Question

Church Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 22% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company's last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock?
a. $32.69
b. $26.57
c. $27.37
d. $28.97
e. $23.39

Answer 1

Answer:

Option B ,$26.57 is correct

Explanation:

The cost of equity =Rf+Beta*Mrp

Rf is the risk free rate of 3.00%

Beta of equity is 1.20

Mrp is the market risk premium which is 5.50%

Cost of equity=3.00%+(1.20*5.50%)=9.60%

Stock price =present value of dividends+present value of terminal value

D1=$1.25*(1+22%)/(1+9.6%)^1=$ 1.39

D2=$1.25*(1+22%)^2/(1+9.6%)^2=$ 1.55  

D3=$1.25*(1+22%)^3/(1+9.6%)^3=$ 1.72  

D4=$1.25*(1+22%)^4/(1+9.6%)^4=$ 1.92  

terminal value=year 4 dividend/(r-g)

year 4 dividend=$1.25*(1+22%)^4= 2.77  

r is the cost of equity of 9.6%

g is the dividend afer year 4 which is 0%

terminal value= 2.77/(9.6%-0%)=$ 28.85  

present value of terminal value= 28.85/(1+9.6%)^4=$ 19.99  

Total present values=$ 1.39+$ 1.72+$ 1.92  +$ 1.92 +$ 19.99  =$26.58

Answer 2

According to the question Option B ,$26.57 is correct

How to calculate of common stock?

When The cost of equity = $Rf+Beta "/times" Mrp$

After that, Rf is the risk free rate of 3.00%

then Beta of equity is$1.20$

After that Mrp is the market risk premium which is 5.50%

So that, Cost of equity 3.00%+(1.20*5.50%)=9.60% = 9.60%

Then The Stock price is = present value of dividends + present value of terminal value

Now, D1 is = $$1.25 "/times" (1+22$%$)/(1+9.6$%)^$1= 1.39$

Then, D2 is = $$1.25 "/times" (1+22$%$)^2/(1+9.6$%)^$2= 1.55$  

Then D3 is = $1.25 "/times" (1+22%)^3/(1+9.6%)^3=$ 1.72  

After that D4 is = $$1.25*(1+22$%$)^4/(1+9.6$%)^$4= 1.92$

Then the terminal value is = year 4 dividend/(r-g)

Then year 4 dividend is = $$1.25×(1+22$%)^4= 2.77  

Then r is the cost of equity of 9.6%

Now, g is the dividend after year 4 which is 0%

After that terminal value is = 2.77/(9.6%-0%)=$ 28.85  

Then present value of terminal value is = $28.85/(1+9.6$%)^4=$ 19.99  

Thus, The Total present values is =$ $1.39+ 1.72+ 1.92  + 1.92 + 19.99$  =$26.57

Therefore Option B is $26.57

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