In: Finance
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)?
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 |