A pension fund that begins with $500,000 earns 15% the first year and 10% the second year. At the beginning of the second year, the sponsor contributes another $300,000. The dollar-weighted and time-weighted rates of return, respectively, were
A) 11.7% and 12.5%.
B) 12.1% and 12.5%.
C) 12.5% and 11.7%.
D) 12.5% and 12.1%.

Question

Quizplus · Accepted Answer

The dollar-weighted rate of return takes into account the timing and amount of cash flows into the fund. To calculate it, we find the internal rate of return (IRR) that equates the present value of cash inflows and outflows. The initial investment is -$500,000, the end of the first year sees no cash flow but an increase in value, at the beginning of the second year, there's an additional -$300,000 contribution, and at the end of the second year, the fund's value is the final cash inflow. The calculation is complex and typically requires a financial calculator or software, but the correct answer is given as 12.1%.The time-weighted rate of return removes the effect of cash flows and measures the compound growth rate of $1 initially invested. It is calculated by multiplying the growth factors of each period and then annualizing. For the first year, the growth factor is 1.15 (for a 15% return), and for the second year, it is 1.10 (for a 10% return). The time-weighted return is found by taking the geometric mean of these growth factors and then annualizing if necessary. The correct calculation leads to a time-weighted return of 12.5%.

A Pension Fund That Begins with $500,000 Earns 15% the First