Question

​RIO's ​ company’s ordinary shares are expected to pay​ $2.22 per share in dividends for 3 years and after which the dividends are expected to grow at 1.9% annually forever. Company​ ABC's shares have a beta of 1.41. The​ long-term return of ASX200 is 9​% and the market risk premium is 5​%.

a.What is the expected return of​ RIO’s shares according to the​ CAPM?

b.What is the implied price per​ share?

Answer 1

Answer :-

a. Expected Return = 11%

b. Implied Price Per Share = $ 23.60

Calculation :-

a. Expected return as per CAPM = Rf + b ( Rm - Rf )

where,

b = beta ( i.e 1.40 )

Rm = Market return ( i.e. 9 % )

(Rm - Rf ) = Market premium ( i.e 5 % )

Rf = Risk free return

9% - Rf = 5%

Rf = 4%

Expected Return = 4% + 1.40 ( 9% - 4% )

= 4% + 1.40 ( 5% )

= 4% + 7%

= 11%

b. Calculation of Implied Price Per Share :-

Implied price per share = D​​​​​​1 / ( 1 + ke)1 + D​​​​​2 / ( 1 + ke )2 + D​​​​​​3​​​ / ( 1+ ke )3 + P​​​​​3 / ( 1 + ke )3

where,

D1,2,3 are dividend of year 1,2 & 3

ke is RIOs expected return

g is growth rate

P​​​​​​3 is Price at year 3, which is calculated as [ D​​3​​​​​ * (1 + g) ] / [ ke - g ]

So P​​​​​​​​​​​​​​​​3 = [ 2.22 * ( 1 + 0.019 ) ] / [ 0.11 - 0.0019 ]

= [ 2.22 * 1.019 ] / [ 0.091 ]

= 2.26218 / 0.091

= 24.859

Year	Dividend	PV factor @ 11%	Present Value
Year 1 ( D​​​​​​1 )	2.22	0.9009	2.00
Year 2 ( D​​​​​​2 )	2.22	0.8116	1.80
Year 3 ( D​​​​​​3 )	2.22	0.7312	1.62
Year 3 ( P​​​​​​3 )	24.859	0.7312	18.18
		Total of Present Value	$ 23.6

Implied Price per share is $ 23.60