Question

A stock just paid an annual dividend of $2.7. The dividend is expected to grow by 6% per year for the next 4 years. The growth rate of dividends will then fall steadily by 0.25% per year, from 6% in year 4 to 5% in year 8 and stay at that level forever.

The required rate of return is 12%.

What is the expected dividend in 8 years?

What is the expected stock price in 8 years?

What should be the current stock price?

Answer 1

1)D4= D0(1+g)^4

       = 2.7(1+.06)^4

         = 2.7*1.26248

         = 3.40870

D5= D4(1+g)

    = 3.40870(1+ .0575)

    = 3.6047

D6 =D5(1+g)

   =3.6047(1+.055)

   = 3.8030

D7= D6(1+g)

    =3.8030 (1+.0.0525)

   = 4.0027

D8= D7 (1+g)

   = 4.0027(1+.05)

= 4.2028

**G5= 6-.25 =5.75 ,G6 = 5.75-.25= 5.5 ,G7 = 5.5-.25= 5.25 and G8 = 5.25-.25 = 5%

2)

D9= D8(1+g)

   = 4.2028(1+.05) = 4.41294

Price at year 8 =D9/(Rs-g)

         = 4.41294/(.12-.05)

       = 4.41294 /.07

        = $ 63.04 per share

3)Current price [PVF 12%,1*D1]+[PVF12%,2*D2]+......+[PVF12%,8*D8]+[PVF12%,8*Price at end of year8]

     =[.89286*2.862]+[.79719*3.0337]+[.71178*3.2157]+[.63552*3.4087]+[.56743*3.6047]+[.50663*3.803]+[.45235*4.0027]+[.40388*4.2028]+[.40388*63.04]

          

= 2.5554+ 2.4184+ 2.2889+ 2.1663+ 2.0454+ 1.9267+ 1.8106+ 1.6974+ 25.4606

= $ 42.37 per share

**find present value from table or using the formula 1/(1+i)^n