## Realized return of buybacks

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) →
*P*_{b}=$100 - Stock price (end of period) →
*P*_{e}=$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 =[(P _{e} – P_{b}) + D] ÷ P_{b}*

*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.

But how about **expected** return?

## Expected return of buybacks

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

- invest in the business
- keep in cash (or short term fixed income securities)
- repay debt
- repurchase shares
- 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.