Question

You obtain the following information for the IYR Inc.'s common stock:

Quarterly dividend 5 years ago=1.0

Quarterly dividend just paid = 1.276

P0 = 30.0

Assuming that the stock is priced in equilibrium, what is IYR's cost of common stock?

a. 16.44%

b. 18.93%

c. 22.86%

d. 20.65%

e. 14.71%

Answer 1

We have following information -

Quarterly dividend 5 years ago= $1.0

Quarterly dividend just paid = $1.276

We can use following the Present value (PV) of the Future Value (FV) formula to calculate dividend growth rate

PV = FV/ (1+i) ^n

Where,

Present Value PV =$1

Future value of divided after 5 years =$1.276

Quarterly growth interest rate i =?

Time period n = 4 quarters *5 years = 20 periods

Therefore,

$1 = $1.276 / (1+i %) ^20

Or i = 1.23%

Therefore annual dividend growth rate = (1+1.23%) ^4 -1

= 1.04995 -1

= 0.04995 or 4.995% per year

Quarterly dividend just paid = $1.276, therefore equivalent annual dividend = $1.276 *4 = $5.104

Now we can use following formula to calculate the rate of return required by investors by dividend discount model

Stock Price P0 = D1 / (k – g)

Where:

P0 = the current stock price = $30.0

D1 = dividend for next year $5.104 *(1+4.995%)

k = IYR's cost of common stock =?

g = growth rate of dividends = 4.995% per year

Therefore,

$30 = $5.104 *(1+4.995%)/ (k- 4.995%)

Or k = ($5.360/$30) +0.04995

=0.1786 + 0.04995

= 0.2286 or 22.86%

The IYR's cost of common stock is 22.86%

Therefore correct answer is option c. 22.86%