I came across this easy question that’s messing with me based on the wording of one part of it. Any helpers?
"A client can choose between receiving 10 annual $100,000 retirement payments, starting one year from today, or receiving a lump sum today. Knowing that he can invest at a rate of 5 percent annually, he has decided to take the lump sum. What lump sum today will be equivalent to the future annual payments? "
I highlighted that last bit because that’s the part that’s tripping me up. I know that the way to solve this with the calculator would be:
N=10, I/Y=5, PMT= 100,000; CPT PV
However, because the problem asks for the lump sum today, am I not supposed to set my calculator into BGN mode? The official answer that is given for this question is $772,173.49 - the calculation based in the default END mode. Shouldn’t the answer be based on the BGN calc_: $810,782.17?_
I could have sworn that any indication of “today” in a TVM problem is meant to signal changing the END to BGN - could someone clear that up for me, please?
As S2000magician said, The PV is always the present value as of today.
However, if the first payment is made today (beginning of the period = BGN-mode) there is no need to discount that payment since it is already as present value. In contrast to a payment at the end of the period (=End-mode). Since this payment is made let’s say 12 months as of today you need to discount it to today to get the present value.
Best is to draw 2 timelines for an equal cash-flow pattern: One with the first payment today (period 0) and another with the first payment at the end of the first period (period 1). You’ll see that in the latter one you have one additional discounting period to consider.
No you still use the end mode for this. You’re trying to figure out the value of the lump sum that would theoretically make him indifferent between the two options. So, since the first payment isn’t received until a year from today, that first payment needs to be discounted a whole year to “today”.
Vast majority of cases will involved END mode. Read the time value of money chapter (Reading 6, I think). Specifically focus on the difference between ordinary annuity and annuity due.
With the case of ordinary annuity, payments will occur at the end of each period, so use END mode. With the case of annuity due, payments will occur at the beginning of each period, so use BEG mode.
In this question, the first payment is received one year from today (today is t=0). Which means that the first payment occurs at the end of the very first year (end of first year is denoted as t=1).