Question

Apple and Pear, Inc earned $6 EPS and paid out 60% of earnings as dividends this year. Investors are optimistic about the prospects for Apple and Pear, Inc and are forecasting that dividend would grow over the next 5 years by about 7% a year. After year 5, growth will gradually settle down to a sustainable rate as 3% a year. The require rate of return of Apple and Pear as 6%. What is the current price of Apple and Pear, Inc.? Hint: 1. Value the firm’s dividends over the period of rapid growth. 2. Estimate Apple and Pear, Inc stock price at end of year 5, when growth should have settled down. 3. Calculate the present value of Apple and Pear, Inc stock by summing the present value of dividends up to the horizon year and the present value of the stock price at the horizon. Provide a timeline and show all formulas used.

Answer 1

Answer=

Step-1: Value of firm in high growth phase=

= D0*1.07/ (1+0.06) + D1*1.07/ (1+0.06)2+ D2*1.07/ (1+0.06)3+ D3*1.07/ (1+0.06)4+ D4*1.07/ (1+0.06)5

=3.6*1.07/ (1+0.06) + 3.85*1.07/ (1+0.06)2+ 4.12*1.07/ (1+0.06)3+ 4.41*1.07/ (1+0.06)4+ 4.72*1.07/ (1+0.06)5

= 3.63+3.67+3.70+3.74+3.77

= $ 18.51

step 2 : value in constant growth phase

Value at the end of 6th year = D5*1.03/(1.06-1.03)= 5.05/0.03= $ 168.33

Value today= $ 168.33/ (1.06)6= $ 118.67

step 3 : Total value per share= Step 1+ step 2= $18.51+$118.67= 137.18