Present value with annuity

CFA Level I Quant
#1

An investment pays €300 annually for five years,n with the first payment occurring today. how is the present value (PV) of the investment discounted at a 4% annual rate is closest to €1,389?

I can find answer closed to €1,336. why is it multiplied by 1.04?

thank you!

#2

Because it’s an annuity due: the first payment occurs today.

Put your calculator in Begin mode.

1 Like
#3

It is a beginning period and not an ending period annuity.

With an ending period annuity your answer (1336) is correct.

you need to change the way your calculator is doing annuities by setting it on “BGN”

another way (that I personally prefer) is to modify the calculation.

PMT + annuity end period(N-1) = Annuity beginning period

in your example:

300 + Annuity end period (4 periods)

300 + 1089 = 1389

#4

Hey man, Try this out in your financial calculator, whilst taking into consideration the advice provided above. 1. [2nd][BGN][2nd][SET] > Puts in BGN Mode. 2. [2nd][QUIT] > Returns to Standard Calc. 3. [2nd][CLR TVM] > Clears TVM work sheet > 0. 4. 5 [N] > Five year periods > N=5. 5. 4 [I/Y] > IR > I/Y = 4%. 6. 300 [PMT] > Set payment annually to > PMT = 300. 7. CPT [PV] > Gives you the PV > 1,388.97. I hope this helps, if you need me to explain anything, let me know. Also, I posted a video in the forum for TVM financial calculations… check it out! Best, RH x

#5

Hi, if you’re using the BAII calculator switch to BGN mode by pressing 2nd BGN(PMT) button then inter the numbers as giving in the question above You get the correct answer of $1,389 /-or also you can treat the question as ordinarily annuity and add back the $300 fst payment to the answer you have got.

plugin the bellow will give the right answer: N =4,I\¥ =4 ,PMT =$-300,FV =0 ,Calculate PV then add to the answer the $300 which the investor received all ready.

I hope this helps

#6

Hi

All depend on the time of receiving cash flow.if the first CF is received today it will not be bcbg discounted.

For more informations you can have a look on my course:

https://www.udemy.com/master-corporate-finance-with-practical-exercices/?couponCode=YOUSSEF04

#7

Because it is an annuity due, you do not discount the first payment (occurring in t=0). Therefore:

  • t=0, €300 (no discounting)
  • t=1, €300/(1+4%)1 = €288
  • t=2, €300/(1+4%)2 = €277
  • t=3, €300/(1+4%)3 = €267
  • t=4, €300/(1+4%)4 = €256

If you sum it all : €300 + €288 + €277 + €267 + €256 = €1,389

If it is an ordinary annuity, you do discount the first payment (occurring in t=1). Therefore:

  • t=1, €300/(1+4%)1 = €288
  • t=2, €300/(1+4%)2 = €277
  • t=3, €300/(1+4%)3 = €267
  • t=4, €300/(1+4%)4 = €256
  • t=5, €300/(1+4%)5 = €247

If you sum it all : €288 + €277 + €267 + €256 + €247 = €1,336

#8

another way to do this quickly and simply without putting calculator in BGN mode could be

Get PV0 (at t=0 since PV is calculated one period before) for the 4 payments of €300 till Year 5
N=4
I/Y=4
PMT=300
FV=0

therefore PV= 1088.96

then add €300 (not discounted due to value today) to PV0 => €1389 approx

#9

Hi.

You could draw a time line. Consider a time line with ordinary annuity with the first payment occurring at t=1. The PV of this ordinary annuity locates at t=0.

Now consider an annuity due. With the first payment occurring at t=0, if you use the formula provided by the curriculum, you would find the PV you got locates at t=-1. So you gotta discount that to t=0.