Question

Assume Gillette Corporation will pay an annual dividend of $0.62 one year from now. Analysts expect this dividend to grow at 12.9% per year thereafter until the 5th year. Thereafter, growth will level off at 1.8% per year. According to the dividend-discount model, what is the value of a share of Gillette stock if the firm's equity cost of capital is 8.3%?

The value of Gillette's stock is $________. (Round to the nearest cent.)

Answer 1

Answer-

Annual dividend after one year = D1 = $ 0.62

Dividend growth for next 5 years = 12.9 % / annum = 0.129

Growth later in perpetuity = g = 1.8 % / annum

D1 = $ 0.62

D2 = $ 0.62 x 1.129 = $ 0.699
D3 = $ 0.699 x 1.129 = $ 0.789
D4 = $ 0.789 x 1.129 = $ 0.89
D5 = $ 0.89 x 1.129 = $ 1.00

Price 5 = P5 = D6 / ( r - g)

r = 8.3 % = 0..083
g = 1.8 % = 0.018

D6 = $ 1.00 x ( 1+ 0.018)

D6 = $ 1.00 x 1.018 = $ 1.018

P5 = $ 1.018 / (0.083 - 0.018)

P5 = $ 1.018 / 0.065

P5 = $ 15.66

The value of the Gillette stock is

CF0 = 0, CF1 = $ 0.62, CF2 = $ 0.699, CF3 = $ 0.789, CF4 = $ 0.89, CF5 = $ 1 + $ 15.66 = $ 16.66

r = 8.3 %

Using the NPV concept the currect value of stock is equal to

NPV = $ 0.62 / 1.083 + $ 0.699 / 1.083² + $ 0.789 / 1.083³ + $ 0.89 / 1.083⁴ + $ 16.66 / 1.083⁵

NPV = $ 0.62 / 1.083 + $ 0.699 / 1.173 + $ 0.789 / 1.27 + $ 0.89 / 1.376 + $ 16.66 / 1.49

NPV = $ 0.572 + $ 0.596 + $ 0.621 + $ 0.647 + $ 11.18

NPV = $ 13.62

Therefore the current value of the Gillette stock is = $ 13.62