# Why Are Some Dollars Worth 20 Dollars While Other Dollars Are Worth Just 50 Cents

Here is a somewhat surprising fact. Sometimes when a corporation earns an extra million dollars, the value of the company increases by about \$20 million dollars but at other times an extra million in earnings might only add a half million in value to the company.

Why is that? Why in some cases is a an extra dollar of income worth say \$20 while in other cases it is worth maybe 50 cents? (In reality this works better with thousands or millions of dollars).

The difference lies in whether we are talking about an earnings increase that is expected to be permanent and recurring – or better yet growing – every year as opposed to a one-time earnings event that is not expected to recur.

If an incremental earnings stream is expected recur every year then in the language of finance math this is known as a perpetuity. The value of each dollar of a growing perpetuity can be calculated by dividing the dollar by (the required return minus the growth rate of the dollar). For example, a dollar that is expected to grow forever by 5% per year and where an investor requires a 10% return, given the risk, is mathematically worth \$1.00 /(0.10-0.05) = \$20!

Of course in the real world earnings are not often expected to grow smoothly at say 5% per year. Also the equation assumes that the earnings are received in cash and do not need to be reinvested in the company. However, the theoretical math does work reasonably well in the real world. For example the above equation explains why a company might be trading at a Price / Earnings multiple of 20.

Because of this math, when “the market” believes that an incremental earnings stream (say from a new product line) will be permanent and will also grow, then it may place a “multiple” on the initial incremental annual earnings of say 20, thus each of these incremental dollars is worth \$20! So, as long as this is a new unexpected (and recurring and growing) earnings source, not previously reflected in a stock’s price, the market may value each of these new dollars at say \$20.

However, consider the value of a one-time unexpected earnings increment of \$1 million. Often, such a one-time earnings increment will be used to pay-down company debt. With today’s interest rates companies may be paying about 7% interest for debt, which then may only cost the company 5% after considering that interest is tax deductible. So, an extra dollar used to pay down debt may save just 5 cents per year. And what is the value of 5 cents per year? If we assume a permanent reduction in debt of \$1.00 then the 5 cents per year is saved in perpetuity. The value can then be calculated with the perpetuity formula above. There is no growth involved. Assuming the same 10% required rate of return applies, then the formula is \$0.05/(.10-0) = \$0.50. In other words the value of permanently reducing debt by \$1.00 may be only 50 cents. Therefore the market often gives very little or almost no value to a one-time non-recurring increment in earnings.

In summary, the market highly values recurrent and growing streams of earnings and may place a value of \$20 on each incremental dollar of earnings. However, the market is not very interested in one-time non-recurrent earnings and may value a one-time dollar at only 50 cents.

The above is meant to illustrate a concept. The exact values will not be \$20 and 50 cents but these figures are reasonably close to reality in many cases and do serve to illustrate the point.

The same concept applies in reverse to declines in earnings. The market will punish quite severely a decline in earnings that it views as permanent, while being very forgiving of earnings declines that are viewed as being one-time events. For example the value of a company may be hardly affected at all if it suffers a one-time unusual expense.

Analysts often value stocks on P/E basis. Some stocks are considered to worth 15 times earnings and others may be worth 20 times current earnings. In doing this analysis it is implicit that the earnings to which the 15 or 20 “multiple” is applied are sustainable base earnings that can be expected to grow. This is why analysts will often talk about “ex-items” or “adjusted” earnings. A P/E multiple is only a useful indicator if applied to earnings that have been cleansed of any one-time items.

This is also why companies often attempt to convince investors that any decline in earnings is a one-time event while any increase in earnings is more often describes as being permanent.

The above analysis is fundamental to how stocks are valued and investors should attempt to become as knowledgeable as they can about such fundamental mathematical concepts. Sometimes investors can get an “edge” over other investors if they understand how to adjust reported earnings to arrive at the “true” core recurrent (and hopefully growing) earnings figure.

END

Shawn Allen, CFA, CMA, MBA, P.Eng.
President, InvestorsFriend Inc.
February 15, 2006

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