As an avid business school student, you are considering a potential investment in a company that appears to be a great value.
a) The company is expected to earn a $9.50 per share at the end of this year. If the fair rate of return for this stock is 8%, what is the appropriate price per share for the stock if the company pays out all earnings as dividends?
b) If the company were to pay out half of its earnings as dividends and re-invest the remainder in the company to earn 10%, how would the value per share change?
c) Interpret the difference between your answers to part (a) and (b).
d) If the value of 10% in part (b) were only 6%, how would your answer to part (c) change?
a) The company is expected to earn a $9.50 per share at the end of this year. If the fair rate of return for this stock is 8%, what is the appropriate price per share for the stock if the company pays out all earnings as dividends?
Answer : $118.75
Working notes
Use no growth formula,
price = $9.50 / 8%
= $118.75
- b) If the company were to pay out half of its earnings as dividends and re-invest the remainder in the company to earn 10%, how would the value per share change?
Answer: Value $158.33
Working notes
.g = ROE
´b
= 10%
´.5
= 5%$9.50
´0.50 / (8% – 5%)
= $158.33
- c) Interpret the difference between your answers to part (a) and (b).
Answer: $ 39.58
Working notes
The difference in your answers to parts a. and b. is called the PVGO. It represents the valuethat the firm creates by reinvesting earnings in future growth opportunities.
PVGO
= $158.33 – $118.75
= $39.58
- d) If the value of 10% in part (b) were only 6%, how would your answer to part (c) change?
Answer: – $23.75
Working notes
If the value of 10 percent in part b. were reduced to 6 percent, the firm would actually have anegative PVGO, representing a reduction in firm value due to reinvestment of past earnings.In this latter case
PVGO
= $9.50
´0.50 / (8% – 0.06´.50) – $118.75
= $95.00 – $118.75
= – $23.75
