Question

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 $1.20 a share last year, and just paid out a dividend of $0.24 per share. Investors believe the company plans to maintain its dividend payout ratio at 20%. ROE equals 22%. 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 answers to 2 decimal places.)

The market price of Chiptech stock

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 0.7. 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 30% 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.)

At time 2
At time 0

c. No one else in the market perceives the threat to Chiptech’s market. In fact, you are confident that no one else will become aware of the change in Chiptech’s competitive status until the competitor firm publicly announces its discovery near the end of year 2. What will be the rate of return on Chiptech stock in the coming year (i.e., between t = 0 and t = 1)? (Hint for parts c through e: Pay attention to when the market catches on to the new situation. A table of dividends and market prices over time might help.) (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Rate of return____%

d. What will be the rate of return on Chiptech stock in the second year (between t = 1 and t = 2)? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Rate of return____%

e. What will be the rate of return on Chiptech stock in the third year (between t = 2 and t = 3)? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Rate of return____%

Answer 1

a) Constant growth rate(g) = plowback ratio * ROE = (1-dividend payout ratio)*ROE = (1-0.2)*22% =17.6%

Dividend next year = D1 = D0*(1+g) = 0.24*(1+0.176) = $0.28224

Price of stock today (as per Gordon's constant growth model)

P0= D1/(required rate -g) = 0.28224/(0.18-0.176)= $70.56

b) New growth rate after t=2 will be = 18%*0.7 = 12.6%

So, the Earnings and Dividends in various years are as follows

	Earnings	Dividends
0	1.2	0.24
1	1.4112	0.28224
2	1.659571	0.497871
3	1.868677	0.560603

So, price of stock at t=2

P2 = D3/(r-g) = 0.560603/(0.18-0.126) =$10.3815

So, price of Stock at t=0

P0= D1/(1+r)+D2/(1+r)^2+P2/(1+r)^2

=0.28224/1.18+0.497871/1.18^2+10.3815/1.18^2

=$8.05

c) If the threat is not discovered by the market

P1= D2/(r-g) =D0*(1+g)^2/(r-g) = 0.24*1.176^2/(0.18-0.176) = $82.98

Return in 1st year = (Price at end of year+ Dividend - Price at beginning of year)/price at beginning of year

= (P1+D1-P0)/P0

=(82.98+ 0.28224-70.56)/70.56

=18% which is the same as the required rate of return from the firm

d) At the end of the year, the discovery is made and the price is $10.3815

Now, Return of the stock in 2nd year= (P2+D2-P1)/P1 = (10.3815+0.497871-82.98)/82.98 = -86.89%

e) Price of stock at end of year 3

P3= D4/(r-g) = D3*1.126/(0.18-0.126) = 0.560603*1.126/(0.18-0.126) = $11.6896

Return of stock in 3rd year = (P3+D3-P2)/P2 = (11.6896+0.560603-10.3815)/10.3815 = 18%