Answer:
Tom's dollar-weighted average return on his investments is 1.20%
Explanation:
According to the given data we have the following:
CF0 = -6,000
CF1 = -3,000
CF2 = -1,000
The above figures are the amount invested by Tom in each year and hence are cash outflows.
CF3 = amount left in the portfolio after all the gains and losses on the portfolio.
So CF3 = ((((6,000*1.08)+3,000)*0.96)+1000)*1.02
The above equation will determine the amount of cash flow at the end of the 3rd year. 1.08 = 1+8% return, 0.96 = 1-4% loss and 1.02 = 1+2% return
Thus CF3 = ((((6,000*1.08)+3,000)*0.96)+1000)*1.02 = (((6480+3000)*0.96)+1000)*1.02
= ((9480*0.96)+1000)*1.02
= (9100.8+1000)*1.02
= 10,302.82
Let the dollar weighted average return be "x".
Thus,
Initial investment = CF1/(1+x)^1 + CF2/(1+x)^2 + CF3/(1+x)^3
6000 = -3000/(1+x) - 1000/(1+x)^2 + 10302.82/(1+x)^3
Solving in excel to find the above IRR (internal rate of return) we get the value of x as 1.20% (first option)
This can be verified also:
6000 = -3000/(1+1.2%)^1 - 1000/(1+1.2%)^2 + 10302.82/(1+1.2%)^3
or 6,000 = -2964.43 - 976.43 + 9940.64
Adding all the numbers in the right hand side gives us 6,000
Therefore, Tom's dollar-weighted average return on his investments is 1.20%
