# TVM Problem Confused

An investor will receive \$365 at the end of each year for 13 years. The first payment will be received 4 years from now. Given that the interest rate is 3%, the present value of this cash flow stream is closest to: \$3,552 \$3,882 \$3,449 You Answered Incorrectly.

N = 13; PMT = \$365; I/Y = 3; CPT PV; PV = \$3,881.76

This is the value of the cash flow stream three years from now. We must discount this value back to t = 0 to compute its present value.

N = 3; I/Y = 3; FV = −\$3,881.76; CPT PV; PV = \$3,552.36

I used N=4 for the second part, as "the first payment will be received 4 years from now" Why is Wiley saying N=3?

Thanks.

It depends on how your calculator is set up.

If it’s in END mode, then the PV will be as of time t = 3 (the end of year 3 (or the beginning of year 4), as the first payment comes at the end of year 4).

If it’s in BEGIN mode, then the PV will be as of time t = 4 (at the end of year 4 (or the beginning of year 5), as the first payment comes at the beginning of year 5).

As always, your best approach is to begin by drawing a timeline. I wrote an article on the value of timelines: https://financialexamhelp123.com/time-value-of-money-using-timelines/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my site. You can get an idea of their worth by looking at free sample articles here: https://www.financialexamhelp123.com/sample-articles/.)

Here’s the more general rule that S2000 is applying to your problem:

One of the keys when solving annuity problems is to remember how present and future values line up with the payments for each type of annuity.

For an ORDINARY annuity (i.e. END mode), the present value is as of one period BEFORE the first payment, and the future value is as of THE SAME TIME as the last payment. So, if your calculator is in END mode, the PV is as of t=3.

For an ANNUITY DUE (i.e. BEGIN mode), the present value is as of THE SAME TIME as the first payment, and the future value is as ONE PERIOD AFTER the last payment. So, if your calculator is in BEGIN mode, the PV is as of t=4.

Thanks to you both. I see what you’re saying, I will just need to wrap my head around this type of problem saying “in four years from now” and thinking beginning of year 4 since I’m more comfortable in END mode.

My pleasure.

And thanks to busprof for providing useful clarification. He does that.

On this topic of begin vs end mode: I have the following query:

There is a specific practice problem in the CFAI 2017 curriculum notes under the TVM section (practice problem no. 8). In this instance, the annuity payments for university tuition are paid at the beginning of each period. The solution does not take into account that these payments are beginning of each annual period and instead these are considered end of year payments. If the BEG mode is used to calculate the initial PV ( used as FV in calculation of required payment amount) the question will be answered incorrectly.

However, there is a similar example in the Schweser notes, where annuities are paid at beginning of each period, with this solution taking into account that the annuities are paid at the beginning of each period.

Not sure which logic correct- any assistance on this one?

^ For practice problem #8 above, is there something in the wording to indicate that the valuation occurs on a date other than the date of the first payment? A timeline might help you visualize the payment stream and which annuity formula to use.

Thanks- much appreciated.

The question does not provide any other information except for the fact that the annuity payments are at the beginning of each year for the payment of university tuition. I agree with the approach followed by CFAI, where the PV of the annuities are considered an ordinary annuity and taken back to the beginning of year 17 (1st payment at beginning of year 18 (end of year 17), where the BEG mode does not have to be used.

However, Schweser follows a totally different approach, where the annuities are calculated using the BEG mode.

Obviously the best approach will be to follow CFAI, but just wanted to confirm which approach is correct?

I never had to use the BEGIN mode. With slight changes, the problem can be understood from END point of view.