rate of return question (early payoff medical bills)

[hotwired]

Hi
I'm usually at least semi geeky with numbers but this one is throwing me a little... we are going to pay off some medical bills that we are currently just paying down so much per month. ($5,000 - paying $200-$300 per month no interest) - we are going to be allowed a 20% discount if we pay $4,000 now. What is my real rate of return..? At first glance I'm thinking 20%. But I'm not so sure ... I have to come up with a reasonable assumption of how many years it would take to pay off, wouldn't I? Then divide that rate of return by the number of years? (i.e. 3 years would be roughly 7% per year?)
Thanks for any help. I have a feeling I'm brain f***ing this to death!

 

[67walkon]

It's a present value question. What is the present value of a stream of payments in the amount of X for Y months, but I think you would have to assume some discount rate. In other words, how much would you pay today to receive that stream of income for whatever the term might be.

Assuming 6% interest or discount rate, the present value of $250 a month for 20 months ($5,000) is $4,746.85. If you pay $4,000 today, wouldn't you be saving $746.85, or an 11% annualized return?

 

[hotwired]

good question!

Now that's a good question and that's where my geekship has some holes in it. I'm not quite up on the concept of "present value of a stream of payments." My education stops at around the IRR 101 class. I'll work on this because it's important and might come up again in some other way. Like buying discounted mortgages, etc.

thank you for taking the time.

 

[FIRE'd@51]

It's an IRR calculation:

PV = $4,000
FV = 0
PMT = $250
N = 20 months

IRR = 2.22% per month, or 26.7% annualized

In other words, you would need to invest the $4,000 at an annual rate of return of 26.7% to generate the payment stream to retire the $5,000 debt in 20 months.

If you paid $200 per month for 25 months, you would need to earn 21.5% annual on the $4,000 to generate the required payment stream.

 

[mystang52]

IRR is the best method, but if that 21.5% required return is not convincing, how 'bout this simplistic approach. Assuming you hold on to $5000 at even 2% (not easy today), and pay $250/month from other sources:
After 20 months debt is paid off and you'll have ~$5170 in the bank.
Or, withdraw $4000, and deposit $250/month back into the account. After 20 months, you'd have ~$6275 in the bank.
No matter how you slice it, accepting that discount offer is a clear-cut winner.

 

[hotwired]

thank you

Thanks so much all of you. I need to go to the next level in my "financial analysis" skills. Take care and be well.