# PV, Present Value (again)

If you prefer \$95 today to \$100 a year from now, the or present value of that \$100 a year from now is \$95. This is the time preference that we all have and it is objectively calculated by using a discount rate that reflects the interest that we forgo by having to wait a whole year, or, alternatively the income we forgo by not being able to invest for a year.

In simple terms the formula is  PV= amount/ (1+ interest rate) . This can then be compounded to incorporate multiple periods and multiple amounts. We will keep it simple, in our example you are indifferent to receiving \$95 now or \$100 a year from now. Using the formula we get 95=100/1+0.05=100/1.05= 95 (not precisely).

When things get a little more complex you either do financial acrobatics or use a table.

You can make your own table on a spreadsheet if you want a wider range but for our purposes this will do. Suppose you are to receive \$1000 a year renting out an apartment for 30 years (anything else that pays a same amount will do), what is that worth today? At 12 %, \$8,055.18, at 6% \$13,764.80 and at 2% \$22,396.46. (of course at the extreme of 0% the present value is simple 30x \$1000=\$30,000.) No big revelation here except when you look at the impact interest rates have. We all know that a rising tide lifts all boats, but this much? From 12% to 2% is 2.8X and from 6% to 2% is 1.7x. Put a different way, a stock that was worth ,say \$20 in the late eighties should now be worth \$56 . If rates go back to equilibrium at, say 6%, that same stock will drop to \$33. All this courtesy the US Fed.