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Selling for a lump sum or payments over time
Note: You can use any financial calculator to do this problem, but if you want the BEST, you can
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THE SCENARIO
My friend recently had the chance to sell a house they own, and they had two offers from prospective buyers.
In both situations, sales costs and commissions will be 6% of the purchase price.
Option 1: The first buyer wants to buy the house for $75,000 cash. After sales costs, my friend would walk away with $70,500.
Option 2: The second buyer wants to buy the house for $85,000. They'd pay my friend $5,000 today, and $925 per month for the next 154 months. This sort of financing is made easier by hiring a servicer, which charges $25 per month for handling the paperwork. After sales costs, my friend would have to bring $100 to the table to close the deal (yes, they'd actually have to
pay to sell their house). If you're interested, check out this
other Money Blog post that goes into this sort of sale in greater detail.
The question is: What is the return on my friend's investment if they choose Option 2? Ignore the fact that taxes exist for the purposes of this exercise.
THE SOLUTION
First things first, make sure the calculator is using 12 Payments per Year.
Also, let's rephrase the situation: my friend is going to give up $70,500 today
and also pay $100 today in order to get $900 per month (the $925 payment minus the $25 servicing fee) for 154 months.
N: 154
I/YR: (this is what I'm trying to find)
PV: -70,600 ($70,500 that's being given up, plus $100 that's paid today)
PMT: 900 ($925 gross payment, minus the $25 that the servicer takes)
FV: 0
The answer to the question is that my friend will earn 11.99% on the $70,600 they're giving up today.
It's tempting to take a pile of cash today instead of a stream of payments over time. In some cases, it's the right answer, and in some cases taking the payments makes more sense. If my friend can easily earn more than 11.99% on their money, then taking the lump-sum payment (and then investing it at that higher rate) makes more sense than taking the payments over time. If, on the other hand, my friend would take the $70,600 and invest it at less than 11.99%, then taking the payments over time has the edge. What would you do in this situation? Leave a comment below and let us know!
