Question

The risk-free rate is 1.58% and the market risk premium is 9.51%. A stock with a β of 1.17 just paid a dividend of $2.65. The dividend is expected to grow at 21.07% for three years and then grow at 4.98% forever. What is the value of the stock?

Round to 2 decimal places.

Answer 1

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

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

Where,

Rf – Risk free return = 1.58%

b – Beta = 1.17

Rm – Expected return on market portfolio

Rm-Rf - market risk premium = 9.51%

Cost of Equity Ke = 1.58+1.17*9.51

= 12.7067%

Step 2: Computation of market price at the end of year 3 using Gordon Growth Mdel

P3 = D4 / (Ke – g)

Where,

P3 – year 3 share price = ?

D4 – year 4 expected dividend = 2.65*1.2107^3*1.0498 = 4.9369879772

Ke – Cost of equity = 12.7067%

G – Growth rate in dividend = 4.98%

P3 = 4.9369879772/(.127067-.0498)

= 4.9369879772/0.077267

= 63.8951684057

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

Year	Dividend	[email protected]%	Present Value (Cashflow*PVF)
1	3.208355	0.887	2.85
2	3.884355399	0.787	3.06
3	68.59795749	0.698	47.91

current share price = 2.85+3.06+47.91

= $53.82