Question

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

Answer 1

Answer:

time-weighted   12.5%

dollar-weighted 12%

Explanation:

time-weighted:

$\sqrt{1.15 + 1.10} - 1 = 0.124722188 = 12.5$

Dollar-value

Return on dollars

$500,000 \times 1.15 \times 1.10\\ = 632,500$

$300,000 \times 1.1 = 330,000$

Present value of the return

$(632,500 + 330,000) \div (1+r)^2$

Present value of the investment:

$500,000 + 300,000 \div (1+r)$

Both this concepts should match as they work with the same weighted rate

$500,000 + 300,000 /(1+r) \times (1+r)^2 = 962,500\\500,000 (1+r)^2 + 300,000 (1+r) - 962,500 = 0$

We use cuadratic equation and solve getting a rate of 12%