Question

Arapiles Ltd paid a dividend of $1 yesterday. The firm is expected to increase this dividend by 12 percent each year for 5 years and from then onward, maintain a steady dividend increase of 4 percent. The firm's cost of equity is 14 percent.

1. What is the value of Arapiles Ltd today?                                                 

2. What capital gains yield is predicted if you buy and hold an Arapiles Ltd share for one year starting from today?
3. What capital gains yield would you predict if you bought an Arapiles share at the start of the 6^th year and sold it at the end of the 6^th year?

Answer 1

Current dividend D0 = $1

Expected Dividend at the end of year 1 = D1 = $1 *1.12 = $1.12

Expected Dividend at the end of year 2 = D2 = $1.12 *1.12 = $1.2544

Expected Dividend at the end of year 3 = D3 = $1.2544 *1.12 = $1.404928

Expected Dividend at the end of year 4 = D4 = $1.4049828 *1.12 = $1.573519

Expected Dividend at the end of year 5 = D5 = $1.573519*1.12 = $1.762342

Expected Dividend at the end of year 6 = D6 = $1.762342 *1.04 = $1.832835

Horizon value at the end of year 5 =H5 = D6/(cost of equity- Constant growth rate)

= 1.832835/(0.14-0.04) = $18.32835

a) Value of Arapiles share today = D1/1.14+D2/1.14^2+D3/1.14^3+D4/1.14^4+D5/1.14^5+H5/1.14^5

  =1.12/1.14+1.2544/1.14^2+1.404928/1.14^3+1.573519/1.14^4+1.762342/1.14^5+18.32835/1.14^5

=$14.262

b) Value of Arapiles share after one year from today

= 1.2544/1.14+1.404928/1.14^2+1.573519/1.14^3+1.762342/1.14^4+18.32835/1.14^4

=$15.13878

So, Capital gains yield = $15.13878/$14.262 -1 =0.06147 or 6.147%

c)

Value of Arapiles share at the start of the 6th year (end of 5th year)

= Horizon value at the end of 5th year

=$18.32835

Value of Arapiles share at the end of the 6th year

= Horizon value at the end of 6th year

=D7/(cost of equity- Constant growth rate)

=D6*(1+constant growth rate)/ (cost of equity- Constant growth rate)

=1.832835*1.04/(0.14-0.04)

=$19.061484

So, Capital gains yield = $19.0161484/$18.32835 -1 =0.04 or 4%