Tom decides to begin investing some portion of his annual bonus, beginning this year with $5,000. In the first year he earns a 10% return and adds $3,500 to his investment. In the second his portfolio loses 5% but, sticking to his plan, he adds $500 to his portfolio. In this year his portfolio returns 2%. What is Tom's dollar-weighted average return on his investments?
A) 0.34%
B) 1.02%
C) 1.54%
D) 2.23%
E) 2.58%

Question

Quizplus · Accepted Answer

The dollar-weighted return, also known as the internal rate of return (IRR), takes into account the timing and amount of cash flows into and out of the portfolio. To calculate it, we need to find the rate of return that equates the present value of cash inflows (investments made by Tom) to the present value of cash outflows (the final value of the portfolio).1. Initial investment: $5,0002. After 1 year at 10% return: $5,000 * 1.10 = $5,500   - Plus additional investment: $3,500   - Total after Year 1: $9,0003. After 2 years at -5% return: $9,000 * 0.95 = $8,550   - Plus additional investment: $500   - Total after Year 2: $9,0504. After 3 years at 2% return: $9,050 * 1.02 = $9,231To find the dollar-weighted return, we solve for the rate $r$ in the equation that equates the present value of cash outflows and inflows:$$5,000(1 + r)^3 + 3,500(1 + r)^2 + 500(1 + r)^1 = 9,231$$This is a complex equation that typically requires numerical methods to solve accurately. However, given the options provided, we can approximate or use a financial calculator to find that the closest match to the solution of this equation is a 1.02% return, which is option B. This reflects the average rate at which Tom's invested money has grown per year, taking into account the size and timing of his investments.

Tom Decides to Begin Investing Some Portion of His Annual