Question

RIO's company's ordinary shares are expected to pay $2.6 per share in dividends for 6 years and after which the dividends are expected to grow 2.1% annually forever. Company ABC's shares have a beta of 1.4. The long-term return of ASX200 is 9.3% and the market risk premium is 4%

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 = 10.90%

b. Implied Price Per Share = $ 27.245245

Calculation :-

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

where,

b = beta ( i.e 1.40 )

Rm = Market return ( i.e. 9 .30% )

(Rm - Rf ) = Market premium ( i.e 4 % )

Rf = Risk free return

9.30% - Rf = 4%

Rf = 5.30%

Expected Return = 5.30% + 1.40 ( 9.30% - 5.30% )

= 5.30% + 1.40 ( 4% )

= 5.30% + 5.60 %

= 10.90%

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 + D​​​​​​4 / ( 1 + ke)4 + D​​​​​5 / ( 1 + ke )5 + D​​​​​​6​​​ / ( 1+ ke )6 +  P​​​​​6 / ( 1 + ke )6

where,

D1,2,3,4,5,6 are dividend of year 1,2,3,4,5 & 6th year

ke is RIOs expected return

g is growth rate

P​​​​​​6 is Price at year 6, which is calculated as [ D​​7​* (1 + g) ] / [ ke - g ]

So P​​6 = [ 2.60 * ( 1 + 0.021 ) ] / [ 0.109 - 0.021 ]

= [ 2.60 * 1.021 ] / [ 0.088 ]

= 2.6546 / 0.088

= 30.166

Year	Dividend	PV factor @ 10.90%	Present Value
Year 1 ( D​​​​​​1 )	2.60	0.9017	2.34442
Year 2 ( D​​​​​​2 )	2.60	0.8131	2.11406
Year 3 ( D​​​​​​3 )	2.60	0.7332	1.90632
Year 4 ( D4)	2.60	0.6611	1.71886
Year 5 (D5)	2.60	0.5961	1.54986
Year 6 (D6)	2.60	0.5375	1.3975
Year 6 ( P​​​​​​6 )	30.166	0.5375	16.214225
		Total of Present Value	$ 27.245245

Implied Price per share is $ 27.245245