Simple Math to Solve Important Discount Cash Flow Problems

The Social Discount Rate (SDR) is the interest rate that can be used to do an economic study like a Cost Benefit Analysis for determining the feasibility of providing a new public good or service.

Developing countries use higher Social Discount Rates while in America; the Environmental Protection Agency and other government agencies typically uses a Discount Rate of 7 percent.

No matter what discount rate is utilized for performing an economic study, the process of discounting is actually very simple. Financiers live by the rule, "A dollar today is worth more than a dollar tomorrow.
" Looking deeper into this axiom think about the Florida Lottery System and how the installments would be paid out to a potential winner.
The following formula can be manipulated to solve for the Present Value (PV) or even the Future Value (FV) of a potential cash flow, FV=PV (1+i)n. The other variables in this formula are 'i' and 'n', which stand for interest rate and the number of terms being compounded.
For a simple example of how this formula works, simply substitute the value of '1' into the value of 'n' and for the PV as well.

Also, use the value of 0.

1 for the interest rate. The Future Value resulting from this example will be 1.
1. This means is that if $1 were invested for a period of one year at an interest rate of ten percent, the value of this investment would be $1.

10 at the end of the year. Now on the other hand, solving for the Present Value of an investment is simple as well.

Manipulating the above formula for Present Value results in, Present Value= Future Value/(1+i)n.

This time, substitute '1' for the Future Value and 'n'.

Also, use 0.10 for in the interest rate.
The result will be 0.
909. In reality, this means that the value of $1 in one year is actually worth $0.

91 dollars today.

So, say you won the Florida Lottery, and were paid $3 million to be paid out in $1 million installments for the next three years.

Also, assume that a discount rate of ten percent.

The Present Value of these cash flows would be illustrated as below if the first payment were to be paid one year from now: Year 1 = 1,000,000 /(1.1)^1= $909,090.
91 Year 2 = 1,000,000 /(1.
1)^2= $826,446.

28 Year 3 = 1,000,000 /(1.
1)^3= $751,314.
80 The Present Value of these cash flows would be illustrated as below if the first payment were to be paid now: Year 1 = 1,000,000 Year 2 = 1,000,000 /(1.
1)^1= $ 909,090.
91 Year 3 = 1,000,000 /(1.
1)^2= $ 826,446.28 The total Present Value would simply be the sum of these three payouts, which would be $2,486,851.99 if the first installment were to be paid one year after the winner was determined or $2,735,537.
19 if the first installment were to be paid now.
In other words, the Florida Lottery is actually costing lottery winners money by not paying their complete winnings upfront.