Understanding and Using Present Values

One of the most valuable additions to a savers toolkit is the present value calculation. Even though it comes off as a bit scary at first, the amount of value it creates as a tool for understanding our financial position by putting the numbers right in front of us. By using the present value function, we can then start to look at how it is that our future obligations and investments impact us today.

equationsThe present value equation looks at money that we will be receiving at a later date, and tells us how much that amount of money is worth to us today. From there, we can compare the different aspects of our financial position to find out which obligation should take on a higher priority to pay off first, or which investment is worth more to us in the longer term.

To calculate the present value of a payment schedule, we need to know the number of payments that will be made/received, the number of periods in which we will receive these payments, and the interest rate under which these payments will be operating. From there, we multiply the dollar value of the payments by the inverse of the interest rate, less the interest rate multiplied by its full percentage amount, to the power of the number of periods in which we will receive/pay those payments. Don’t let the verbal explanation confuse you, it’s much simpler when you see it symbolically:

Present Value=Payments 1Interest Rate-1Interest Rate(1+Interest Rate) #Periods

If we therefore have a bond that will pay us $200 twice per year, in an environment where the interest rate is at 3%, the present value of the investment after 5 years will be as follows:

$1844.44=200 1.03-1.0015(1+.0015) 10

This equation tells us two things about the bond. Firstly, it shows us that the investment should be worth no more than $1844.44 because we could simply put those funds into a savings account to earn the same amount of returns risk free. Secondly, the equation allows us compare these funds to similar investments with longer time periods or different payment amounts. If we were to therefore be considering a number of investment opportunities, we would want to choose the opportunity that is associated with the highest present value possible, because it represents a higher dollar-value return for our portfolio.

To simplify the process of calculating present value, we can use a spreadsheet to do the hard math for us. The “FV” function in Excel will let you easily calculate, and manipulate the function to help you understand how different interest rates and payment amounts will change the present value of your investment. Just copy and paste the table below into a spreadsheet and you’re on your way.

Payment 200
Interest Rate 0.0015
#Periods 10
Present Value =PV(B2,B3,B1)

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