Question

Downloads for Cheap, Inc. has a new business that allows customers to download music and movies directly onto their IPhones or MP3 players in grocery stores. The downloaded items can be played on their TVs or computers at home. The firm is in the high growth phase and does not currently pay dividends. Managers are estimating that the firm will begin paying an annual dividend per share of $1.70 in four years and that dividends will then grow at 4% per year thereafter. What is the most you should be willing to pay for the stock today if the required return on the stock is 11%?

a)$18.42 b)$7.00 c) $17.76 d)$16.90

Daisy Pixie Stix pays out 55% of its earnings as dividends. The firm has been earnings $0.12 cents per dollar of equity invested in the firm and investors require a 8.50% return. The last annual earnings were $4.00 per share. What is the P/E ratio of the stock?

a) 35.16 b)43.75 c)26.41 d)17.74

Answer 1

Using Gordon's dividend growth model,

Value of share at the end of year 3 (P3) = D4 / (ke-g)

Where, D4 is dividend for year 4

ke is required return on equity

g is growth rate

Value of share at the end of year 3 (P3) = 1.7 / (11%-4%) = $24.29

Present Value of share (P0) = P3 / (1+ke)ⁿ

Present Value of share (P0) = 24.29 / (1+11%)³ = $17.76

Therefore option c 17.76 is correct

Question 2

Return on Equity = 12% ($0.12 per $1)

Required return on Equity = 8.50%

last EPS = $ 4

therefore last DPS = EPS x Dividend payout ratio

therefore last DPS = 4 x 55% = $ 2.20

growth rate = Retention ratio x return on equity

growth rate = (1-dividend payout ratio) x return on equity

growth rate = (1-0.55) x 0.12 = 5.40%

Using Gordon's dividend growth model,

Price per share (P0) = D1 / (ke-g)

Price per share (P0) = $2.2 / (0.085 - 0.054)

Price per share (P0) = $70.97

Therefore PE = Price / EPS = 70.97 / 4 = 17.74

Therefore option (d) is correct

Correct answer according to me is 18.70 which is not mentioned in options. While calculating price per share, D0 is assumed as D1 is above solution in order to match the answer with options. Ideally, $2.20 is D0 and accordingly $ 2.32 is D1 adding growth rate of 5.40%