In my last post, I looked at the leavening effect that large cash balances have on PE ratios, especially in a low-interest rate environment. In making that assessment, I used a company with no debt to isolate the effect of cash, but many of the comments on that post raised interesting points/questions about debt. The first point is that while cash acts as an upper for PE, debt can act as a downer, with increases in debt reducing the PE ratio, and that if we are going to control for cash differences in the market across time, we should also be looking at debt variations over the years. The second is the question of which effect on PE dominates for firms that borrow money, with the intent of holding on to the cash. In this post, I will start by looking at debt in isolation but then move to consider the cross effects of cash and debt on PE.

**Debt and PE: A simple illustration**

To examine the relationship between PE and debt, I went back to the hypothetical software firm that I used to evaluate the effect of cash on PE. Initially, I assume that the firm has no cash and no debt and is expected to generate $120 million in pre-tax operating income next year, expected to grow at 2% a year in perpetuity. Assuming that the cost of equity (and capital) for this firm is 10%, that the tax rate is 40% and that its return on equity (and capital) on new investments is 36%, the company's income statement and intrinsic value balance sheet are as follows:

[drizzle]Now, assume that this firm chooses to move to a 40% debt ratio with a pre-tax cost of borrowing of 4%. The effects of the debt on the are traced through in the picture below:

Note that the value of the business has increased from $850 million to $988.37 million, with __the bulk of the value increase coming from the tax subsidies generated by debt__.

The effects of borrowing show up everywhere, with almost almost every number shifting, and the effects at first sight seem to be contradictory. Higher debt __raises the cost of equity__ but __lowers the cost of capital__, __reduces net income__ but __increases earnings per share__ and results in a __lower PE ratio__, while increasing the __value per share__. The intuition, though, is simple. Borrowing money to fund the business increases both the expected returns to equity investors (captured in the EPS increase) and the riskiness in those equity returns (pushing the PE ratio down) and at least at a 40% debt ratio, the benefits outweigh the costs. In fact, if you are able to continue to borrow money at 4% at higher debt ratios, the PE ratio will continue to drop and the value per share continue to increase as the debt ratio increases.

Note that at a 90% debt to capital ratio, the PE ratio drops to 2.75 but the value per share increases to $11.41. If it is sounds too good to be true, it is, because there are two forces that will start to work against debt, especially as the debt ratio increases. The first is that the__ rate at which you borrow will increase as you borrow more__, reflecting the higher default risk in the company. The second is that at a high enough debt level, with high interest rates, __the interest expenses may start to exceed your operating income__, eliminating the tax benefits of debt. In the table below, I highlight the effects on PE and value per share of different borrowing rates:

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The breakeven cost of borrowing, at least in this example, is around 8.6%; if the company borrows at a rate that exceeds 8.6%, debt reduces the value per share. The effect on PE, though, is unambiguous. As you borrow more money, the PE ratio decreases and it does so at a greater rate, if the borrowing rate is high.

**Debt, Cash and PE: Bringing it all together**

Now that we have opened to the door to cash and debt separately, let's bring them together into the same company. A measure that incorporates both cash and debt is the net debt, which is the difference between the cash and debt balances of the company.

Net Debt = Total Debt - Cash and Marketable Securities

This number will be negative when cash balances exceed total debt, zero, when they offset each other, and positive, when debt exceeds cash. In the table below, I have estimated the PE ratio for the company with different combinations of debt ratios (from 0% to 50%) with cash ratios (from 0% to 50%), with debt borrowed at 4% and cash invested at 2%:

Note that both the cash effect, which pushes up PE ratios, and the debt effect, which pushes down PE ratios, is visible in this table. Interesting, a zero net debt ratio (which occurs across the diagonal of the table) does not have a neutral effect on PE, with PE rising when both debt and cash are at higher values; thus the PE when you have no cash and no debt is 11.81, but it is 12.66 when you have 40% debt and 40% cash. Before you view this as a license to embark on a borrow and buy treasury bills scheme, note that the value per share effect is negative of borrowing money and holding it as cash is negative; the value per share declines $0.22/share when you move from a net debt ratio of zero (with no debt and no cash) to a net debt ratio of zero (with 40% debt and 40% cash). Again, there is no mystery as to why. If you borrow money at 4% and invest that money at 2%, which is effectively what you are doing when cash offsets debt, you are worse off than you would have been if you had no cash and no debt. In fact, the only scenario where the value effect of borrowing money and buying T.Bills is neutral is __when you can borrow money at the risk free rate__ but even in that scenario, the PE ratio still increases. In short, the cash effect dominates the debt effect and you can check it out for yourself by downloading the spreadsheet that I used for my computations.

**Cash and Debt Effects on PE: US Stocks from 1962 to 2014**

In my last post, I noted the difficulty with dealing with cash balances at financial service firms, where the cash serves a very different purpose than it does at non-financial service firms. That statement is even more applicable when it comes to debt, since debt to a financial service firm is less a source of capital and more raw material. Hence,