A stock will pay a dividend of amount Y at the end of each year for...

A stock will pay a dividend of amount Y at the end of each year for the next 14 years. At the end of the 15-th year the dividend increases by 1:5% and increases by 1:5% each year thereafter. Assuming an annual e?ective interest rate of 5%, the price of this stock is 123. Determine the value ofY.

Expert Solution

Value of "Y" is 5.00

As per dividend discount model, current share price is the sum of present value of futrue dividends.

Step-1:Present value of next 14 years dividend

Present value	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.05)^-14)/0.05		i	=	5%
	=	9.90		n	=	14

Step-2:Present value of dividends after year 14

Present value	=	D14(1+g)/(Ke-g)DF14			Where,
	=	14.65			D14			=	1.00
					g			=	1.50%
					Ke			=	5%
					DF14	=	1.05^-14	=	0.505068

Step-3:Calculation of sum of present value of future dividends

Sum of present value of future dividends	=	9.90	+	14.65
	=	24.55

Step-4:Calculation of "Y"

As per dividend discount model, current share price should be $ 24.55 if Value of "Y" is 1.00.
But, as pe question current share price is 123.

So,

Value of Y	=	123	/	24.55
	=	5.01

jeff jeffy answered 3 days ago

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