Question

An important application of the Dividend Discount Model (DDM) and the CAPM is in regulating public utilities. Suppose the State of Iowa allows MidAmerican to yield a 15% return on equity, and in return, MidAmerican would re-invest 60% of its earnings in its business operations, including improvements on natural gas infrastructure.

MidAmerican is expected to pay $6 dollar per share in dividends one year from now. Answer the following questions.

1. If the risk-free rate is 1%, market’s risk premium is 12%, and public utilities on average have of 0.8, use the CAPM to find MidAmerican’s required rate of return.

2. If MidAmerican’s cost of capital is exactly what you should find in part (a), find its P/E ratio, assuming DDM is a valid way for valuation.

Answer 1

1) Required rate of return = Risk free rate + [Beta *market risk premium]

                              = 1 + [.8 * 12]

                              = 1+ 9.6

                               = 10.6 %

2)Growth Rate =Return on equity * reinvestment rate

                = 15 * 60%

                = 9%

Price using Dividend discount model =D1/(RS-G)

                         = 6 /(.106 -.09)

                         = 6/ .016

                         = $ 375 PER SHARE

D1 =D0(1+g)

6 =D0(1+.09)

D0 = 6/1.09 =$ 5.50459 per share

Earning per share = D0/(1-reinvestment rate)

                        = 5.50459/(1-.60)

                        = 5.50459/.40

                        = $ 13.76147 per share

PE Ratio =market price per share /earning per share

           = 375 /13.76147

           = 27.25