Question

Assume the risk-free rate is 2% and the expected rate of return on the market is 8%.

a. ABC stock is now selling for $40 per share. It will pay a dividend of $2 per share at the end of the year. Its beta is 1.4. What do you expect the stock to sell for at the end of the year?

b. Peter is buying a firm with an expected perpetual cash flow of $2,400 but is unsure of its risk. If Peter thinks the beta of the firm is 0.6, when the beta is really 1.3, how much more will he offer for the firm than it is truly worth?[Hint: Value of perpetual cash flow = CF/r]

c. A stock has an expected rate of return of 12%. What is its beta?

***Need Full Steps, THXXXX!!!***

Answer 1

a)Required return on equity = Risk free rate+ [Beta*(Market return -risk free rate)]

                                = 2 + [1.4(8-2)]

                                 = 2+ [1.4 *6]

                                 = 2 + 8.4

                                 = 10.4%

Current price = D1/(Rs-g)

     40 = 2 /(.104-g)

   (.104-g )= 2/40

   (.104-g) = .05

   g= .104 -.05

       = .054 or 5.4%

Price at end of year =P0(1+g)

                    = 40 (1+.054)

                    = 40*1.054

                   = $ 42.16 per share

b)If Beta = 1.3

Required return on equity = Risk free rate+ [Beta*(Market return -risk free rate)]

                                = 2 + [1.3(8-2)]

                                 = 2+ [1.3 *6]

                                 = 2 + 7.8

                                  = 9.8%

Value of cash flow = 2400/.098 = $ 24489.80   (rounded to 24490)

If Beta = .6

Required return on equity = Risk free rate+ [Beta*(Market return -risk free rate)]

                                = 2 + [.6(8-2)]

                                 = 2+ [.6 *6]

                                  = 2 + 3.6

                                  = 5.6%

Value of cash flow = 2400/.056 = $ 42857

Amount excess offered = 42857- 24490 = $ 18367

c)

Required return on equity = Risk free rate+ [Beta*(Market return -risk free rate)]

                     12           = 2 + [B(8-2)]

                    12 -2 = [B*6]

                     10 = 6B

                     B= 10/6

                         = 1.66667

Beta = 1.67 (rounded to 2 decimal places]