Question

Nemiraja, the manager of BAV Bits Ltd, is planning to pay the shareholders Rs.10 dividends this year and want to increase it 15% per year for next five years and then 5% per annum forever. The shareholders know that the systematic risk exposure of this firm is 1.25 times that of the market. The average return of the market is 15% and the risk free rate is 5%. Please calculate the value of its share in the market.

Answer 1

Required rate of return as per capital asset pricing model is given by

Re = Rf + ( Rm – Rf ) x Beta

Where,

Re = Required rate of return

Rf = Risk free rate = 5%

Rm = Return on market = 15%

Beta = Systematic risk = 1.25

So, Re = 5 + ( 15 – 5 ) x 1.25

= 5 + 10 x 1.25

= 5 + 12.5

= 17.5% or 0.175

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

Growth rate = 15% till year 5 and 5% thereafter

D0 = Current dividend = Rs 10

D1 = Expected dividend next year = D0 x ( 1 + Growth ) = Rs 10 x 1.15 = Rs 11.50

D2 = Expected divided in year 2 = D1 x ( 1 + Growth rate ) = Rs 11.50 x 1.15 = Rs 13.22

Similarly, D3 = Rs 13.22 x 1.15 = Rs 15.21

D4 = Rs 15.21 x 1.15 = Rs 17.49

D5 = Rs 17.49 x 1.15 = Rs 20.11

After this, dividends will increase at a constant growth rate of 5%

So, we need to calculate the terminal value of all future dividends receivable at the end of year 5 at 5% growth rate

= D6 / ( Re – G)

= D5 x 1.05 / ( 0.175 – 0.05 )

= Rs 20.11 x 1.05 / (0.175 – 0.05)

= Rs 168.95

Present value factor

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

So, PV Factor for year 2 will be

= 1 / ( 1.175 ^ 2)

= 1 / 1.380625

= 0.724309

The following table shows the calculations

Calculations	A	B	C = A x B
Year	Cash Flow	PV Factor	Present Value
1	11.50	0.851064	9.79
2	13.22	0.72431	9.58
3	15.21	0.616434	9.38
4	17.49	0.524624	9.18
5	20.11	0.446489	8.98
5	168.95	0.446489	75.43
		Price	122.33

So, the price of the stock is Rs 122.33