Chapter 4, Problem 29PS

Constant-growth DCF formula The constant-growth DCF formula:

$P_0=\frac{{\text{DIV}}_1}{r-g}$

is sometimes written as:

$P_0=\frac{\text{<x-custom-btb-me data-me-id="2172" class="microExplainerHighlight">ROE</x-custom-btb-me>}(1-b)\text{BVPS}}{r-b\text{ROE}}$

where BVPS is book equity value per share, b is the plowback ratio, and ROE is the ratio of earnings per share to BVPS. Use this equation to show how the price-to-book ratio varies as ROE changes. What is price-to-book when ROE = r?