Question

a) ABC Co. just paid a dividend of $1.75 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year indefinitely.

Part 1: If investors require a 12 percent return on the stock, what is the current price?

Part 2: What will the price be in 8 years?

b) A. Corp, B. Corp, and C. Corp each will pay a dividend of $1.35 next year. The growth rate in dividends for all three companies is 6 percent. The required return for each company's stock is 9.80 percent, 12.70 percent, and 15.30 percent, respectively.

Part 1: What is the stock price for A. Company?

Part 2: What is the stock price for B. Company?

Part 3: What is the stock price for C Company?

Part 4: What is the relation between the required return and the stock price?

c) ABC Inc., will pay no dividends over the next 13 years because the firm needs to retain its earnings for growth purposes. The company will pay an $4 per share dividend in 14 years and will increase the dividend by 4 percent per year thereafter. If the required return on this stock is 9 percent, what is the current (t=0) share price?

d) Tally Co. just paid a dividend of $1.75 per share. The company will increase its dividend by 28 percent next year and will then reduce its dividend growth rate by 7 percentage points per year until it reaches the industry average of 7 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on the stock is 12 percent, what will a share of stock sell for today?

e) ABC Corp. just paid a dividend of $1.40 per share. The dividends are expected to grow at 25 percent for the next 7 years and then level off to a 7 percent growth rate indefinitely. If the required return is 15 percent, what is the price of the stock today?

Answer 1

a. Part 1: P0=D1/r-g

g=6%;r=12%

D1=D0*(1+g)=1.75*(1+6%)=$1.855

P0=$1.855/(12%-6%)=$30.92

Part 2: Price in 8 Years (P8)= D9/(r-g)

D9=D0*(1+6%)^9=$1.75*(1+6%)^9=$2.96

P8=$2.96/(12%-6%)=$49.28

b.Stock price of A=(D1/r-g)=$1.35/(9.80%-6%)=$35.53

Stock price of B=(D1/r-g)=$1.35/(12.70%-6%)=$20.15

Stock price of C=(D1/r-g)=$1.35/(15.30%-6%)=$14.52

The required rate of return and stock price are always inversely related. The required rate of return is the minimum rate that investors need to hold this stock. High risk to hold the stock will result in higher required rate of return for an investor.

c. D14=$4

D15=$4*(1+4%)=$4.16

r=9%

P14=(D15/r-g)=$4.16/(9%-4%)=83.2

Todays' price=($4+$83.2)/(1+9%)^14=$26.09

d.D0=1.75

D1=D0*(1+28%)=1.75*(1+28%)=2.24

D2=D1*(1+21%)=$2.24*(1+21%)=$2.71

D3=D2*(1+14%)=$2.71*(1+14%)=$3.09

D4=D3*(1+7%)=$3.09*(1+7%)=$3.31

P3=(D4/r-g)=$3.31/(12%-7%)=$66.12

Price today=(D1/(1+12%))+(D2/(1+12%)^2)+((D3+P3)/(1+12%)^3)

=(2.24/1.12)+(2.71/1.12^2)+(69.21)/1.12^3

=$53.43

e.D1=D0*(1+25%)=1.4*(1+25%)=1.75

D2=1.75*(1+25%)=2.19

D3=2.19*(1+25%)=2.73

D4=2.73*(1+25%)=3.42

D5=4.27

D6=5.34

D7=5.34*(1+25%)=6.68

D8=6.68*(1+7%)=7.14

P7=D8/(r-g)=7.14/(15%-7%)=89.29

Price today (P0)=( D1/1.15)+(D2/1.15^2)+.......(D7+P7)/(1.15)^7

P0=(1.75/1.15)+(2.19/1.15^2)+.......+(95.96)/1.15^7

P0=47.44