Question

The dividend for Should I, Inc., is currently $1.67 per share. It is expected to grow at 16 percent next year and then decline linearly to a perpetual rate of 4 percent beginning in four years. If you required a return of 11 percent on the stock, what is the most you would pay per share?

Answer 1

Number of years in which dividend growth rate will be 4% perpetually = 4 years

So, decline each year

= Current rate / Years of decline

= 16 / 4

= 4% each year

So, Dividend will grow at 16% for year 1, at ( 16 – 4 ) = 12% in year 2, ( 12 – 4 ) = 8% in year 3 and ( 8 – 4 ) = 4% perpetually thereafter

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 annual dividends and terminal value of dividends whose growth rate will be constant

D1 = Expected dividend next year = Current Dividend ( D0 ) x ( 1 + Growth rate )

= $1.67 x 1.16

= $1.94

Similarly,

D2 = Expected divided in year 2 = D1 x ( 1 + Growth rate )

= $1.94 x 1.12

= $2.17

Similarly, D3 = $2.17 x 1.08

= $2.34

After this, dividends will increase at a constant growth rate of 4%

So, we need to calculate the terminal value of all future dividends receivable at the end of year 3 at 4% growth rate

= D4 / ( Re – G)

Where,

Re = Required rate of return = 11% or 0.11

= $2.34 x 1.04 / ( 0.11 – 0.04 )

= $2.44 / 0.07

= $34.81

Present value factor

= 1 / ( 1 + Re ) ^ Number of years

So, PV Factor for year 2 will be

= 1 / ( 1.11 ^ 2)

= 1 / 1.2321

= 0.811622

The following table shows the calculations

Calculations	A	B	C = A x B
Year	Cash Flow	PV Factor	Present Value
1	1.94	0.900901	1.75
2	2.17	0.811622	1.76
3	2.34	0.731191	1.71
3	34.81	0.731191	25.46
		Price	30.68

So, as per above calculations, the price of the stock is $30.68