I made an exam for a job position were they asked me this:
If the WACC goes down, what happens to equity value? The answer was (the analyst told me for the 2nd interview) it goes up.
What I answered was: cannot say without more detailed information, because your WACC can go down because your cost of debt went down and your cost of equity remained the same. For example, if you are more creditworthy now, the debt you could now issue would be less expensive, thus making your cost of debt after taxes less expensive driving your WACC down, and mantaining your cost of equity in the same level (ceteris paribus).
Your discount rate for equity value isnt the WACC but it is your cost of equity, so really you cannot say there was an impact without further information on what really made the WACC down (was it the cost of debt, the cost of equity, or both?). In the last two scenarios it would make a bigger equity value because of a lower cost of equity.
You don’t use cost of equity with FCFF because FCFF is what’s available to all providers of capital; therefore, WACC is used because it’s the discount rate that incorporates debt and equity. Cost of equity is used when calculating equity value from FCFE. Lower discount rate=higher Firm Value
I think you made the question more difficult than it should have been. The answer they were looking for was that equity value goes up when WACC falls. This is because a lower discount rate leads to a higher Firm Value. There are 2 formulas you need to know to understand this
Equity Value = Firm Value - Mkt. Val. of Debt
Firm Value= FCFF(1+g)/(WACC-g)
For example
ABC Company has FCFF of $700 million, it’s WACC is 10.2%, and the company is expected to grow forever at 5%. ABC Company’s debt has $2.2 billion market value.
Firm Value = 700*(1+0.05)/(0.102-0.05) = 14,134.6
Equity Value = 14,134.6-2,200= $11,934.6
What happens to equity value if we assume the WACC is now 9.2% instead of 10.2%?
What if it is a company that is 100%-equity financed and then it does an LBO? You increase leverage - does your WACC go down? Most likely. Your equity value most likely goes down as well because any increase in firm value is more than offset by the increase in debt.
all BS man. Just make your models pretty and make sure you dress sharp and look good and you’re golden. Of course when the market is doing its normal thing, models work quite well. The models become useless when we need them the most - predicting downturns, bear markets, corrections, etc. For this reason I am out of public equities hedge fund world which by the way is on its way to automation. Place to join are real estate PE or venture funds. Of course the models here are also more of an art than a science.
christoph, brah - what i was trying to demonstrate via (counter)example and what my man benzo summarized in his reflective musings on the subject is that most problem sets in finance have enough degrees of freedom that you can arrive at and support any answer you want. once you leverage that skill into an ability to sell a product or service you’ll be on a path to success