Question

In practice, a common way to value a share of stock when a company pays dividends is to value the dividends over the next five years or so, then find the “terminal” stock price using a benchmark PE ratio. Suppose a company just paid a dividend of $1.29. The dividends are expected to grow at 14 percent over the next five years. The company has a payout ratio of 40 percent and a benchmark PE of 24. The required return is 12 percent.
a.	What is the target stock price in five years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the stock price today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

a- Target price in 5 years

B- Current price

Answer 1

Given

Company just paid a dividend = D0 = $1.29

Dividends are expected to grow for next five years = g = 14% = 0.14

Payout ratio = 40% = 0.40

PE = 24

In order to calculate the dividend in the coming 5 years, we need to use the following formulas,

Dividend in the year 1:

D1 = D0*(1+g)

D1 = 1.29*(1+0.14)

D1 = 1.29*(1.14)

D1 = 1.4706

Dividend in the year 2:

D2 = D1*(1+g)

D2 = 1.4706*(1+0.14)

D2 = 1.4706*(1.14)

D2 = 1.6765

Dividend in the year 3:

D3 = D2*(1+g)

D3 = 1.6765*(1+0.14)

D3= 1.6765*(1.14)

D3 = 1.9112

Dividend in the year 4:

D4 = D3*(1+g)

D4 = 1.9112*(1+0.14)

D4= 1.9112*(1.14)

D4 = 2.1788

Dividend in the year5:

D5 = D4*(1+g)

D5 = 2.1788*(1+0.14)

D5= 2.1788*(1.14)

D5 = 2.4838

a) In order to calculate target price in five years, we need to use the formula

P5 = (EPS5)*(PE ratio)

Where,

EPS5 = D5/ Payout ratio

EPS5 = 2.4838/ 0.40

EPS5 = 6.2095

Now substitute EPS5 and PE in P5, we get

P5 = (EPS5)*(PE ratio)

P5 = (6.2095)*(24)

P5 = 149.03

Therefore, target price in five years P5 = 149.03

b) Given Required rate of return = r = 12% = 0.12

Stock price today is calculated using the formula,

P0 = D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D5/(1+r)^5 + P5/(1+r)^5

Substituting the above values in thie formula, we get

P0 = $1.4706/1.12 + $1.6765/1.12^2 + $1.9112/1.12^3 + $2.1788/1.12^4 + $2.4838/1.12^5 + $149.03/1.12^5

  P0 = $1.4706/1.12 + $1.6765/1.2544 + $1.9112/1.4049 + $2.1788/1.5735 + $2.4838/1.7623 + $149.03/1.7623

  P0 = $1.3130 + $1.3365 + $1.3603 + $1.3846 + $1.4094 + $84.5620

P0 = $91.37

Therefore, stock price today = $91.37