The equivalent value of a payment stream.

[joannaw]

I need help with the business math problem question:

"Ninety days ago Stella signed an agreement with Manon requiring her to make three payments of $400 plus interest 90, 150, and 210 days, respectively, from the date of the ageement. Each payment was to include interest on the $400 principal at the rate of 13.5% from the date of the ageement. Stella now wants Manon to renegotiate the agreement and accept a single payment 30 days from now, insted of the three scheduled payments. What payment should Manon require in the new agreement if money is worth 8.5%?"

Thank you in advance for your help!
Joanna
[/b]

 

[stapel]

What is the value of the current agreement? What payment now would be required to generate the same income?

Please reply showing how far you have gotten in applying the various formulas you have learned. Thank you.

Eliz.

 

[Denis]

Quite a "poorly written" problem : tell your teacher!

I can't even tell for sure who the borrower is! Make B = borrower, L = lender.
Assuming month=30 days, make the payment dates: 3, 5 and 7 months from original loan date.

L expects 3 flows:
3 months: 413.50
5 months: 422.50
7 months: 431.50
(simple interest; example at 5 months: 400 * .135/12 * 5 = 22.50)

These 3 flows are theoretically invested to earn 8.5%;
with the interest calculated the same way as in my example,
this means L expects $1,285.20 at end of month 7.
(1st flow = 425.22, 2nd flow = 428.48, 3rd flow = 431.50)

B wants to make 1 payment only, at end of month 4.
That payment must be such that with interest at 8.5% for 3 months,
it accumulates to 1285.20; so (p = payment):
p + p(.085/12 * 3) = 1285.20
p = 1258.45

That's my take on this mess; I'm sure Stapel and TK will both
see it in a different way

 

[tkhunny]

...include interest...at the rate of 13.5% from the date of the ageement.... if money is worth 8.5%?

These statements are simply inadequate. The problem statement must tell us how interest is calculated. Lacking that, the solution depends on the assumption of the solver.

Simple?
Compound? Monthly? Daily? Continuously?
Are 13.5 and 8.5 nominal annual rates? Effective rates?

It is possible you just had some discussion in class - a discussion that would give you the "right" assumption. In any case, the problem statement should provide this information. The author should fix it or the grader should be aware that there are many possible valid responses.

 

[joannaw]

\These 3 flows are theoretically invested to earn 8.5%;
with the interest calculated the same way as in my example,
this means L expects $1,285.20 at end of month 7.
(1st flow = 425.22, 2nd flow = 428.48, 3rd flow = 431.50)

Can you please explain what calculation you did to get "(1st flow = 425.22, 2nd flow = 428.48, 3rd flow = 431.50)"? thank you

 

[marcmtlca]

i agree that the question is poorly written, just make some assumptions like that th 13.5 is annual effective rate and etc... then comment on your solution that you made these assumptions due to the professor being sloppy as to the way he wrote it up. (not in those words)

 

[Denis]

Can you please explain what calculation you did to get "(1st flow = 425.22, 2nd flow = 428.48, 3rd flow = 431.50)"? thank you

L expects 3 flows:
3 months: 413.50 : 413.50 + 4 months @ 8.5% = 425.22
5 months: 422.50 : 422.50 + 2 months @ 8.5% = 428.48
7 months: 431.50 : 431.50 + 0 months @ 8.5% = 431.50