Time is Money

The earlier post entitled What IS the Right Price ended with a question. To answer it, we need to tackle a fundamental concept in finance called Time Value of Money (TVM).

Does money make the world go round?

What it means simply is that the same number of dollars in the future is worth less than the same number of dollars today. This may appear intuitively strange, but the explanation is rather simple. Consider this: if you were given a choice between being paid $10 today or $10 in 1 year’s time, which would you prefer?

Clearly the former is preferable since having gotten the cash today, you can then use it straight away as opposed to waiting for an entire year to utilise it. You could use it to buy a pizza (or maybe not, $10 isn’t much nowadays), or pay for a movie ticket OR invest it. If you had decided to put it in a savings bank account, in 1 year’s time, you would receive $10 + (interest rate*$10). If the interest rate were 5%, you would have $10.50 in a year’s time, which certainly beats $10.

I had ended the What IS the Right Price post with this poser:

A completely trustworthy and honest man tells you, I have this wonderful machine, which would pay you $10 a year, every year, forever, but it is not free. How much would you pay for this machine? What IS the correct price for this machine?

Firstly, such a machine actually exists, except it isn’t quite a money churning machine. An example of such a financial product can be an annuity (if it pays out forever, it is called a perpetual annuity). A preferred stock also might have such a characteristic. Just to add a detail to make the question clearer, the first payout happens this year, or immediately.

Let’s say the risk free rate (RFR) of a government bond was 5%. (The current RFRs can be found at Singapore Government Securities website for Singapore government bonds and on Bloomberg for the US Government treasuries.) The $10 that would be given next year would be really worth only $10/(1+RFR)=10/(1+0.05) today. We are, in the parlance, discounting the future dollars into its present value. The following year’s $10 then needs to be discounted by (1+RFR) twice, once for each year we move into the future, i.e. 10/(1+RFR)². If we sum all the future yearly payouts discounted to its present value (PV), that would tell us the value of this annuity today:

Present value=10+10/(1+RFR)+ 10/(1+RFR)²+10/(1+RFR)³+…+10/(1+RFR)ⁿ, where n=infinity

You can work out the above in a spreadsheet or using a financial calculator using its TVM function. (The CFA program uses the Texas Instrument BA II Plus, or a HP 12C financial calculator. I use the TI one myself, and it is fantastic!).

I have done this calculation in a spreadsheet, and you would notice that as the further out in the future you get, the $10 in present value is worth less and less. By year 130, it is worth 1.76 cents. The answer here is $200.

Some finer points to note: I had used a risk free rate. Since that man, however honest he might be, is likely less credit worthy than the full faith and credit of the government, you would need to use a higher discount rate, meaning, a percentage greater than the RFR.

OK, I think that might be enough to mull over for 1 day. TVM is a very important concept for AV and I would talk about Absolute Valuation in a future post.