The risk$-$free rate of return is $5\%,$ the expected rate of return on the market portfolio is $15\%,$ and the stock of Xyrong Corporation has a beta coefficient of $2\mathrm{.}4.$ Xyrong pays out $40\%$ of its earnings in dividends, and the latest earnings announced were $$8\mathrm{.}00$ per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of $20\%$ per year on all reinvested earnings forever.

a$.$ What is the intrinsic value of a share of Xyrong stock? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$.$ If the market price of a share is currently $$15,$ and you expect the market price to be equal to the intrinsic value one year from now, what is your expected $1-$year holding$-$period return on Xyrong stock? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

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 $$2\mathrm{.}60$ a share last year, and just paid out a dividend of $$1\mathrm{.}17$ per share. Investors believe the company plans to maintain its dividend payout ratio at $45\%.$ 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 $18\%,$ and the company has just gone ex$-$dividend $($i$.$e$.,$ the next dividend will be paid a year from now, at t $=1).($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

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 two years, will force Chiptech to reduce the prices of its chips to remain competitive. This will decrease ROE to $18\%,$ and, because of falling demand for its product, Chiptech will decrease the plowback ratio to $0\mathrm{.}45.$ The plowback ratio 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 $55\%$ of that year$$s earnings. What is your estimate of Chiptech$$s intrinsic value per share? $($Hint: Carefully prepare a table of Chiptech$$s earnings and dividends for each of the next three years. Pay close attention to the change in the payout ratio in t $=2.)($Round your answers to $2$ decimal places.$)$