Buybacks and Stock Prices: Good or bad news?

XYZ Inc., a publicly traded company, has the following characteristics:
a. 100 million shares trading at $ 10 a share. (Market cap = $1000)
b. A cash balance of $ 200 million, earning 2% a year annualized.
c. Total net income of $ 40 million (giving the company a PE ratio of 25 today).
XYZ Inc. uses its cash balance of $ 200 million to buy back shares. What will happen to the share price after the transaction?
a. It will go up
b. It will go down
c. It will remain unchanged
Classic corporate finance question, right? Let's see what the answer will be at the two limiting extremes: an extremely "lazy" market and a completely rational one.

a. Markets are really lazy: Here is how it goes. Assuming that you can buy the shares back at the current price (unrealistic, but you have to start somewhere), you will buy back 20 million shares with the $ 200 million, reducing the number of shares to 80 million. The loss of the income on the cash (2% of 200 million = $ 4 million) will reduce net income by $ 4 million to $ 36 million.
Earnings per share = $36/80 = $0.45
Applying today's PE ratio of 25 to this earnings per share:
Price per share = $0.45 * 25 = $11.25
Even if you iterate and reduce the number of shares bought back (by dividing the $ 200 million by $ 11.25), you will still end up with a hefty increase in the price per share. In fact, for the math to work out, this is all you need for a buyback to increase price per share:
a. Current E/P ratio > Riskfree rate (Current E/P ratio for this firm is =1/25 =4% > Riskfree rate of 2%)
b. PE ratio remains has to remain unchanged after the buyback.
You are implicitly making the assumption that the market was mispricing cash prior to the buyback and here is why:
Net income from cash (prior to buyback) = $ 4 million
Since you are assuming that the PE ratio of 25 applies to all income, the estimated value of cash is $ 100 million (25*4), half of the actual cash balance of $200 million.

b. Markets are rational: Is equity in the pre-buyback firm as safe as equity in the post-buyback firm? After all, the firm is eliminating not just 20% of its assets, but its safest asset. Presumably what is left behind in the firm will be riskier than before and you will therefore pay a lower multiple of earnings for the stock. As a limiting case, assume that the market was valuing the cash correctly before the transaction. The implicit PE ratio for cash is 50 (1/ riskfree rate=1/.02). The observed PE for the company is then a weighted average of the PE for risky operating assets and riskless cash, with the weights based on the income you make on each one:
PE for stock = 25 = PE for operating assets (36/40) + 50 (4/40)
Solving for the PE of the operating assets, we get:
PE for operating assets = (25-5)/.9 = 22.22
New price per share = 0.45 * 22.22 = $10.00
In a rational market,  where assets are fairly priced, a buyback by an all-equity funded firm will have no effect on the stock price because it is a value neutral transaction.

So, what will actually happen after the buyback? I think that either extreme is unlikely to hold, but looking at both allows us to crystallize the factors that will determine the effects of a stock buyback:
a. Market's valuation of cash: A buyback reduces the cash balance at the company by the amount of the buyback. The effect it will have on the stock price will depend upon whether the market was pricing cash as a neutral asset (a dollar in cash is valued at a dollar). If the market was "discounting" cash in the hands of a company (viewing it as likely to be wasted), a buyback will increase the stock price. If the market was attaching a premium to the cash (viewing it a strategic asset), a buyback will decrease the stock price.

b. Financial leverage: In the example above, the buyback had no effect on the firm's debt ratio because the firm had no debt and was using cash to fund the buyback. However, a firm that borrows money to fund a buyback will change its debt ratio, and consequently may change its cost of capital. In what direction? It depends on whether the company was under levered, correctly levered or over levered prior to the transaction. An under levered firm will lower its cost of capital with a buyback funded with debt and thus increase its value (and price per share). A correctly levered or over levered firm will increase its cost of capital by borrowing money (the higher cost of equity and debt from the additional borrowing will overwhelm the advantage of using debt) and see value (and stock price) go down.

c.Value of operating assets: The value that the market attaches to operating assets is a function of expectations about future cash flows. A buyback can alter this value assessment by changing market expectations: this is the signaling story for buybacks but it can cut both ways. In its positive form, a firm that buys back stock is signaling to the market that it's stock is cheap and that investors are under estimating the cash flow potential from operating assets.  In its negative form, a firm that buys back stock is telling the market that its growth opportunities are starting to dry up and that future cash flows may not have the growth that investors had presumed.

The net effect of all three of these variables will determine the stock price impact of stock buybacks. Using them to make overall judgments, here is what I would expect to see in response to a stock buyback:

1. The most positive impact on stock prices should be at mature firms that have a history of earning poor returns on operating assets and are under levered. You get a triple whammy at these firms: the market probably is discounting cash at these firms because it does not trust the management, the firm is under levered and there is little likelihood of the buyback being viewed as a negative signal (since expectations for growth were low to begin with).
2. The most negative impact on stock prices will be at high growth firms with a history of generating high returns on operating assets and little debt capacity. Cash at these firms is unlikely to be discounted (and may be even be viewed as a strategic asset), there is little potential for value gain from financial leverage and the buyback is more likely to be viewed as a negative signal about future growth potential.

In my earlier post on Apple, this is why I argued against a buyback. Apple meets two of the three criteria for the second group: superb returns on operating assets and perceptions that there is still growth potential. It is true that Apple has some debt capacity (though its effect on value is muted). The debate about whether and when Apple should use this debt capacity is a good one to have, but I think that the argument for using debt right now is weak. That will change, as the debt capacity continues to grow, and returns on operating assets weaken (as they inevitably will).

A stock buyback is not a magic bullet. If you are a firm that should not be doing buybacks, don't go down that road, even if every other firm in your sector is doing so. You may be able to fool the market initially and get a stock price pop, but the truth will eventually come out to hurt you (perhaps after the top managers have cashed out their options and moved on.. but that is another story...)