CoE of different market cap companies
Going through the M&I guides and wanted to make sure I understand: they ask whether CoE should be higher for a 5b or 500m market cap company and then say that it should be higher for the 500m. I think that's an oversimplification; if the 5b company is 90% debt and the 500m has no debt, for example, the CoE of the 5b one would probably be higher. Am I tripping?
You're thinking of cost of capital (for the entire company), Cost of equity of the cost just for the equity piece.
As mentioned above, WACC is not equal to CoE. CoE will correlate (assuming the same industry) with size of company, where larger companies have lower costs of equity, primarily because they are more mature than their counterparts so equity investors face less risk investing in them. The question you are alluding to is whether or not a 500m or 5b company has a higher WACC. The answer to that is, as you mentioned, it depends. Theoretical lower levels of debt decrease WACC, because debt financing is less 'costly' than equity financing, but that only goes to some theoretical point. Beyond this point, the cost of debt, due to being over levered, risk of bankruptcy, now outweights the cost of equity financing. There is never a correct way to answer this question other than it depends, but make sure you don't accidentally give the WACC answer to a CoE question and vice versa.
So then, in another part of the M&I guide, it says
"What’s the relationship between debt and Cost of Equity?
More debt means that the company is more risky, so the company’s Levered Beta will be higher – all else being equal, additional debt would raise the Cost of Equity, and less debt would lower the Cost of Equity."
Would this just be wrong then?
Nope, that is still correct. The amount of debt can increase, with the cost of equity increasing but WACC decreasing. Remember, the WACC is about costs of capital, not just the absolute amount of capital. Let's think about what the WACC calculations are, assuming no preferred stock.
WACC = [(% equity)*(CoE)]+[(% debt)*(CoD)]
So even if you introduce debt and, as the question you put in your second comment suggests, CoE may increase, but, by virtue of going from 0 debt to some debt a few things change. So let's see the impact on all downstream variables with just an addition of debt.
% of equity decreases - going from 1 funding source to now 2 funding sources means the % contribution of the initial one must drop.
CoE increases - for the reasons you mentioned with beta increasing (see Hammada formula or whatever it's called)
% of debt increases - same rational but flipped as % of equity decreasing
CoD - goes from 0 to something non-zero.
The NET impact of all of these changes can still result in WACC dropping. The CoD is going to be lower than CoE at lower levels of debt - for example interest rates on debt are never going to equal the returns equity investors are seeking and if they are then you are on the flip side of that graph I laid out above where more debt now increases WACC. So introducing debt does not imply WACC has to increase, even though it does imply CoE has to increase. Let me know if that makes sense
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