Question

Storico Co. just paid a dividend of $1.85 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 $58.04, 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

Price of the share today = Present Value of Dividend for first three years + Present Value of Terminal Value of the share at the end of 3^rd year

.

Terminal Value of the share at the end of 3^rd year = D4/(Re-g)

= 3.213655/(Re-0.06)

.

Present Value of Terminal Value of the share at the end of 3^rd year = [3.213655/(Re-0.06) ] / (1+Re)^3

.

.

Present Value of Dividend for first three years = 2.294/(1+Re)^1 + 2.70692/(1+Re)^2 + 3.03175/(1+Re)^3

.

.

Therefore,

Price of the share today = [ 2.294/(1+Re)^1 + 2.70692/(1+Re)^2 + 3.03175/(1+Re)^3 ] + [3.213655/(Re-0.06) ] / (1+Re)^3

.

.

Trial & Error Method:

At Re = 11% ,

Price of the share today = [ 2.294/(1+0.11)^1 + 2.70692/(1+0.11)^2 + 3.03175/(1+0.11)^3 ] + [3.213655/(0.11-0.06) ] / (1+0.11)^3

Price of the share today = $53.4764

.

.

At Re = 10% ,

Price of the share today = [ 2.294/(1+0.10)^1 + 2.70692/(1+0.10)^2 + 3.03175/(1+0.10)^3 ] + [3.213655/(0.10-0.06) ] / (1+0.10)^3

Price of the share today = $66.96205

.

.

Therefore, Price of $58.04 is in between the two Re (11% and 10%)

.

.

At ,

Price 53.48 , Re = 11% , (x1,y1) , (53.4764,11)

Price 66.96 , Re = 10% , (x2,y2) , (66.96205,10)

Price 58.04 , Re = ? , (x,y) , (58.04,y)

.

.

Using Interpolation,

y = y1 + (x−x1)/(x2−x1) × (y2−y1)

y = 11 + (58.04-53.4764)/(66.96205-53.4764) * (10-11)

y = 11 + (4.5636/13.48205)*(-1)

y = 11 – 0.39

y = 10.61

.

.

Therefore, Re is 10.61%.......(Answer)