Question

Storico Co. just paid a dividend of $1.55 per share. The company will increase its dividend by 24 percent next year and then reduce its dividend growth rate by 6 percentage points per year until it reaches the industry average of 6 percent dividend growth, after which the company will keep a constant growth rate forever. If the stock price is $27.28, what required return must investors be demanding on the company's stock? (Hint: Set up the valuation formula with all the relevant cash flows, and use trial and error to find the unknown rate of return.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Current price of stock (P0) = 27.28

D0 = 1.55

growth rate next year = 24%

D1 = 1.55*(1+24%) =1.922

growth rate 24% -6% = 18%

D2 =1.922*(1+18%) =2.26796

growth rate 18%-6% = 12%

D3 =2.26796*(1+12%) =2.5401152

grwoth rate afterwards 12%-6% =6%

This will contine to be forever.

Value of stock at year 3 (P3) D3*(1+g)/(ke-g)

=2.5401152*(1+6%)/(ke-6%)

=2.692522112/(ke-6%)

Price of stock formula = (D1/(1+ke)^1) + (D2/(1+ke)^2) + (D3/(1+ke)^3 + (P3/(1+ke)^3

27.28 = (1.922/(1+ke)^1) + (2.26796/(1+ke)^2) + (2.5401152/(1+ke)^3 + ( (2.692522112/(ke-6%))/(1+ke)^3)

Assume ke is 14%

Value of stock = (1.922/(1+14%)^1) + (2.26796/(1+14%)^2) + (2.5401152/(1+14%)^3 + ( (2.692522112/(14%-6%))/(1+14%)^3)

=27.86278855

Assume ke is 15%

Value of stock = (1.922/(1+15%)^1) + (2.26796/(1+15%)^2) + (2.5401152/(1+15%)^3 + ( (2.692522112/(15%-6%))/(1+15%)^3)

=24.72723041

interpolation formula= Upper rate -((upper rate - lower rate)/(Upper value - lower rate)*(Upper value-actual value))

=14% +((15%-14%)/(27.86278855-24.72723041)*(27.86278855-27.28))

=0.1418586437 or 14.19%

So required return on stock (ke) is 14.19%