# Math Help - Present Value of Cash Streams-Rent Payment-Rate of Return

1. ## Present Value of Cash Streams-Rent Payment-Rate of Return

Hi, here is the scenario we have regarding our rent we pay for our business office.

Normally, rent is $2,300/month, paid on the 1st of the month. Our landlord has offered to give us a 7% discount if we pre-pay. That means rent is$2,139/month.

We are considering pre-paying rent for 6 months out. We plan to make that payment December 31, 2010 and it will be for the January-June (6 months) 2011 period. This would mean we pay $12,834 on December 31. What sort of calculations should we be doing to evaluate this deal? Do we want to find the rate of return? The Future Value of our pre-payment? We know getting this discount is good, but we aren't sure how good and how to properly evaluate it. Thank you! 2. You need to find the PV of 2300 for 6 periods. If the PV < 12,834, it is better to not take the discount. If the PV > 12,834, then it is a good deal. Were you given a discount rate? 3. dear dwsmith, thank you for such a fast reply. No we were not given a discount rate. By that, I am guessing you mean the interest rate we could get with another investment??? Thanks! 4. Yes. I just put in 6 periods, PV = 12,834, and PMT = 2139 to determine the rate they were using is 0.00% $\displaystyle \lim_{\mbox{interest rate}\to\ 0.00} \sum_{n=0}^{5}\frac{2300}{(1+i)^n}=13800=\mbox{PV}$ $\mbox{PV of 2300}>12,834$ 5. Wow that's awesome, how do you do those formulas and get them to display like that? And thank you so much!!!!!!!!!!!!!!!!!! 6. You type the word math between brackets [ ] then you type in latex and then enclose the latex in \math []. Helpisplaying a formula - Wikipedia, the free encyclopedia LaTeX Online Equation Editor 7. By the way, what is the formula for figuring out the rate of return? Or since we are getting a 7% discount, that IS our rate of return?? 8. I noticed something about you question when I was playing around with it last night. If we use 5 payment periods, we obtain a more realistic discount rate. I have to go to a function now but I will think about your rate of return question. 9. Code: month payment interest balance 0 12834.00 1 -2300.00 271.27 10805.27 : 12834 * .021137... = 271.27 2 -2300.00 228.39 8733.66 3 -2300.00 184.60 6618.26 4 -2300.00 139.89 4458.15 5 -2300.00 94.24 2252.39 6 -2300.00 47.61 .00 You can "look" at this as YOU lending the landlord$12,824, then the landlord
paying you back with 6 monthly payments of $2,300 (what YOU'd pay if no deal). The resulting "interest rate per month" is ~2.1137% Calculating this rate requires iteration. Take over, D.W.Smith 10. Originally Posted by dwsmith I noticed something about you question when I was playing around with it last night. If we use 5 payment periods, we obtain a more realistic discount rate. I have to go to a function now but I will think about your rate of return question. Thanks for the reply. We are pre-paying 6 months, so how would that translate to 5 payment periods? 11. This seems like a real life scenario not a question from a student. The current 1 year T-Bill is paying 0.31% I discounted back 2300 at beginning of year payments. The PV of those payments is$13,693.82

The PV of 2139 is $12,735.25 However, in order to obtain the deal, you have to pay up front and can't pay monthly. You will save 13,693.82 - 12,834 =$859.82

Or looking at FV

FV 12834 is 13074

FV of 6 2300 payments 13950.51

The discount is the better deal.

12. Originally Posted by Wilmer
Code:
month  payment  interest  balance
0                       12834.00
1   -2300.00    271.27  10805.27 : 12834 * .021137... = 271.27
2   -2300.00    228.39   8733.66
3   -2300.00    184.60   6618.26
4   -2300.00    139.89   4458.15
5   -2300.00     94.24   2252.39
6   -2300.00     47.61       .00
You can "look" at this as YOU lending the landlord $12,824, then the landlord paying you back with 6 monthly payments of$2,300 (what YOU'd pay if no deal).

The resulting "interest rate per month" is ~2.1137%
Calculating this rate requires iteration.

Take over, D.W.Smith
I am not sure how you obtained your method so you are more than welcome to explain it.

I just went with what I knew.

13. Originally Posted by dwsmith
I am not sure how you obtained your method so you are more than welcome to explain it.
Not much to explain:
Lessee:
1: we know that $12,834 is paid upfront 2: we know that because of that,$2,300 monthly will not be paid for 6 months
Landlord:
1: will receive $12,834 2: will repay with 6 monthly payments of$2,300 (equivalent to not receiving these payments...);
...or, if you wish, will receive $2,300 but give it right back to the lessee as loan repayment! 14. Another way to "look" at it: Landlord sells an annuity of 6 monthly payments of$2,300 for $12,834; the$2,300 rent payments are then remitted to the purchaser.

In this case, the purchaser is the lessee.
The fact that $12,834 = 6 * .93(2300) has nothing to do with the exercise... 15. One other matter...PremiumCans, when are those monthly rent payments due? If you're paying$12,834 on or about Dec 31 to save 6 cash outflows of \$2,300 on Jan 1, Feb 1, ...., Jun 1, then your actual annualized return comes in at just south of 36% (~ 3.0 % per month).