Perpetual Annuity Question

I know you used EAY. But your final n value still used 3 years of compoundung (6 half years)
n =7, i = 2%, FV = 618,812
PV is 538,607
n = 3.5, i = 4.04%, FV = 618,812
PV = 538,607
n = 3, i = 4.04%, FV = 618,812
PV = 549,487
n = 6, i = 2%, FV = 618,812
PV = 549,487
There’s a difference. Hence, I’m wondering why the last half year is left out.
 
Again, re-read my answer. FV for N=7 case is different. it must be 611811*1.02=631188, which should lead you to the same answer.
 
Actually, frankly speaking, I didn’t quite understand what you meant by “will get the same answer if you adjust the FV to P(3.5)”. The FV is fixed from a previous calculation using a different set of numbers… The question involves working backwards from the FV.
 
inCLYNEd.Honoka wrote:
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?
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No: you’re using an EAY of 4.04%. So the amount at the beginning of year 3 earns 2% in the first 6 months, then 2% (compounded) in the second 6 months.
 
FV is not fixed - you need to adjust it. You actually move forward in this case - 611811 is P(3) using my notation. To get to P(3.5) you need to multiply by 1.02 (NOT divide) because you are going forward. Just see first if you get the answer using FV of 611811*1.02 and then try to reconstruct the argument from the timeline.
 
S2000magician wrote:
I tell you guys to draw a timeline
Click to expand...
Timeline
Yr0 – 0.5 – Yr1 – 1.5 – Yr2 – 2.5 – Yr3 – 3.5 – Yr4
X^0 – X^1 - X^2 – X^3 - X^4 – X^5 - X^6 – X^7 - FV (X = 1 + 0.02)
This is what my timeline and how I ended up with 7 periods… Is there something not right?
 
inCLYNEd.Honoka wrote:
S2000magician wrote:I tell you guys to draw a timeline
Click to expand...
Timeline
Yr0 – 0.5 – Yr1 – 1.5 – Yr2 – 2.5 – Yr3 – 3.5 – Yr4
X^0 – X^1 - X^2 – X^3 - X^4 – X^5 - X^6 – X^7 - FV (X = 1 + 0.02)
This is what my timeline and how I ended up with 7 periods… Is there something not right?
Click to expand...
Yes: payments are annual, not semiannual. You need to measure time in the same intervals as the payments. Thus, you get i = 4.04%, not i = 2%.
 
In your notation FV at X^8 IS NOT 611811. It is 611811*(1.02)^2. You have wrongly applied Annity/4.04% as the value of cashflows at the 8th period. Annuity/4.04% is the value of cashflows at 6th period, not 8th period.
 
S2000magician wrote:
Yes: payments are annual, not semiannual. You need to measure time in the same intervals as the payments. Thus, you get i = 4.04%, not i = 2%.
Click to expand...
Maybe I’m too used to my school where the saving period and payout period aren’t necessarily in the same intervals… =S
 
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