Question 7.1: Suppose you expect Longs Drug Stores to pay an annual divide...
Suppose you expect Longs Drug Stores to pay an annual dividend of $0.56 per share in the coming year and to trade for $45.50 per share at the end of the year. If investments with equivalent risk to Longs’ stock have an expected return of 6.80%, what is the most you would pay today for Longs’ stock? What dividend yield and capital gain rate would you expect at this price?
Plan
We can use Eq. 7.1 to solve for the beginning price we would pay now (P_{0}) given our expectations about dividends (Div_{1} = \$0.56) and future price (P_{1} = \$45.50) and the return we need to expect to earn to be willing to invest (r_{E} = 0.068). We can then use Eq. 7.2 to calculate the dividend yield and capital gain rate.
P_{0}=\frac{Div_{1}+P_{1} }{1+r_{E} } (7.1)
r_{E}=\frac{Div_{1} +P_{1} }{P_{0} } -1=\frac{Div_{1} }{P_{0} } +\frac{P_{1}-P_{0} }{P_{0} } (7.2)
Execute
Using Eq. 7.1, we have
P_{0} =\frac{Div_{1}+P_{1} }{1+r_{E}} =\frac{\$0.56+\$45.50}{1.0680} =\$43.13Referring to Eq. 7.2, we see that at this price, Longs’ dividend yield is Div_{1}/P_{0} = 0.56/43.13 = 1.30\%. The expected capital gain is $45.50 – $43.13 = $2.37 per share, for a capital gain rate of 2.37/43.13 = 5.50%.
Evaluate
At a price of $43.13, Longs’ expected total return is 1.30% + 5.50% = 6.80%, which is equal to its equity cost of capital (the return being paid by investments with equivalent risk to Longs’). This amount is the most we would be willing to pay for Longs’ stock. If we paid more, our expected return would be less than 6.8% and we would rather invest elsewhere.