Question

Assume Gillette Corporation will pay an annual dividend of $0.64 one year from now. Analysts expect this dividend to grow at 11.4% per year thereafter until the 55th year.​ Thereafter, growth will level off at 2.3% 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 7.9%​?

Answer 1

Step-1, Calculation of Dividend per share for the next 6 years

Dividend in Year 1 (D1) = $0.6400 per share

Dividend in Year 2 (D2) = $0.7130 [$0.6400 x 111.40%]

Dividend in Year 3 (D3) = $0.7942 [$0.7130 x 111.40%]

Dividend in Year 4 (D4) = $0.8848 [$0.7942 x 111.40%]

Dividend in Year 5 (D5) = $0.9856 [$0.8848 x 111.40%]

Step-2, Calculation of Stock Price for the Year 5 (P5)

Stock Price for the Year 5 = D5(1 + g) / (Ke – g)

= $0.9856(1 + 0.0230) / (0.0790 – 0.0230)

= $1.008315 / 0.0560

= $18.01 per share

Step-3, Value of the Stock

As per Dividend Discount Model, the Value of the Stock is the aggregate of the Present Value of the future dividend payments and the present value the stock price for the year 5

Year	Cash flow ($)	Present Value Factor (PVF) at 7.90%	Present Value of cash flows ($) [Cash flows x PVF]
1	0.6400	0.92678	0.59
2	0.7130	0.85893	0.61
3	0.7942	0.79604	0.63
4	0.8848	0.73776	0.65
5	0.9856	0.68374	0.67
5	18.01	0.68374	12.31
TOTAL			15.48

Therefore, Value of Gillette’s Stock is $15.48

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.