Question

Hank’s Barbecue just paid a dividend of $2.35 per share. The dividends are expected to grow at a 17.5 percent rate for the next five years and then level off to a 12.5 percent growth rate indefinitely. If the required return is 15.5 percent, what is the value of the stock today? What if the required return is 20.5 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Given about Hank's Barbecue,

Last dividend paid D0 = $2.35

dividends are expected to grow at 17.5% for next 5 years

thereafter growth rate g = 12.5%

Required return r = 15.50%

Dividend in year 1, D1 = 2.35*1.175 = $2.7613

D2 = 2.7613*1.175 = 3.2445

D3 = 3.2445*1.175 = 3.8123

D4 = 3.8123*1.175 = 4.4794

D5 = 4.4794*1.175 = 5.2633

So, value of stock in year 5 using constant dividend growth rate is

P5 = D5*(1+g)/(r-g) = 5.2633*1.125/(0.155-0.125) = $197.3733

So, stock value today is

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

=> P0 = 2.7613/1.155 + 3.2445/1.155^2 + 3.8123/1.155^3 + 4.4794/1.155^4 + 5.2633/1.155^5 + 197.3733/1.155^5

=> P0 = $108.40

So, price of the stock is $108.40

If required return r = 20.5%

value of stock in year 5 using constant dividend growth rate is

P5 = D5*(1+g)/(r-g) = 5.2633*1.125/(0.205-0.125) = $74.0150

So, stock value today is

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

=> P0 = 2.7613/1.205 + 3.2445/1.205^2 + 3.8123/1.205^3 + 4.4794/1.205^4 + 5.2633/1.205^5 + 74.0150/1.205^5

=> P0 = $48.38

So, price of the stock is $48.38