Question

Because of a lucky breakthrough, Philadelphia Pharmaceutical’s current dividend per share of $2.00 is expected to grow at a very high 32 percent per year for the next three years and then to grow at a more normal 6 percent per year. What is the value of a Philadelphia share if the investors’ expected return is 20 percent?

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 annual dividends and expected value of share at the end of the period from where it is expected to grow at a constant rate

Expected dividend next year D1

= Current dividend x (1 + Growth)

= $2 x 1.32

= $ 2.64

Expected dividend for the second year D2

= D1 x (1 + Growth)

= $2.64 x 1.32

= $3.48

Similarly, D3

= $3.48 x 1.32

= $4.60

Expected price of the stock at the end of 3^rd year

= D4 / (Re – G)

= D3 x (1 + Growth) / (Re – G)

= $4.60 x 1.06 / (0.20 – 0.06)

= $ 34.83

Present value factor

= 1 / (1 + r) ^n

Where,

r = Required rate of return = 20% or 0.20

n = Years 1 to 3

So, PV Factor for year 2

=1 / 1.20^2

= 1 / 1.44

= 0.694444

The following table shows the calculations

Calculations	A	B	C = A x B
Year	Cash Flow	PV Factor	Present Value
1	2.64	0.833333	2.20
2	3.48	0.694444	2.42
3	4.60	0.578704	2.66
3	34.83	0.578704	20.16
		Price	27.43

So, as per above calculations, price of the stock today is $27.43