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#1
09-20-2012, 10:43 PM
 ChrisL Junior Member Join Date: Sep 2012 Posts: 2
Please assist me with this problem on Annuity.

Hello Finance Forums, I just started taking an introductory Financial Management course and need help understanding how to get the answer from the following question.

Quote:
 Assume that you just inherited an annuity that pays you \$10,000 per year for 10 years, with the first payment being made today. A friend of your mother offers to give you \$60,000 for the annuity. If you sell it, what rate of return would your mother's friend earn on his investment? If you think a "fair" return would be 6%, how much should you ask for the annuity?
I am trying to solve this problem using excel but I cannot figure out how to get the answers that the book provides which is (13.70%; \$78,016.92). What I do understand though is that this is an annuity due.
Any tips on how to work this out using financial functions in excel would be much appreciated

#2
09-21-2012, 08:17 AM
 ArcSine Member Join Date: Oct 2010 Location: North Carolina, USA Posts: 89
Re: Please assist me with this problem on Annuity.

The fact that it's an 'annuity due' (with the initial 10K cash flow occurring immediately) can be dealt with as follows. Not the only way, but it's pretty straightforward.

To answer the first question, the purchaser gives you 60,000 but immediately gets back 10K from the annuity. In effect, the seller is out 50K up front, but then owns 9 inflows of 10K each, beginning one year from now. Treat this, then, as the purchase of a 9-payment ordinary annuity for 50,000. So set up 10 cash flows in Excel, the first being -50,000 followed by 9 at +10,000 each. Hit that stack of numbers with Excel's IRR function and you're done.

For the second question, just use the spreadsheet's NPV function to determine the present value of 9 cash flows of 10K each, at a 6% discount rate. Disregarding the first cash flow for a moment, this would be the price you'd charge the purchaser to sell her cash flows numbers 2 through 10 (i.e., a 9-payment ordinary annuity). Then simply add \$10K to that total price, since you'd obviously charge her \$10,000 to sell her the first cash flow, given that it occurs immediately.

#3
09-24-2012, 08:49 PM
 ChrisL Junior Member Join Date: Sep 2012 Posts: 2
Re: Please assist me with this problem on Annuity.

Thank you ArcSine, you are a big help!

#4
09-24-2012, 10:40 PM
 ArcSine Member Join Date: Oct 2010 Location: North Carolina, USA Posts: 89
Re: Please assist me with this problem on Annuity.

#5
10-01-2012, 07:40 PM
 Fredy Atwater The Finance Forums Join Date: Aug 2011 Posts: 516
Re: Please assist me with this problem on Annuity.

Chris L why would you exchange 60,000.00 dollars for \$100,000.00 ?

It sounds like a good deal for the one who made you the offer.

I wouldn't sell it. You will probably spend those \$60,000.00. or will you invest the 60 k into an investment vehicle that can guarantee you at least 100k in 10 years ?

#6
10-15-2012, 04:47 AM
 AlisonMalambri Junior Member Join Date: Oct 2012 Location: york Posts: 18
Re: Please assist me with this problem on Annuity.

Annuities Practice Problems

Prepared by Pamela Peterson Drake
Congrat! You just won the \$64 million Florida lottery. Now the Surely Company is offering you \$30 million in exchange for your 20 installments on your winnings. If your opportunity cost of funds is 8%, should you agree to this deal?

Carol Calc plans on retiring on her 60th birthday. She wants to put the same amount of funds aside each year for the next twenty years -- starting next year -- so that she will be able to withdraw \$50,000 per year for twenty years once she retires, with the first withdrawal on her 61st birthday. Caol is 20 years old today. How much must she set aside each year for her retirement if she can earn 10% on her funds?

Have I got a deal for you! If you lend me \$100,000 today, I promise to pay you back in twenty-five annual installments of \$5,000, starting five years from today (that is, my first payment to you is five years from today). You can earn 6% on your investments. Will you lend me the money?

You have choice when subscribing to our magazine: you can
pay \$100 now for a four year subscription,
pay \$28 at the beginning of each year for four years, or
pay \$54 today and \$54 again two years from today.
Which is the best deal for you, the subscriber, if your opportunity cost of funds is 10%?

The Trust Worthy loan company is willing to lend you \$10,000 today if you promise to repay the loan in six monthly payments of \$2,000 each, beginning today. What is the effective annual interest rate on Trust Worthy's loan terms?

[source: educ[.]jmu[.]edu]

#7
10-15-2012, 06:06 PM
 Fredy Atwater The Finance Forums Join Date: Aug 2011 Posts: 516
Re: Please assist me with this problem on Annuity.

I wouldn't lend you the money Alison.

#8
03-17-2013, 01:51 AM
 abc201879456 Junior Member Join Date: Mar 2013 Posts: 22
Re: Please assist me with this problem on Annuity.

2 things to be considered for annuity calcualtion:

1.There are two basic types of annuities: deferred and immediate. With a deferred annuity, your money is invested for a period of time until you are ready to begin taking withdrawals, typically in retirement.
If you opt for an immediate annuity you begin to receive payments soon after you make your initial investment. For example, you might consider purchasing an immediate annuity as you approach retirement age.

The deferred annuity accumulates money while the immediate annuity pays out. Deferred annuities can also be converted into immediate annuities when the owner wants to start collecting payments.
Within these two categories, annuities can also be either fixed or variable depending on whether the payout is a fixed sum, tied to the performance of the overall market or group of investments, or a combination of the two.

2.Cash flow calculation:In calculation timelining the cash flow is important is it now or t+1(1 year afterwards).discounting the cash flow till wat time

Annuity is covered in details in CFA level 1 course

#9
05-22-2013, 06:26 PM
 Armando Junior Member Join Date: May 2013 Posts: 5
Re: Please assist me with this problem on Annuity.

I dont understand annuity either.

#10
09-16-2016, 03:26 PM
 birchtree402 Junior Member Join Date: Sep 2016 Location: Kentucky Posts: 2
Re: Please assist me with this problem on Annuity.

The bank has incentive to lend sums of money if their potential gain is high enough with respect to the opportunity cost. For a sum such as \$10,000 that would require the borrowers assets to match the amount of the loan.

So a borrower will only benefit if they have potential income. Otherwise the loan will default, and the borrowers credit rating is damaged. However, in the case of a direct loan, the borrower can begin to partially return their loan, if they don't see the potential gain assuming that they didn't spend the money upfront (tuition, car, housing).

That is, a personal loan can be consolidated in part by spending conservatively.
Returning \$2000 On a \$10,000 loan would leave the borrower with a smaller debt, and may also improve the borrowers interest rate.

That said, consolidating an annuity into a single payment is not really a smart decision because as you said, a 6% or even 10% dividend will at best equal the full payment over 10 years.

A full \$100,000 loan upfront would be a really good offer, but unless you are a millionaire, that kind on loan would be paid to the College or Real Estate.

#11
02-21-2017, 01:15 AM
 GarageDoor Junior Member Join Date: Jul 2016 Location: IL, USA Posts: 28
Re: Please assist me with this problem on Annuity.

I have dont understand Annuity.

#12
06-19-2017, 02:59 AM
 Cammi Member Join Date: May 2016 Posts: 36
Re: Please assist me with this problem on Annuity.

I dont understand annuity either.