACC and you stick in here.
Yay, you did it! You calculated the value of a company, taking into account the effects of tax shield on the financial weights, assuming debt ratios and business risks differed, but that the capital structure of the company as a whole stays constant, as least for the duration of the investment being calculated. High-five!
Now, let us say that — I don’t know — your company pays off some debt or something amazing happens to increase the value of your company in the stock market or any other normal, definitely probable thing that will change the capital-structure of a company. Well, then you can forget everything you learned in these two posts because you are screwed!
You will have do the whole thing over again using a second method, APV.
Isn’t learning fun?