Chiptech, Inc., is an established computer chip firm with several profitable existing products as well as some promising new products in development. The company earned $1 a share last year, and just paid out a dividend of $.50 per share. Investors believe the company plans to maintain its dividend payout ratio at 50%. ROE equals 20%. Everyone in the market expects this situation to persist indefinitely.

a. What is the market price of Chiptech stock? The required return for the computer chip industry is 15%, and the company has just gone ex-dividend (i.e., the next dividend will be paid a year from now, at t = 1).

b. Suppose you discover that Chiptech's competitor has developed a new chip that will eliminate Chiptech's current technological advantage in this market. This new product, which will be ready to come to the market in 2 years, will force Chiptech to reduce the prices of its chips to remain competitive. This will decrease ROE to 15%, and, because of falling demand for its product, Chiptech will decrease the plowback ratio to .40. The plowback ratio (and ROE) will be decreased at the end of the second year, at t = 2: The annual year-end dividend for the second year (paid at t = 2) will be 60% of that year's earnings. What is your estimate of Chiptech's intrinsic value per share?

For question b, in your anwsers you find the dividend paid in period 2 and 3 by multiplying the previous dividend by the growth rate to help solve the problem. But when you times the EPS by the payout ratio you don't get the same value as your anwsers.

For example for period 2: you get the dividend to be paid as $0.605, which is not 60% of the EPS (60% is the payout ratio)

I am curious which method is best to use, Because I would have though using the payout ratio on the EPS would be more accurate, but that isn't how your anwsers are done.