Mathematically why does leverage amplify returns??
Does it have to with the fact that your cost of debt is less than your return on equity? Just trying to get a better understanding of this mathematically.
Appreciate the help.
Yes + all upside accrues to your equity. So if you bought a company for $2 and the value goes up $1, your return if financed all equity is 3/2=50% (equity value/initial investment) but if you financed 50/50 debt/equity your return is 2/1=100%.
Let’s clear up your second point because I think it could confuse people. If you acquire a company for $100 of equity and $50 of debt, you pay off the debt upon maturity (or in a sale), in exchange for cash that the business creates or cash (assuming no rollover) offered by a buyer. Now, let’s say you purchased the company for $150 of equity instead. You’d never have $50 of debt to pay back, so that $50 will be accrued as cash generated by the business or equity value implied by the buyer. If you use $50 leverage to finance this company’s acquisition, you’re essentially delaying how long this cash / equity (one and the same!) actually leaves your pocket. This creates “time value”, in addition to the margin of cost of debt / equity.
Thanks, didn't realize my point would be confusing. It's the exact same as the "mortgage" example used by the other poster in less words.
I assume you are thinking about things from like a WACC / technical question perspective. Instead I’d back it out logically then go deeper.
I have a house that costs $100, it goes to $150. Without leverage 50% return.
Now I have $50 of debt, so $50 debt $50 equity in a $100 asset. It goes to $150. I pay back the debt and my $50 becomes $100. This is a 100% return.
Now the $100 asset goes to $50. Without leverage, -50%, with leverage I lost all my equity -100%.
It’s really just the mechanics of paying back a loan and the principal being relatively fixed versus an asset appreciating.
But getting more technical, the cost of debt is just the interest rate and the cost of equity is often different than your return on equity. The cost of equity is better described as the market price people need to justify taking risk in holding equity in a company. This is why people often use the capm to determine the cost of equity financing.
Again, backing it out logically, because debt is senior to equity, generally debt is going to be less risky from the markets perspective and they will charge a lower price for that funding option. However, the cost of debt and the cost of equity is different from the return on equity and what the asset realizes for returns.
All that make sense?
The above is correct, but additional detail might be helpful for your learning. From a mathematical perspective (and also thinking about it from a structuring perspective as a PE buyer), the point at which you are indifferent on using leverage is when the after tax cost of the incremental debt = return on equity. When debt is cheaper than your unlevered return on equity, it is accretive to equity returns and when it is more expensive then it is dilutive.
Using the example above, if you buy an asset for $100 and you model that its value will be $150 in 5 years (with 0 free cash flow along the way), your unlevered IRR is 8.4% (1.5x TVPI over 5 years). If you structured that acquisition 50% LTV with 10% after tax cost of debt (for simplicity, assume interest is paid annually), your equity IRR will be 7.3%. If the cost of debt was 5%, your IRR would be 11.0%. As you can see, you would only seek to use leverage in this example if the after tax cost of debt was below 8.4% (if you assume your modeled exit value to be correct), otherwise you’re better off paying in full equity from a returns perspective. Note you also obviously have to factor in source of funds and whether you have the capacity to make the purchase with equity capital or if you need debt to bridge the funding gap.
nice this is good and should help people with intuition
Debt and equity holders agree to split the total expected returns unequally in exchange for an unequal split of return volatility risk, and by doing so they increase the total returns overall through an interest tax shield the government gives them for having debt.
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