Question 7.3: Crane Sporting Goods expects to have earnings per share of $...
Crane Sporting Goods expects to have earnings per share of $6 in the coming year. Rather than reinvest these earnings and grow, the firm plans to pay out all of its earnings as a dividend. With these expectations of no growth, Crane’s current share price is $60.
Suppose Crane could cut its dividend payout rate to 75% for the foreseeable future and use the retained earnings to open new stores. The return on its investment in these stores is expected to be 12%. If we assume that the risk of these new investments is the same as the risk of its existing investments, then the firm’s equity cost of capital is unchanged. What effect would this new policy have on Crane’s stock price?
Plan
To figure out the effect of this policy on Crane’s stock price, we need to know several things. First, we need to compute its equity cost of capital. Next, we must determine Crane’s dividend and growth rate under the new policy.
Because we know that Crane currently has a growth rate of 0 (g=0), a dividend of $6, and a price of $60, we can use Eq. 7.7 to estimate r_{E} . Next, the new dividend will simply be 75% of the old dividend of $6. Finally, given a retention rate of 25% and a return on new investment of 12%, we can use Eq. 7.12 to compute the new growth rate (g). Finally, armed with the new dividend, Crane’s equity cost of capital, and its new growth rate, we can use Eq. 7.6 to compute the price of Crane’s shares if it institutes the new policy.
r_{E}=\frac{Div_{1}}{p_{0}} +g (7.7)
g = Retention Rate \times Return on New Investment (7.12)
P_{0} =\frac{Div_{1} }{r_{E}-g } (7.6)
Execute
Using Eq. 7.7 to estimate r_{E} , we have
r_{E}=\frac{Div_{1} }{P_{0} } +g=\frac{\$6}{\$60} +0\%=0.10+0In other words, to justify Crane’s stock price under its current policy, the expected return of other stocks in the market with equivalent risk must be 10%.
Next, we consider the consequences of the new policy. If Crane reduces its dividend payout rate to 75%, then from Eq. 7.8 its dividend this coming year will fall to Div_{1}=EPS_{1}\times 75\%=\$6\times 75\%=\$4.50.
\text { Div }_{t}=\underbrace{\frac{\text { Earnings }_{t}}{\text { Shares Outstanding }_{t}}}_{E P S_{t}} \times \text { Dividend Payout Rate } e_{t} (7.8)
At the same time, because the firm will now retain 25% of its earnings to invest in new stores, from Eq. 7.12 its growth rate will increase to
g = Retention Rate \times Return on New Investment =0.25\times 0.12=0.03=3\%Assuming Crane can continue to grow at this rate, we can compute its share price under the new policy using the constant dividend growth model of Eq. 7.6:
P_{0}=\frac{Div_{1}}{r_{E}-g} =\frac{\$4.50}{0.10-0.03} =\$64.29Evaluate
Crane’s share price should rise from $60 to $64.29 if the company cuts its dividend in order to increase its investment and growth. By using its earnings to invest in projects that offer a rate of return (12%) greater than its equity cost of capital (10%), Crane has created value for its shareholders.