# Money- Weighted Return

An investor buys one share of stock for \$100. At the end of year one she buys three more shares at \$89 per share. At the end of year two she sells all four shares for \$98 each. The stock paid a dividend of \$1.00 per share at the end of year one and year two. What is the investor’s moneyweighted rate of return? 5.29%. 0.06%. 6.35%. ✗ A) ✗ B) ✓ C)

Explanation T = 1: Dividend from first share = +1.00 Purchase of 3 more shares = 267.00 T = 2: Dividend from four shares = +4.00 Proceeds from selling shares = +\$392.00 The moneyweighted return is the rate that solves the equation: 100.00 = 266.00 / (1 + r) + 396.00 / (1 + r) . CFO = 100; CF1 = 266; CF2 = 396; CPT → IRR = 6.35%.

Shouldn’t CF1 be 264 instead of 266 seeing it’s \$1 dividend / share?

CF_0 = (\$100), because we bought one share, so it’s a cash outflow

CF_1 = (\$89) x 3 + \$1 x 1 = (\$266), because we bought three shares and received dividends on the share that we purchased in CF_0. You don’t get dividends on shares if those dividends are distributed on the day you purchase them.

CF_2 = \$98 x 4 + \$1 x 4 = \$396, because we sold 4 shares and received dividends on each of them