Question

Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $2.00 coming 3 years from today. The dividend should grow rapidly-at a rate of 23% per year-during Years 4 and 5; but after Year 5, growth should be a constant 10% per year. If the required return on Computech is 14%, what is the value of the stock today? Round your answer to the nearest cent. Do not round your intermediate calculations.

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Answer 1

present value factor = 1 /(1+r)^n

here,

r = 14%=>0.14

n= number of the year

year	cash flow	present value factor	cash flow* present value factor
3	$2	1/(1.14)^3=>0.674972	($2*0.674972)=>$1.349944
4	$2+23%=>$2.46	1/(1.14)^4=>0.592080	($2.46*0.592080)=>$1.4565168
5	$2.46+23%=>$3.0258	1/(1.14)^5=>0.519369	($3.0258*0.519369)=>$1.571507
5	$83.2095	1/(1.14)^5=>0.519369	($83.2095*0.519369)=>$43.216435
		value of the stock	$47.59.

note;

horizon value at end of year 5 = dividend of year 5*(1+growth rate) / (required return - growth rate)

=> $3.0258 *(1+0.10) /(0.14-0.10)

=>$3.0258*(1.10)/0.04

=>$83.2095