Question

1. Fama Corp.’s current stock price is $36, and its last dividend (D0) was $2.40. The required rate of return for Fama Corp. is 12%. If dividends are expected to grow at a constant rate, g, what is Fama Corp.’s expected stock price four years from now?

2. Albanian Technology Corp. (ATC) has been growing at the phenomenal rate of 20% per year due to the recent development of a new irrigation method. This growth rate is expected to last for two more years after which other companies will have developed similar systems, and ATC’s growth rate will drop to 6% thereafter. The most recent annual dividend (D0), which was paid yesterday, was $1.75 per share. If the growth in dividends matches the company’s overall growth rate and if stockholders require a 12% return on ATC’s stock, what is the current share price?

3. You want to estimate the current price of a share of Duffie Corp. stock. You know that next year’s dividend is expected to be $2.20 and the growth rate of dividends is 5%. You look in the Wall Street Journal and find that the riskfree interest rate is 4%. You also know from looking in Valueline that Duffie Corp. has a beta of 1.35. If the required return on the market is currently 12%, what is Duffie’s current share price?

PLEASE SHOW ALL WORK AND FORMULAS

Answer 1

1. Fama Corp.’s current stock price is $36, and its last dividend (D0) was $2.40. The required rate of return for Fama Corp. is 12%. If dividends are expected to grow at a constant rate, g, what is Fama Corp.’s expected stock price four years from now?

Dividend (in 5th year) = D5 = 2.4*(1+g)^5

Price (4 years from now) = D5/(r-g) = 2.4*(1+g)^5 / (0.12 - g)

for getting g use current stock price

Po = D1 / (r - g )

36 = 2.4*(1+g) / (0.12-g)

g = 0.05 = 5%

Plugging value of g in Price (4 years from now) = D5/(r-g) = 2.4*(1+g)^5 / (0.12 - g)  

Price ( 4 years from now) = $43.758225

2. Albanian Technology Corp. (ATC) has been growing at the phenomenal rate of 20% per year due to the recent development of a new irrigation method. This growth rate is expected to last for two more years after which other companies will have developed similar systems, and ATC’s growth rate will drop to 6% thereafter. The most recent annual dividend (D0), which was paid yesterday, was $1.75 per share. If the growth in dividends matches the company’s overall growth rate and if stockholders require a 12% return on ATC’s stock, what is the current share price?

D1 = 1.75*1.2 = $2.1

D2 = 2.1*1.2 = $2.52

D3 = 2.52*1.06 = $2.6712

Price at end of year 2 = P2 = D3/(r - g) = 2.6712/(0.12-0.06) = $44.52

Current Price = Po = D1/1.12 + (D2+P2)/1.12^2 = $39.375

3. You want to estimate the current price of a share of Duffie Corp. stock. You know that next year’s dividend is expected to be $2.20 and the growth rate of dividends is 5%. You look in the Wall Street Journal and find that the riskfree interest rate is 4%. You also know from looking in Valueline that Duffie Corp. has a beta of 1.35. If the required return on the market is currently 12%, what is Duffie’s current share price?

Required rate of return on equity = r = rf + beta*(rm - rf) = 4% + 1.35*(12% - 4%) = 14.8%

Current Price = D1/(r-g) = 2.2/(0.148 -0.05) = $22.449