Finance Simtek currently pays a $2.50 dividend (D 0 ) per share. Next year’s div

Question

Finance

Simtek currently pays a $2.50 dividend (D 0 ) per share. Next year’s dividend is expected to be $3 per share. After next year, dividends are expected to increase at a9percentannualratefor3yearsanda6percentannualratethereafter. a. What is the current value of a share of Simtek stock to an investor who requires

a.15 percent return on his or her investment?

b. If the dividend in year 1 is expected to be $3 and the growth rate over the fol- lowing 3 years is expected to be only 7 percent and then 6 percent thereafter, what will the new stock price be?

Explanation / Answer

a.                                               4

                 Po = D1/(1 + ke) +   S [D1(1 + g1)t-1/(1 + ke)t]

                                                 t=2

                         + [D5/(ke - g2)]/[(1 + ke)4]

                 ke = .15     Do = $2.50     D1 = $3.00     g1 = .09     g2 = .06

                 Present Value of First Year Dividend

                    PV(D1) = 3.00/(1 + .15) = 3.00(PVIF.15,1)

                                = 3.00(.870) = $2.610

                 Present Value of Next 3-Years' Dividends

         Year           Dividend                  P.V. Interest Factor      Present Value

             t    Dt = 3.00(1 + .09) t-1             PVIF.15,t             Dt x PVIF.15,t

              2        3.00(1 + .09)1 =                   .756                   $2.472

                              $3.270

             3         3.00(1 + .09)2 =                   .658                    2.345

                              $3.564

           4        3.00(1 + .09)3 =                     .572                    2.222

                            $3.885

                 PV(Next 3-Years' Dividends)                                 $7.039

           Value of Stock at End of Year 4

                 D5 = D4(1 + g2) = 3.885(1 + .06) = $4.118

                 P4 = D5/(ke - g2) = 4.118/(.15 - .06) = $45.756

           Present Value of P4

                 PV(P4) = P4/(1 + ke)4 = P4 x PVIF.15,4

                             = 45.756 x .572 = $26.172

                 Value of Common Stock:

           Po = PV(D1) + PV(Next 3-Years' Dividends) + PV(P4)

                = $2.610 + $7.039 + $26.172 = $35.82 (tables)

    b.    ke = .15     Do = $2.50     D1 = $3.00     g1 = .07     g2 = .06

           Present Value of First Year Dividend

                 PV(D1) = $2.610 (same as part (a))

           Present Value of Next 3-Years' Dividends

           Year        Dividend               P.V. Interest Factor       Present Value

               t     Dt=3.00(1 + .07)t-1            PVIF.15,t                 Dt x PVIF.15,t

               2        3.00(1 + .07)1 =                     .756                       $2.427

                             $3.210

               3        3.00(1 + .07)2 =                     .658                         2.260

                             $3.435

               4        3.00(1 + .07)3 =                     .572                         2.102

                             $3.675

                 PV(Next 3-Years' Dividends)                                 $6.789

           Value of Stock at End of Year 4

                 D5 = 3.675(1 + .06) = $3.896

                 P4 = 3.896/(.15 - .06) = $43.289

           Present Value of P4

                 PV(P4) = 43.289 x .572 = $24.761

           Value of Common Stock:

                 Po = $2.610 + $6.789 + $24.761 = $34.16 (tables)

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