Question

Old Quartz Gold Mining Company is expected to pay a dividend of $8 in the coming year. Dividends are expected to decline at the rate of 3% per year (negative growth rate). The risk-free rate is 6% and the market risk premium is 8%. The stock of Old Quartz Gold Mining Company has beta of 0.25. The intrinsic value of the stock is

	A.	$163.33
	B.	$81.33
	C.	$133.33
	D.	$72.73

Answer 1

Solution:

Calculation of Required rate of return :

As per Capital Asset Pricing Model, required return of a stock is calculated using the following formula :

RS = RF + [ β * ( RM - RF ) ]

Where

RS = Required return of stock ; RF = Risk free rate of return   ; β = Beta of the stock ;

( RM – RF ) = Market risk Premium

As per the information given in the question we have

RF = 6 % = 0.06 ;    ( RM - RF ) = Market Risk Premium = 8 % = 0.08 ;   β = 0.25

RS = Required return ;

Applying the above information we have

= 6 % + ( 0.25 * 8 % )

= 6 % + 2 % = 8%

Thus the Required rate of return = 8 %

Calculation of Intrinsic value of the stock :

The Intrinsic value of a stock is calculated using the following formula:

P0 = D1 / ( ke – g )

Where

P0 =Intrinsic value of the stock    ;      D1 = Dividend per share payable in the coming year ;

g = growth rate ;    ke = Required rate of return ;

As per the information given in the question we have ;

D1 = $ 8.00 ;       g = - 3 % = - 0.03 ;    ke = 8.00 % = 0.08

Applying the above values in the formula we have

= 8 / ( 0.08 - ( - 0.03 ) )

= 8 / ( 0.08 + 0.03 )

= 8 / 0.11

= 8 / 0.035

= $ 72.727273

= $ 72.73 ( when rounded off to two decimal places )

Thus the Intrinsic value of the stock is = $ 72.73 .

The solution is option D. $ 72.73