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 $1.00 in four years and that dividends will then grow at 5% 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 15%?

Answer 1

Required Rate of Return (ke) = 15%

Expected Dividend at the end of Year 1 to Year 3(D1-D3) = $ 0

Expected Dividend at the end of Year 4 (D4) = $ 1

Dividends will grow at a Constant Rateof 5% from Year 4

Price of a Share if dividends are growing at Constant Rate,

Pn = Dn (1+g) / (Ke - g)

Price at the end of 4th year (P4) = D4 (1+g) / (Ke - g)

P4 = $1 (1+0.05) / (0.15 - 0.05)

P4 = $ 1.05 / 0.10

P4 = $ 10.5

Price of Share (Po) = Present value of Future Expectd Cash flows

Price of Share (Po) = Present value of (D4 + Price of Share at the end of 4th year immediately after payment of D4)

Price of Share (Po) = ($1 + $ 10.5) * PV(15%, 4yr)

Price of Share (Po) = ($1 + $ 10.5) / (1.15)^4

Price of Share (Po) = ($1 + $ 10.5) * 0.5718

Price of Share willing to pay = $ 6.575 (approx)