Question

Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years. The last dlividend paid was $2. The discount rate is 15% and the steady growth rate after 3 years is 4 % a. What is the capital gain in stock price from year O to year 1? (Do not round intermediate calculations. Enter your answer as a dollar amount rounded to 3 decimal places.) Capital gain b. Calculate the expected rate of return. (Do not round intermediate calculations. Round your answer to the nearest whole percent) Expected rate of return

Answer 1

1. To find the capital gain, first we need to find the price of stock at Year 1 and 2

As the formula goes: capital gain = P1- P0

Last year Dividend		2.00
growth rate		0.20
dis rate		0.15
3+ growth		0.04
	working
Div 1	Div 1= 2*(1+0.2)	2.40
Div 2	Div 2= 2.4*(1+0.2)	2.88
Div 3	Div 3= 2.88*(1+0.2)	3.46
TV	= 3.456* (1+0.04)/(0.15-0.04)	32.67
CF3	Div 3+ CF3	36.13
NPV=	=NPV(0.15,2.4,2.88,36.13)	28.02

So Price of stocl at year 0= $28.02

Working:

Dividend = last years dividend* (1+ growth rate)

after 3 years , he will receive dividend at a constant growth of 4%

so we need to find the value of dividend for infinite time

which is = next years dividend/(discount rate – growth)

next years dividend = This years dividend * (1+growth)

so = 3.456* (1+0.04)/(0.15-0.04)

This is the Price of the stock at year 0

Now, similarly we need to find the value of stock at year 1

For this we will now start with Div 2,

Last year Dividend		2.00
growth rate		0.20
dis rate		0.15
3+ growth		0.04
	working
Div 1	Div 2= 2.4*(1+0.2)	2.88
Div 2	Div 3= 2.88*(1+0.2)	3.46
TV	= 3.456* (1+0.04)/(0.15-0.04)	32.67
CF3	Div 2+ CF3	36.13
NPV=	=NPV(0.15,2.88,36.13)	₹ 29.82

So price in year 1= $29.82

So the capital gain = $29.82-28.02

= $1.80

2. Expected return = (P1-P0+D1)/P0

= (29.82-28.02+2.4)/28.02

=0.15 or 15%