Question

The risk-free rate is 8%, the expected return on the market portfolio is 15%, and the stock of Hudson Corp. has a beta of 1.2. Hudson pays 40% of its earnings as dividends. The earnings next year are expected to be $12 per share. You expect Hudson to earn an ROE of 20%.

A. What is the value of Hudson Corp. stock?

B. What is the present value of growth opportunities?

C. What is the P/E ratio of Hudson Corp.?

Answer 1

Solution :-

a) calculation of the price of Hudson Corp. stock

          Price of the stock =DPS/(Ke-g)

          where,

          DPS=Dividend per share at y1

          Ke= Required return from the share or cost of equity

          g=growth

Note1:- Since growth is not given we have to calculate growth

          Growth =Retention ratio×ROE

                      =0.60*20%

                   =12%

Note2:- Calculation of required return

          AS per CAPM, Required return=Rf+?(Rm-Rf)

                                                    =8%+1.20(15%-8%)

                                                   =16.40%

Hence value of the stock =DPS/(Ke-g)

                                      =(EPS×dividend payout ratio)/(Ke-g)

                                      =($12×0.40)/(16.40%-12%)

                                      =$4.80/4,4%

                                      =$109.10

b) Present value of growth opportunities

            =value of share with growth -value of share without growth

            =$109.10(calculated above)-(EPS/Ke)

            =$109.10-($12/16.40%)

            =$35.93

c) P/E ratio= Market price per share/Earning per share

                        =$109.10/$12