Question

We use the formula PV = FV (1/1+R)^N to calculate Present Value.

The formula is used to figure out how much a future sum is worth today, given that there is always a discount rate.

In class, we imagined a $20 million lottery win, in which the Lottery officials make the following offer: either take $1 million per year for 20 years, or accept the Present Value using a discount rate of 5%.

There is a factor that is NOT in the Present Value formula. What is it?

		A) Risk. Even if one can easily calculate the Present Value because we already know the Future Value and the Discount Rate, one still has to assess risk -- either the risk that the income stream will stop, or the risk that the discount rate is wrong, or that one will have too high an opportunity cost by waiting for the term (or by not waiting for the term).
		B) Inflation.
		C) War, social disruption, government collapse, all of which could change Future Value.
		D) War, social disruption, government collapse, any of which could change Term of Years.

Answer 1

Option (A) makes sense. We can compute PV if we know FV, number of periods and the discount rate. But, future is always uncertain. We are assuming that we can get our $1 million every year for 20 years and be able to reinvest at 5%. This is a big assumption. There are chances that we may not get the money (think what happens if there is severe recession in coming years), or we may not get 5% for next 20 years. The money you have today is always worthier than the money you will have later. Hence, mere comparing the PV with FV solely based on the discount factor and the risk is not a wise idea.

Note: If everything else is perfect and there is no uncertainty in the future, then the offer should not make any difference between accepting PV and accepting FV. Because, PV= Discounted FV, where discount rate is assumed to be a perfect rate to account for all uncertainty. But what we are ignoring is the risk of cash flow stream and change in rates in the future. We are assuming that the conditions we have today will prevail in future too. The quality of decision depends on how exactly we can predict future risks and figure-out the rate appropriate for all such risks. That is almost always a near impossible thing to predict the future exactly due the risk inherent in future.