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%
-25+5/r = 0 r=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…
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.
8.333/25 = 33%. CP
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
nice post, dreary
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%
33.3% in my opinion Milos
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
33,333-25,000/25,000=33.33%
20%