# What's the expected return on buybacks (a theoretical view)

When we think about returns on buyback programs, we normally look back and estimate the realized return of holding the company’s stock.

For example, company X has the following characteristics:

• Stock price (beginning of period) → Pb=\$100
• Stock price (end of period) → Pe=\$150
• Dividends → D=\$10
• Buybacks: 1 share repurchased at the beginning of the period

In this example, the realized return (Return) on the one share repurchased is calculated as:

Return =[(Pe – Pb) + D] ÷ Pb

Return=[( 150- 100) + 10] ÷ 100

Return = 0.60

So 60% it is.

From here you cross sectionalize and analyze ad nauseam to show how companies that do buybacks outperform or underperform companies that don’t and et cetera.

When it comes to allocating capital, we can imagine a basic menu such as:

2. keep in cash (or short term fixed income securities)
3. repay debt
4. repurchase shares
5. pay a dividend

Each menu item has an expected return. Investing in the business presumably has an expected return higher than our cost of capital. Keeping a marginal dollar in cash will probably have the lowest return in this menu.

What’s the expected return of allocating a dollar to buy stock back?

I think the answer is the weighted average cost of equity.

### Why the weighted average cost of equity

This is why: buying back shares is not an investment. We are not manufacturing a product or delivering a service with buybacks. We are returning capital to shareholders. It’s a return of capital mechanism.

The capital that shareholders provided came with the expectation of a certain amount of return represented by the cost of equity.

### e.l.i.5: Home mortgage example

Here’s how I make sense of the cost of equity element. Imagine that you have a mortgage on your house with a 5% interest rate. You know that, for every dollar borrowed, you have to pay interest. The lender provided funds to you with the expectation of earning a 5% return.

If you have extra cash at month-end and decide to make an additional payment to reduce your mortgage balance, you’re saving the 5% interest on the additional payment. In other words, you returned capital to the capital provider and the expected “return” on this capital is 5% (because you know for a fact that you won’t owe interest anymore).

## But it gets tricky: marginal or historical cost of equity?

In the mortgage example, things are simple. We have a fixed interest rate and we know with certainty that the expected return of making a principal payment is this fixed rate, even if mortgage rates subsequently changed (i.e., you owe 5% even if current mortgage rates are at 10%).

Current mortgage rates represent the marginal cost of mortgage money (i.e., the cost of borrowing another dollar today for a mortgage), but the expected return of a principal payment is the historical cost (i.e., the cost at which we borrowed our funds).

For share repurchases then, the expected return is the historical cost of equity, not the marginal cost.

## Conclusion

When making capital allocation decisions, I suggest using the weighted average historical cost of equity as the expected return on buybacks, not the current cost of equity and not historical returns of your company’s stock.