Homework 5

Due July 22 2020

1.Suppose PQR Corp. just paid a dividend of $0.75. The firm has a payout ratio of 25%, and its dividends are expected to grow in perpetuity at 15%. You estimate that its market capitalization rate is 16%.

(a)At what price should the stock of PQR sell if it is priced by the constant dividend growth model?

Answer: P0=D1/(r-g)=0.75/(25%-15%)

(b)Decompose the price into PVGO and the present value of Assets-in-Place

Answer:

(c)What is the return on book value of equity for this firm, assuming that the growth rate can be estimated by the product of the retention ratio and the return on book value of equity?

(d)ComputeB₀, the current book value of equity for the firm on a per share basis.

2. (a):XYZ Inc. just paid out a dividend (D₀) of $3.60. The firm anticipates that its annual dividends will grow atg_H= 22.5% a year over the next 6 years. From t=6 onwards, the management expects that the firm's dividends will grow in perpetuity atg_L= 4.5% per year. Work out the price of the stock assuming that the risk of its future cash flows justifies a discount rate ofr= 13.5%.

2. (b):Rework your answer to part (a) assuming thatr= 22.5%

3.Assuming that the constant growth rate dividend discount model can be applied, work out the rate at which the dividends of the following firms are expected to grow:

(a).XYZ Inc. pays out 25% of its earnings as dividends, has a "historical" P/E ratio [current price to trailing twelve months' earnings] of 6, and a market capitalization rate of 12.5% per year, and

(b).PQR Inc. pays out 30% of its earnings as dividends, has a "forward-looking" P/E ratio [current price to next twelve months' earnings] of 10, and a market capitalization rate of 20% per year.