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 \(1 per share last year and just paid out a dividend of \).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 two 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 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?

( 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.)

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)? In the second year (between t = 1 and t = 2)? The third year (between t = 2 and t = 3)? ( Hint: Pay attention to when the market catches on to the new situation. A table of dividends and market prices over time might help.)

Short answer

a. $11

b. At time 2: $8.551 and at time 0: $7.493

c. 15%

Step-by-step solution

Step by Step SolutionStep 1: Given information

ROE = 20%

b = 5%

g =ROE x b = 20% x 0.5 = 10%

Calculation of market price of Chiptech stock ‘a’

P₀ = D₁ / k – g = D₀ (1 + g) / k – g

= $0.50 x 1.10 / 0.15 – 0.10

= $11

Calculation of estimate of intrinsic value per share ‘b’

Time	EPS	Dividend	Comment
0	$1.0000	0.5000
1	$11000	0.5500	g =10%, Plowback = 0.50
2	$1.2100	0.7260	EPS has grown by 10% based on last year's earning; This year's earning plowback ratio falls to 0.40 and payout ratio = 0.60
3	$1.2826	0.7696	EPS grows by (0.4)(15%) = 6% and payout ratio = 0.60

At time 2: P₂= D₃/ k – g = $0.7696 / 0.15 – 0.06 = $8.551

At time 0: V₀= $0.55 / 1.15 + $0.726 + $8.551 / (1.15)²=$7.493

Calculation of rate of return on Chiptec stock, the coming year ‘c’

P₀ = $11 and

P₁= P₀(1 + g) = $12.10 (because market believes the stock would grow at 10% every year)

P₂= $8.551 (when market knows about its competitive situation)

P₃= $8.551 x 1.06 = $9.064 (new growth rate = 6%)

Year Return

1 ($12.10 - $11) + $0.55 / $11 = 0.150 = 15%

2 ($8.551 - $12.10) + 0.726 / $12.10 = -0.223 = -.23.3%

3 ($9.064 - $8.551) + $0.7696 / $8.551 = 0.150 = 15%

This implies that in case of no special information in normal cases, the stock return k = 15%