Time Value of Money Part XII
What is a Perpetuity? – Getting Paid Forever
On my first time over to England, we took a little side trip from London to visit the city of Dover. This city is known for its famous white cliffs and also has a pretty cool castle overlooking the English Channel. Let’s pretend that I was walking along the Dover beach and discovered a chest that looked like it came from an old ship. At the same time, we’ll say that an archaeologist conveniently walks by and offers me $10,000 per year for the rest of my life if I give her the chest. While this all sounds awesome, we should do a couple of quick calculations to figure out how much $10,000 per year for the rest of my life is really worth to me today. In other words, we want to calculate the present value of a perpetuity. When asked “What is a Perpetuity?” I usually answer that it is payments of a set amount of money that occur on a routine basis and continues forever (pretty much like an annuity without an end date).
While I won’t live forever, I plan to be around for a while so we’ll say that it’s close to a perpetuity. Let’s also say that I could currently save at 3% in my savings account. To figure out how much the $10,000 per year is worth to us, we can use the formula below:
Value of Perpetuity = Value of Payment / Interest Rate
All we have to do for this problem is take the $10,000 per year and divide by 3%:
Value of Perpetuity = $10,000 / 3% = $10,000 / 0.03 = $333,333.33
So the steam of $10,000 per year forever is worth $333,333.33 to me today. We’ll just say that I’d accept the deal if this really happened.
One More Perpetuity Example to Try
To get a little more small business financial management practice, let’s say that you find out a good secret about your sibling and they promise to pay you $100 per year for the rest of your life to never reveal it. At the time you could save at 5% in your savings account. To figure out how much that is worth to you today (the present value), we can just divide the $100 by the interest rate 5% to calculate the present value of a perpetuity:
Value of Perpetuity = $100 / 0.05 = $2000
So really, it’s like you sibling is paying you $2000 to keep their little secret quiet.
Key Takeaway: When asked “What is a Perpetuity?” we can say that it is payments of a set amount of money that occur on a routine basis and continues forever. To calculate how much a never ending stream of payments is worth to us today, we can take the value of each payment divided by the interest rate we could get over that period.