Question 7.6: Titan Industries has 217 million shares outstanding and expe...

Plan

Based on the equity cost of capital of 10% and an expected earnings growth rate of 7.5%, we can compute the present value of Titan’s future payouts as a constant growth perpetuity. The only input missing here is Titan’s total payouts this year, which we can calculate as 50% of its earnings. The present value of all of Titan’s future payouts is the value of its total equity. To obtain the price of a share, we divide the total value by the number of shares outstanding (217 million).

Execute

Titan will have total payouts this year of 50% × $860 million = $430   million. Using the constant growth perpetuity formula, we have

$PV  (  Future   Total   Dividends   and   Repurchases  )  =\frac{\$430  million}{0.10-0.075} =\$17.2$  billion

This present value represents the total value of Titan’s equity (i.e., its market capitalization). To compute the share price, we divide by the current number of shares outstanding:

Evaluate

Using the total payout method, we did not need to know the firm’s split between dividends and share repurchases. To compare this method with the dividend- discount model, note that Titan will pay a dividend of 30% × ( $860 million/217 million shares) = $1.19 per share, for a dividend yield of 1.19/79.26 = 1.50%.

From Eq. 7.7, we can solve for Titan’s expected growth rates of EPS, dividend, and share price:

$r_{E}=\frac{Div_{1} }{P_{0} } +g$         (7.7)

This growth rate exceeds the 7.50% growth rate of earnings because Titan’s share count will decline over time owing to its share repurchases.$^{8}$