Kazuo Uto is analyzing the stock of Brother Industries, Ltd$.,$ a diversified Japanese company that produces a wide variety of products. Brother distributes its products under its own name and under original$-$equipment manufacturer agreements with other companies. Uto has concluded that a multistage DDM is appropriate to value the stock of Brother Industries and the company will reach a mature stage in four years. The ROE of the company has declined from $16\mathrm{.}7$ percent in the fiscal year ending in $2004$ to $12\mathrm{.}7$ percent in the fiscal year ending in $2008.$ The dividend payout ratio has increased from $11\mathrm{.}5$ percent in $2004$ to $22\mathrm{.}3$ percent in $2008.$ Uto has estimated that in the mature phase Brother$$s ROE will be $11$ percent, which is approximately equal to estimated required return on equity. He has also estimated that the payout ratio in the mature phase will be $40$ percent, which is significantly greater than its payout ratio in $2008$ but less than the average payout of about $50$ percent for Japanese companies. With reference to the formula for the sustainable growth rate, a colleague of Uto asserts that the greater the earnings retention ratio, the greater the sustainable growth rate because g is a positive function of b$.$ The colleague argues that Brother should decrease payout ratio. Explain the flaw in that argument.

$($Select all answers which are correct$)$

Kazuo Uto is analyzing the stock of Brother Industries, Ltd$.,$ a diversified Japanese company that produces a wide variety of products. Brother distributes its products under its own name and under original$-$equipment manufacturer agreements with other companies. Uto has concluded that a multistage DDM is appropriate to value the stock of Brother Industries and the company will reach a mature stage in four years. The ROE of the company has declined from $16\mathrm{.}7$ percent in the fiscal year ending in $2004$ to $12\mathrm{.}7$ percent in the fiscal year ending in $2008.$ The dividend payout ratio has increased from $11\mathrm{.}5$ percent in $2004$ to $22\mathrm{.}3$ percent in $2008.$ Uto has estimated that in the mature phase Brother$$s ROE will be $11$ percent, which is approximately equal to estimated required return on equity. He has also estimated that the payout ratio in the mature phase will be $40$ percent, which is significantly greater than its payout ratio in $2008$ but less than the average payout of about $50$ percent for Japanese companies. With reference to the formula for the sustainable growth rate, a colleague of Uto asserts that the greater the earnings retention ratio, the greater the sustainable growth rate because g is a positive function of b$.$ The colleague argues that Brother should decrease payout ratio. Explain the flaw in that argument.

$($Select all answers which are correct$)$

If the return accruing to additional investments is lower than expected, overall ROE will be lower than expected.

If the payout ratio decreases, the retention ratio increases.

Uto should correctly compute the sustainable growth rate in the mature phase to be $4\mathrm{.}4\%$

Uto should correctly compute the sustainable growth rate in the mature phase to be $6\mathrm{.}6\%$

Based on the formula for sustainable growth rate, as the retention ratio increases, growth rate increases, holding all else constant.

Decline in ROE may lead to a lower growth rate even if the retention ratio increases.