Twitter pays a dividend of $1. Its dividend is expected to grow by 10% for the...

Twitter pays a dividend of $1. Its dividend is expected to grow by 10% for the next 5 years. Its expected return is going to be 7% for the next 5 years. Thereafter, its dividend will grow by 5% and its expected return will be 10%. What is its price today? Show all calculations.

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Expert Solution

	Required rate=	10.00%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	1	10.00%	1.1		1.1	1.1	1
2	1.1	10.00%	1.21		1.21	1.21	1
3	1.21	10.00%	1.331		1.331	1.331	1
4	1.331	10.00%	1.4641		1.4641	1.4641	1
5	1.4641	10.00%	1.61051		1.61051	1.61051	1
6	1.61051	7.00%	1.7232457		1.7232457	1.771561	0.97
7	1.7232457	7.00%	1.843872899		1.843872899	1.9487171	0.9462
8	1.843872899	7.00%	1.972944002		1.972944002	2.14358881	0.92039
9	1.972944002	7.00%	2.111050082		2.111050082	2.357947691	0.89529
10	2.111050082	7.00%	2.258823588	47.435	49.69382359	2.59374246	19.15912
	Long term growth rate (given)=	5.00%			*Value of Stock =*	*Sum of discounted value =*	27.89

Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year

Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 10 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor

Price = current dividend*(1+year 1 growth rate)/(1+required rate)+ current dividend*(1+year 1 growth rate)^2/(1+required rate)^2+ current dividend*(1+year 1 growth rate)^3/(1+required rate)^3+ current dividend*(1+year 1 growth rate)^4/(1+required rate)^4 current dividend*(1+year 1 growth rate)^5/(1+required rate)^5+ current dividend*(1+year 1 growth rate)^5*(1+year 6growth rate)/(1+required rate)^6+ current dividend*(1+year 1 growth rate)^5*(1+year 6growth rate)^2/(1+required rate)^7+ current dividend*(1+year 1 growth rate)^5*(1+year 6growth rate)^3/(1+required rate)^8+ current dividend*(1+year 1 growth rate)^5*(1+year 6growth rate)^4/(1+required rate)^9+ current dividend*(1+year 1 growth rate)^5*(1+year 6growth rate)^10/(1+required rate)^10+ current dividend*(1+year 1 growth rate)^5*(1+year 6growth rate)^10/(1+required rate)^10*(1+long term growth rate)/(required rate-long term growth rate)

=1*(1+0.1)/(1+0.1)+ 1*(1+0.1)^2/(1+0.1)^2+ 1*(1+0.1)^3/(1+0.1)^3+ 1*(1+0.1)^4/(1+0.1)^4+ 1*(1+0.1)^5/(1+0.1)^5+ 1*(1+0.1)^5*(1+0.07)/(1+0.1)^6+1*(1+0.1)^5*(1+0.07)^2/(1+0.1)^7+1*(1+0.1)^5*(1+0.07)^3/(1+0.1)^8+1*(1+0.1)^5*(1+0.07)^4/(1+0.1)^9+1*(1+0.1)^5*(1+0.07)^5/(1+0.1)^10+1*(1+0.1)^5*(1+0.07)^5/(1+0.1)^10*(1+0.05)/(0.1-0.05)

=27.89

jeff jeffy answered 3 days ago

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