Tuesday, May 27, 2008

A sometime series: Valuing securities (this time by using discounted cash flow)

A friend offers to sell you a dollar bill right now. How much should you pay for it today? Assuming there's nothing special about the bill, such as it being a rare silver certificate from the 1930s, offering anything other than the $1.00 face value seems absurd, doesn’t it?

But suppose your friend offers to give you a dollar bill exactly one year from now in exchange for a cash payment from you today. How much is that future dollar worth today? If you pay face value today you're likely overpaying, since there's opportunity cost associated with the dollar you currently have. At the very least, that buck could be earning interest in at a bank account somewhere. Plus, inflation may eat away at its purchasing power.

You estimate that the buck in your pocket will net you 5% over the next 365 days. If so, then you'll need to ‘discount’ the value of that future dollar into present day terms. By applying your estimated ‘discount rate’ of 5%, you value that future dollar as being worth 1/(1+0.05) = $0.95 today. If you pay less than $0.95 today, then this transaction should be a good deal for you. If you offer more than 95 cents today, then you're better off keeping that dollar in your pocket.

Let’s look at one more scenario. Your friend proposes a longer term deal. Beginning exactly one year from now, your friend will pay you one dollar on this day for each of the next 10 calendar years.

Assuming the same 5% discount rate you employed earlier, how much is this stream of future dollars worth today? The analytical process proceeds similar to the one you employed earlier, but there are now 10 periods to discount instead of one. The math looks like this:

1st year dollar is presently worth 1/(1+.05) = 0.95
2nd year dollar is presently worth 1/(1+.05)2 = 0.91
3rd year dollar is presently worth 1/(1+.05)3 = 0.86
4th year dollar is presently worth 1/(1+.05)4 = 0.82
5th year dollar is presently worth 1/(1+.05)5 = 0.78
6th year dollar is presently worth 1/(1+.05)6 = 0.75
7th year dollar is presently worth 1/(1+.05)7 = 0.71
8th year dollar is presently worth 1/(1+.05)8 = 0.68
9th year dollar is presently worth 1/(1+.05)9 = 0.65
10th year dollar is presently worth 1/(1+.05)10 = 0.61

Summing all those present values equals about $7.72. If you pay less than $7.72 for this future stream of cash, then you’re likely to benefit. If your friend wants more than $7.72, then you are better off not making this trade.

Note the underlying assumptions. One is that that your friend will make good on those yearly payments. If your buddy misses one or more future payout, then the future cash stream is worth less today. We’re also assuming that you estimated the correct discount rate. For example, greater declines in forecast purchasing power require higher discount rates. Applying a higher discount rate to that future cash stream will reduce its value today.

The general form of the present value formula we used above looks like this:

PV = C / (1+r)n

PV = present value of future cash payment
C = future cash payment amount
r = discount rate
n = term (number of periods)

While bonds are commonly valued using variations of the approach described above, similar 'discounted cash flow' methodology can also be useful when estimating the 'fair value' of stocks. Ever wonder what price you should pay for General Electric (GE), Pfizer (PFE), Exxon (XOM) or other equities? We’ll consider this in future missives.

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