Apple has just paid an annual dividend of $3.5. Dividends are expected to grow by 22%...

Apple has just paid an annual dividend of $3.5. Dividends are expected to grow by 22% per year for the next 4 years, and then grow by 14% thereafter. Apple has an annual required return of 31%.

a) What is the value of the expected dividends in four years?

b) What is the intrinsic value in the fourth year (V4)?

c) What is the value of the stock now (V0)?

Solutions

Expert Solution

a) The value of the expected dividends in four years = Current Dividend * ( 1+ Growth Rate) ^ Time

= $ 3.5 * ( 1+ 22/100) ^ 4

= $ 7.75367096

Hence the correct answer is $ 7.75

b) Intrinsic value in the fourth year (V4) = Expected Dividend in Year 5 / ( Required Rate of Return - Growth Rate)

= ($ 7.75367096 * 114%) / ( 31% -14%)

= $ 51.99521

= $ 52.00

Hence the correct answer is $ 52.00

c) The value of the stock now (V0) = Present value of Dividends + (Intrinsic value in the fourth year (V4) * Discounting Factor at 31% in the 4th Year)

= 11.7550231702779 +( 51.99521* 0.339558664941034)

= $ 29.41

Hence the correct answer is $ 29.41

Note:

`	Dividend	Discounting Factor (31%)	Present Value ( Dividend * Discounting factor)
0	3.5000
1	4.27	0.7633587786259540	3.2595419847328200
2	5.2094	0.5827166249053090	3.0356039857817100
3	6.355468	0.4448218510727550	2.8270510401936600
4	7.75367096	0.3395586649410340	2.6328261595696600





Present Value of Dividends			11.755023170277900

jeff jeffy answered 9 months ago

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