Explanation

In the single-stage residual income model, the formula for the price-to-book (P/B) ratio is:

$\frac{P}{B} = 1 + \frac{ROE - r}{r - g}$

Where:

• P/B = 3.0
• ROE = 12% = 0.12
• r (cost of equity) = 8.5% = 0.085
• g = implied growth rate (unknown)

Rearranging the formula to solve for g:

$3.0 = 1 + \frac{0.12 - 0.085}{0.085 - g}$ $2.0 = \frac{0.035}{0.085 - g}$ $2.0(0.085 - g) = 0.035$ $0.17 - 2g = 0.035$ $2g = 0.17 - 0.035$ $2g = 0.135$ $g = 0.0675 = 6.75\%$

Therefore, the implied growth rate is 6.75%, which corresponds to option B.