Tom decides to begin investing some portion of his annual bonus, beginning this year with $6,000. in the first year he earns a 8% return and adds $3,000 to his investment. in the second his portfolio loses 4% but, sticking to his plan, he adds $1,000 to his portfolio. in this year his portfolio returns 2%. what is tom's dollar-weighted average return on his investments?

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%

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