Question

Sun TV Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 22% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company’s last dividend, D₀, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock?

a.              $26.57

b.              $32.69

c.              $28.97

d.              $23.39

e.              $27.37

Answer 1

Step 1: Calculation of cost of equity using Capital Asset Pricing Model

Using Capital Asset Pricing Model

Cost of Equity Ke = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 3%

b – Beta = 1.20

Rm – Expected return on market portfolio

Rm-Rf – Market risk premium = 5.50%

Cost of Equity Ke = 3+1.2*5.5

= 3+6.6

= 9.60%

Step 2: Calculation of share price in year 4 using Gordon Growth Model

Using Gordon Growth Model

P4 = D5 / (Ke – g)

Where,

P4 - Market price at the end of year 4 =?

D5 - Expected dividend in year 5 = 1.25*1.22^4 = 2.7691682

Ke – Cost of equity = 9.6%

G – Growth rate in dividend = 0%

P4 = 2.7691682/.096

= $28.85

Step 3: Computing current share price by discounting the cashflow at required return

Year	Dividend	[email protected]%	Present Value (Cashflow*PVF)
1	1.53(1.25*1.22)	0.912	1.39
2	1.86(1.25*1.22^2)	0.832	1.55
3	2.27(1.25*1.22^3)	0.760	1.72
4	31.62(1.25*1.22^4628.85)	0.693	21.91

current share price = Cashflow*PVF

= 1.39+1.55+1.72+21.91

= $26.57

You can use the equation 1/(1+i)^n to find PVF using calculator