$($Related to Checkpoint $14\mathrm{.}2$ and Checkpoint $14\mathrm{.}3)($Cost of common equity$)$The common stock for the Hetterbrand Corporation sells for $$59\mathrm{.}12,$ and the last dividend paid was $$2\mathrm{.}24.$ Five years ago the firm paid $$1\mathrm{.}91$ per share, and dividends are expected to grow at the same annual rate in the future as they did over the past five years.

a$.$ What is the estimated cost of common equity to the firm using the dividend growth model?

b$.$ Hetterbrand's CFO has asked his financial analyst to estimate the firm's cost of common equity using the CAPM as a way of validating the earlier calculations. The risk$-$free rate of interest is currently $4\mathrm{.}6$ percent, the market risk premium is estimated to be $4\mathrm{.}7$ percent, and Hetterbrand's beta is $0\mathrm{.}82.$ What is your estimate of the firm's cost of common equity using this method?

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Part $1$

a$.$The estimated cost of common equity to the firm using the dividend growth model is $\%.($Round to two decimal places.$)$