Question 8: can anyone explain the upward/downward (question b and c)? (mathemat

Question

Question 8: can anyone explain the upward/downward (question b and c)? (mathematically)

If the stock is selling at $66 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. Omit the "%" sign in your response.) If dividend growth forecasts for MBI are revised downward to 11% per year, what will happen to the price of MBI stock? What (qualitatively) will happen to the company's price-earnings ratio?

Explanation / Answer

b1) As per Constant Dividend Growth model,

P = D1/(ke - g)

where, D1 = $3.6

ke = 24%

g = 18.55% (cacluted using the equation)

P = $66

Now if the g =11% instead of 18.55%

P = D1/(ke -g)

The denominator (ke - g) will increase

Since the denominator will increase, D1/(ke -g) will reduce.

Thus, price will fall.

P = D1/(ke -g) = 3.6 / (24% - 11%) = $27.69

b2) Price to Earnings Ratio
Again using the same equation

P = D1/(ke -g)

D1 = (1 - b) * E1

where b is the retention ratio

P = (1 - b) * E1 / (ke -g)

P/E1 = (1 - b) / (ke -g)

Again if growth forecast reduces, the denominator (ke - g) will increase and (1 - b) / (ke - g) will reduce.

Thus, the price to earnings ratio will fall.

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