Perpetuity IRR

D

Dreary

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
An investment is purchased for $25,000 and will pay the holder $5,000 per year in perpetuity. If the required rate of return is 15%, the money-weighted return for this investment is closest to:
a. 15%
b. 33%
c. 16%
d. 20%
 
How much is the $5,000 per year in perpetuity worth today? Answer first, then consider whether that would change your answer.
 
I probably am confused about the Money weighted return and Time weighted return.
I believe MWR = IRR.
So -25 + 5 / IRR = 0
IRR = 5/25 = 20%
To calculate NPV
-25 + 5/.15 = 8.3333
 
Money weighted (also called dollar weighted) is the IRR (sensitive to cash inflows/outflows). Time weighted is the geometric rate, not sensitive to cash withdrawals or capital infusion.
Today, the perpetuity would value $33,333.33. But this is irrelevant. Make your PV=($25,000), PMTof $5,000 for (say) N = 100, that will give the I/Y=20%. And that’s the right answer. I think.
 
You’re all correct. I was just checking to make sure you’re all up and sharp on this Sunday evening. Good for you.
 
You’re mean :) But I just got back inside. What a gorgeous day in Chicago…
 
Why the complex calculations? Invest $25k, get back $5k a year ==> 20% return!
 
Good point njblain. The required rate of return is not relevant, unless you want to calculate NPV. For this problem, the key was to know that money-weighted rate is IRR.
Incidently, what’s the time-weighted return for this investment? Initially, you paid $25k and you kept on getting $5k forever.
 
I’m not sure cpk… but I think it should be 20%, just like the money-weighted return. Aren’t you earning 20% every year on your original investment?
 
I orginally got CPK 123s answer. Then I calculated it the Map1 suggested, which is how would normally solve this type of problem. It seems more intuitive that it would be 20%.
Does anybody know the answer without a doubt.
 
CPK is right the answer is 33%
5,000 / 0.15 = $33,333 <—- PV of Perpetuity
Cash Flow at 0 ($25,000)
PV of Perpetutity $33,333
Get the IRR and it’s 33.33%
Even though it is a perpetuity, you still have to wait one year to get the first payment…
 
So we seem to have a bit of a dispute here. Both answers seem reasonable.
 
No dispute on the IRR (money-weighted return), we all say it is 20%.
Question is what’s the time-weighted return? Some say 20%, some others say 33.3%
 
School of hard knocks… both time-weighted return and money-weighted return should be 20%. This is how I see it:
Since time-weighted return is not sensitive to additions and withdrawals of money, this investment does not have any additions/withdrawals anyway. So, its return should be same as IRR. But lets look at it this way:
Jan1, 2000, the investment is worth $25k, that’s what you just paid for it.
Dec 31, 2000, the investment pays $5k
Your return = 20% ($5k/$25k) - i.e., you started with $25k and now you have earned $5k and the investment is still worth $25k…if anyone wants to buy it, they pay $25k!
Jan1, 2001, the investment is still worth $25k
Dec 31, 2001, the investment pays $5k
Your return = 20% ($5k/$25k) - i.e., you started with $25k and now you have $5k and the investment is still worth $25k.
And so on, but we must assume that the investment always costs $25k.
Also, we have just calculated the holding period rates…if you keep this investment for 5 years, what’s your CAGR (compunded) rate?
 
Dreary in my opinion, if the security is correctly priced then you will have a security that has a value of 33,333.33 and still you paid only 25k. So you have P0=25,000; P1=33,333.33 and no additions/withdrawals. So, assuming one year holding period, HPY=(P1-P0)/P0 or previously calculated 33.33%. My 0.02$.
Cheers,
Milos
 
You must log in or register to reply here.
Back
Top