Computer stocks currently provide an expected rate of return of 15%. MBI, a larg
ID: 2776119 • Letter: C
Question
Computer stocks currently provide an expected rate of return of 15%. MBI, a large computer company, will pay a year-end dividend of $3 per share. If the stock is selling at $50 per share, what must be the market's expectation of the growth rate of MBI dividends? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
If dividend growth forecasts for MBI are revised downward to 5% per year, what will be the price of the MBI stock? (Round your answer to 2 decimal places.)
What (qualitatively) will happen to the company's price–earnings ratio?
a.Computer stocks currently provide an expected rate of return of 15%. MBI, a large computer company, will pay a year-end dividend of $3 per share. If the stock is selling at $50 per share, what must be the market's expectation of the growth rate of MBI dividends? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Explanation / Answer
a) Using the Gordon Growth Model
Price of the stock = D1/(ke - g)
where, D1=expected dividend next year
ke = expected return on the stock
g = forecasted growth rate
50 = 3 / (15% - g)
15% - g = 3/50
g = 15% - 3/50 = 15% - 6% = 9.00%
Thus, market's expectation of the growth rate of MBI dividends must be 9.00%
b1)Forecasted growth rate = 5%
Using Gordon Growth Model
Price of the stock = D1/(ke - g) = 3/ (15% - 5%) = 3/10% = $30.00
If dividend growth forecasts for MBI are revised downward to 5% per year, the price of the MBI stock will be $30.00
b2) Leading PE ratio = P/E1 = (1 - b) /(ke - g)
where E1 is the next year's earnings
b = retention ratio
1 - b = dividend payout ratio
ke = expected return on the stock
g = forecasted growth rate
If g decreases, then the value of denominator (ke - g) will increase and the P/E1 ratio will decrease.
Trailing PE ratio = P/E0 = [(1 - b) * (1+g)] /(ke - g)
where E0 is the previous year's earnings
Now, if g decreases then the value of denominator will increase and the value of numerator will decrease (as (1 + g) will decrease). Thus, the value of trailing PE ratio (P/E0) will also decrease.
Hence, if the forecasted growth rate decreases, the company's price–earnings ratio decreases.
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