Question

Assume Gillette Corporation will pay an annual dividend of $ 0.66 one year from now. Analysts expect this dividend to grow at 11.3 % per year thereafter until the 4th year.​ Thereafter, growth will level off at 1.7 % 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 8.7 %​?

Answer 1

Price of a stock is the present value of all future cash flows receivable from the stock discounted at required rate of return

Future cash flows are expected dividends and expected share price

D1 = Expected dividend next year = $0.66

D2 = D1 x (1 + Growth)

= $0.66 x 1.113

= $ 0.73

D3 = $0.73 x 1.113

= $0.82

D4 = $0.82 x 1.113

= $0.91

D5 = $0.91 x 1.017

= $0.93

Expected price of stock at the end of year 4

= D5 / (Re – G)

= $0.93 / (0.087 – 0.017)

= $13.22

Present value factor

= 1 / (1 + r) ^ n

So, PV Factor for year 2 will be

= 1 / (1.087^2)

= 1 / 1.181569

= 0.846332

The following table shows the calculations:

Calculations	A	B	C = A x B
Year	Cash Flow	PV Factor	Present Value
1	0.66	0.919963	0.607176
2	0.73	0.846332	0.617823
3	0.82	0.778595	0.638448
4	0.91	0.716278	0.651813
4	13.22	0.716278	9.4692
		Price	11.98

So, as per above calculations the expected price is $11.98