I am reviewing this question, but I couldn’t understand when discounting the annuity back, why it is using 4 for years instead of 5? It said 5 years from now…
An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?
If you treat it as an ordinary annuity, you get the PV as of 4 years from today.
draw a timeline.
This used to confuse me too. The key is to remember that annuities pay out at the beginning of the year. Discounted cash flow calculations assume payment at the end of the year. … so when calculating like a normal cash flow, a payment at the beginning of 5 years from now is like a regular cash payout (at the end of the year) 4 years from now
thanks!
I see the problem / confusion here.
“5 years from now” is different than “in year 5”. The first one means exactly 5 periods ahead, but the second could mean at the beggining of year 5 (which is end of year 4) or end of year 5, so the problem will need to specify well.
Where is the confusion about 4 years discounted? This is because when you calculate the present value of a stream of cash flows starting at end of year 5, the PV is already at end of period 4. This is the same when you discount a payment to be received at the end of year 1, the PV is on year 0 right?. This case is the same, the PV of the cash annuity is at end of year 4, not at end of year 5 anymore. So that PV will be discounted 4 periods.
Hope this helps.
I wrote an article about using timelines that may be of some help here: http://financialexamhelp123.com/time-value-of-money-using-timelines/
I think this explained why. I wasn’t thinking that discounted cash flow assum end of the year and I also made the assumption that “annuity” here is “ordinary annuity”.