Year Assets Under Management at the Beginning of Year (€) Net Return (%)
1 30 million 15
2 45 million -5
3 20 million 10
4 25 million 15
5 35 million 3
Thanks
Investment in t0: -30
Return in t1: 30*0.15 = 4.5 Investment in t1: 45-4.5-30 = 10.5
Return in t2: 45*-0.05 = -2.25 Investment in t2: 20+2.25 - 45 = -22.75 (apparently the investor retired this amount from his account) Return in t3: 20*0.1 = 2 Investment in t3: 25-2-20 = 3
Return in t4: 25*0.15 = 3.75 Investment in t4: 35-3.75 = 6.25
Return in t5: 35*0.03 = 1.05 Account end value : 35+1.05 = 36.05
You have the following cash flows:
t0: - 30 t1: -10.5 t2: +22.75 t3: -3 t4: -6.25 t5: +36.05
Calculating the IRR gives you approximately a MWR of 5.855%.
Regards, Oscar
Hello Oscar,
Why is it in investment t2 2.25 was added to 20 and in account end value 1.05 was added to 35?
Also in investments t1, t2, and t3 30, 45, 20 were subracted respectively while in return t4 and t5 25 and 35 were no longer subtracted?
Thank you for answering.
Anmuriel,
What you need to do is to calculate the cash flows of the investment because you are told to get the Money-weighted rate of return or IRR.
Solving in detail:
From T=0 to T=1 you have invested 30 and you got 15% rate of return from that investment, so it is a profit of 4.5, therefore at end of t=1 you have 30+4.5 = 34.5 million, but your balance says you have 45 million, what is this? The investor must added they difference, 10.5 million. That 10.5 million added are the cash flow of period 1.
At the beginning of period 2 you have 45 million to invest and you are told you will get -5% of that investment (a loss), so you lose -2.25 during period 2. Now, your balance at end of period 2 is 20 million, but how? you only lost 2.25 millions, the only way to get that number is to withdraw the difference (the investor did it), so your cash flow is 45 - 2.25 - 20 = 22.75 (an income for the investor). This amount is the cash flow at end of period 2.
The following two periods have the same logic, try to calculate them.
For the last period, at the beginning of period 5 you have 35 million assets to invest and you will get 3% return so it is a gain of 1.05 million. At the end of period 5 you will have 36.05 million which will be withdrawn by the investor (it is an income)
The resultant is:
t0: - 30 t1: -10.5 t2: +22.75 t3: -3 t4: -6.25 t5: +36.05
Oscar was right.
Note: quoting Oscar:
Return in t4: 25*0.15 = 3.75 -------- Investment in t4: 35-3.75 - 25 = 6.25, he just forgot to type the 25, but the calculation is right.
Regards