Perpetual Annuity Question

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sweetmilkcreek

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Just want to understand the logic behind why we have to use effective annual yield below:
[question removed by admin]
 
What’s the answer? I initially took a preferred stock price approach (treating 25k as a divident) then discounted that amount semiannually for four years, but arrive at a number that is close to a, but not exact.
 
The answer is b. 25,000/.0404 = 618,811. Major part is to discount using N=3 not N=4. Not too confident why it’s N=3 tho.
 
I don’t understand why it wouldn’t be four given the first disbursement isn’t for 4 years from today. Anyone have a rationale for this?
 
The answer is B) $549,487.
$618,812 is the correct amount to have in the account in 3 years, but the question is how much to have in the account today. So you discount $618,812 back to today at 2% for 6 periods:
$618,812 / (1.02)^6 = $549,487.
My mistake: the payment four years from now is at the end of year 3. It’s now fixed.
(This is what I get for not drawing a timeline. I tell you guys to draw a timeline … .)
 
S2000magician wrote:
The answer is A) $528,150.
$618,812 is the correct amount to have in the account in 4 years, but the question is how much to have in the account today. So you discount $618,812 back to today at 2% for 8 periods:
$618,812 / (1.02)^8 = $528,150.
Click to expand...
So the 4% is the BEY (rather than EAY) ?
 
This is from the a Schweser mock exam 1, morning and the answer is B (according to them). It reads:
The investor has to ensure that the amount deposited now will grow into the amount needed to fund the perpetuity. With semiannual compounding, the effective annual rate earned on the fund is (1 + .04/2)^2 - 1 = 4.04%
PV of the perpetuity is 25,000/.0404 = 618,811
Note that since the first scholarship award is paid out in four years, the PV of the perpetuity represents teh amount that must be in the account at time t = 3. We can find the required deposit from:
FV = - 618,811; N =3; I = 4.04; CPT - PV = 549,487
 
This is from the a Schweser mock exam 1, morning and the answer is B (according to them). It reads:
The investor has to ensure that the amount deposited now will grow into the amount needed to fund the perpetuity. With semiannual compounding, the effective annual rate earned on the fund is (1 + .04/2)^2 - 1 = 4.04%
PV of the perpetuity is 25,000/.0404 = 618,811
Note that since the first scholarship award is paid out in four years, the PV of the perpetuity represents teh amount that must be in the account at time t = 3. We can find the required deposit from:
FV = - 618,811; N =3; I = 4.04; CPT - PV = 549,487
Sorry, keep forgeting to hit reply.
 
alpha668 wrote:
S2000magician wrote:The answer is A) $528,150.
$618,812 is the correct amount to have in the account in 4 years, but the question is how much to have in the account today. So you discount $618,812 back to today at 2% for 8 periods:
$618,812 / (1.02)^8 = $528,150.
Click to expand...
So the 4% is the BEY (rather than EAY)?
Click to expand...
Yes. It says 4% compounded semiannually.
 
S2000, you seem to really know your stuff as I see you helping everyone out. I did some more digging and this seems to be an old question that Schweser has been recycling for a while with the answer being B, not A. Thoughts?
 
sweetmilkcreek wrote:S2000, you seem to really know your stuff as I see you helping everyone out. I did some more digging and this seems to be an old question that Schweser has been recycling for a while with the answer being B, not A. Thoughts?
Click to expand...
Yes: I’m an idiot.
I edited my reply; the answer is, indeed, B).
 
Sorry, I am really confused. Maybe because English is not my native language.
Is it that “In four years from today” means 4 years later ( t =0: today, t =1: one year later, t =2: 2 years later and t =4: 4 years later) and n =8 (copounded semiannally) ?
 
alpha668 wrote:Sorry, I am really confused. Maybe because English is not my native language.
Is it that “In four years from today” means 4 years later ( t =0: today, t =1: one year later, t =2: 2 years later and t =4: 4 years later) and n =8 (copounded semiannally)?
Click to expand...
Because it’s an ordinary perpetuity, the first payment (at the beginning of year 4/end of year 3) comes from the beginning of the period 3 value; thus, we need $618,812 in three years.
 
S2000magician wrote:
alpha668 wrote:Sorry, I am really confused. Maybe because English is not my native language.
Is it that “In four years from today” means 4 years later ( t =0: today, t =1: one year later, t =2: 2 years later and t =4: 4 years later) and n =8 (copounded semiannally)?
Click to expand...
Because it’s an ordinary perpetuity, the first payment (at the beginning of year 4/end of year 3) comes from the beginning of the period 3 value; thus, we need $618,812 in three years.
Click to expand...
OK, this is an “ordinary perpetual” ! Thank you so much !
 
S2000magician wrote:
The answer is B) $549,487.
$618,812 is the correct amount to have in the account in 3 years, but the question is how much to have in the account today. So you discount $618,812 back to today at 2% for 6 periods:
$618,812 / (1.02)^6 = $549,487.
Click to expand...
Since it’s compounded semi-annually, then shouldn’t the number periods be 7? If it’s 6 periods, then that means it’s missing out on the last half a year of compounding…
 
Still confused about the time line, the question says to be paid out in exactly 4 years from today, says nothing about beginning or end of period, so why 6 prds and not 8?
 
So here it is with a timeline and crosschecking with how perpetuity formula arrived in the first place:
0—-0.5—-1—-1.5—-2—-2.5—-3—-3.5—-4—-4.5—-5—-etc
EAY=r=4.04%, A=25000 at start of year 4
Value of cashflow at start of year 3 is =A*[1/(1+r)+1/(1+r)^2+.. inf]=A/r
Value of cashflow at start of year 0 is obtained by BEGIN mode, N=3, FV=A/r, PMT=0, which gives 549487
Solved. It’s important to draw a timeline and not warp the ordinary annuity formulas, i.e. if you use the ordinary annunity formula the value A/r is for cashflow at start of year 3- AND NOT year 4. (This is similar to P0=D1/(k-g) in stock valuation- that also follows from similar infinite series math.)
 
jondoe wrote:
So here it is with a timeline and crosschecking with how perpetuity formula arrived in the first place:
0—-0.5—-1—-1.5—-2—-2.5—-3—-3.5—-4—-4.5—-5—-etc
EAY=r=4.04%, A=25000 at start of year 4
Value of cashflow at start of year 3 is =A*[1/(1+r)+1/(1+r)^2+.. inf]=A/r
Value of cashflow at start of year 0 is obtained by BEGIN mode, N=3, FV=A/r, PMT=0, which gives 549487
Solved. It’s important to draw a timeline and not warp the ordinary annuity formulas, i.e. if you use the ordinary annunity formula the value A/r is for cashflow at start of year 3- AND NOT year 4. (This is similar to P0=D1/(k-g) in stock valuation- that also follows from similar infinite series math.)
Click to expand...
Just to ask again, since it’s semi-annual compounding and you use 3 years, doesn’t that mean that it’s missing one compounding period between year 3.5 and 4?
 
I am using EAY, please re-read my answer; the ambiguity of 3-3.5-4 versus 3-4 shouldn’t come up since I am finding P(3) itself using annuity valuation with r=EAY.
Even if you were to use semiannual compunding in the annuity, the value P(3) = A/((1+r_s)^2-1) where r_s=2% and (1+r_s)^2-1 = r i.e. EAY.
And if you were to use 7 periods, you get the same answer if you adjust the FV to P(3.5) = 611811*(1+0.02) in your BEGIN mode calculation with I/Y=2.
Thanks for the question, my mind is clearer.
 
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