Question

When a stock is going through a period of nonconstant growth for T periods, followed by constant growth forever, the residual income model can be modified as follows: P0 = T EPSt + Bt–1 – Bt + PT Σ (1 + k)t (1 + k)T t = 1 where PT = BT + EPST (1 + g) – BT × k k – g Al’s Infrared Sandwich Company had a book value of $16.00 at the beginning of the year, and the earnings per share for the past year were $7.65. Molly Miller, a research analyst at Miller, Moore & Associates, estimates that the book value and earnings per share will grow at 18.00 and 16.50 percent per year for the next four years, respectively. After four years, the growth rate is expected to be 6 percent. Molly believes the required return for the company is 10.40 percent. What is the value per share for Al’s Infrared Sandwich Company? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Given

Growth rate = 6%

Growth rate for EPS = 16.50%

Previous year EPS = $7.65

Now,

Current year EPS = $8.91

Beginning year Book value of share is = $16

ROE = EPS/Book value

ROE = $8.91/$16

= $0.56

Growth = (1-Dividend payout ratio)*ROE

6% = (1- Dividend payout ratio)*$0.56 ( #putting the value of ROE)

so,

Dividend payout ratio = $1.11   

where,

Dividend payout ratio = Dividend per share / Earning per share

$1.11 = Dividend per share / $8.91

Dividend per share = $9.89

Hence,

Value of share of Infrared Sandwich Company = Dividend / Book value + Growth

= $9.89/$16+6%

= $0.68