Delta Less Than One: Debt Overhang and Underinvestment Explained

Imagine a company as a house that you and a bank jointly own. You, the equity holder, represent the owner who gets the upside, the increased value of the house. The bank, the debt holder, has a loan secured against the house, and they get paid back their loan regardless of how much the house value increases, as long as it’s not worthless.

Now, let’s talk about opportunities to improve this house, say, by adding a new kitchen. This kitchen renovation is like a new investment project for the company. For the project to be worthwhile, the value it adds to the house must be greater than the cost of the renovation. Makes sense, right?

However, consider a situation where the house already has a very large mortgage – a lot of debt. This is the debt overhang situation. Think about it: if you invest in the new kitchen, and the house value goes up significantly, who benefits? Both you and the bank benefit. But, if the house value only goes up a little, or even stays flat, you still have to pay for the renovation, and the bank is still owed their original loan amount.

Here’s where the concept of Delta comes in. In the world of finance, we can think of your equity in the house, your ownership stake, as being similar to a call option on the house’s value. A call option gives you the right, but not the obligation, to buy something at a certain price. In our analogy, you have the option to benefit from the house’s value exceeding the debt owed.

The ‘Delta’ of this equity option is like a measure of how much your ownership value changes for every dollar change in the house’s overall value. If the Delta were 1, it would mean that for every dollar increase in the house’s value, your equity value also increases by a full dollar. However, in reality, especially when there’s a lot of debt, the Delta is less than 1.

Why is Delta less than 1? Because when the house value increases, some of that increase goes to benefiting the bank, by making their loan safer, in addition to benefiting you, the equity holder. If the house value increases by one dollar, not all of that dollar increase directly translates into a dollar increase in your equity value. Some of it goes to the debt holders because their claim on the house becomes more secure.

Now, let’s connect this back to the underinvestment problem. Imagine you’re considering that new kitchen. Let’s say the kitchen renovation costs $50,000 and is expected to increase the house value by $60,000. On the surface, this seems like a great investment, adding a net value of $10,000.

But because of the debt overhang and the Delta being less than 1, you, the equity holder, don’t capture the full $10,000 benefit. Let’s say the Delta is 0.5. This means that for every dollar increase in the house value, your equity value only increases by 50 cents. In our kitchen example, even though the house value increases by $60,000, your equity value only increases by half of that, which is $30,000.

You spent $50,000 on the renovation but only gained $30,000 in equity value. Suddenly, this investment, which was beneficial for the house overall, looks unprofitable for you personally, the equity holder. Even though adding the kitchen makes the house worth more, you might choose not to do it because you don’t get to keep enough of the upside. A significant portion of the benefit accrues to the debt holders, making their existing loan safer.

This is the essence of the debt overhang problem and how a Delta less than 1 contributes to underinvestment. Because equity holders, with their Delta less than one, don’t capture the full benefit of new investments, they may rationally choose to forgo projects that would be value-enhancing for the company as a whole. The presence of significant debt effectively discourages beneficial investments because the benefits are shared with, and in some cases primarily accrue to, the existing debt holders rather than those who are making the investment decision – the equity holders. This leads to companies passing up good opportunities, resulting in underinvestment and hindering overall economic growth.