EXAM 2 Topic 7 Quiz

Question 1

A firm’s preferred stock pays a $4.25 dividend per year. Suppose the requred rate of return on the stock is 9%. What is the price of one share of preferred stock?

Answer 1

Price of preferred stock = Annual Preferred Dividend / Required Return

= $4.25 / 0.09 = $47.22

Question 2

A preferred stock with a face value of $25 is sold at 95% of its par value. If the annual dividend of the stock is $3, what is the required rate of return on this stock?

Answer 2

Current price=$25*95%=$23.75

Hence required return=Annual dividend/Current price

=(3/23.75)

=12.63

Question 3

You are valuing a common stock that just paid a dividend of $1.25 per share. You are expecting the stock to grow at the rate of 4% annually, and the stock to give you a return of 9%. What should be the price of the stock?

Answer 3

Price = Expected Dividend / ( Required Return - Growth Rate)

= [Dividend *(1+ Growth rate)]/ ( 9% - 4 %)

= [$ 1.25 * (1+4%)] / 5%

= 1.30 / 5%

= $ 26.00

Question 4

An issue of common stock has an expected dividend to be paid at the end of the year of $5 per share, and has an expected growth rate for the foreseeable future of 5% per year. If investors’ required rate of return for this particular security is 12% per year, how much should it be selling for?

Answer 4

Current price=D1/(Required return-Growth rate)

=5/(0.12-0.05)

=$71.43

Question 5

The Big Dude Company, whose common stock is currently selling for $50 per share, is expected to pay a $4.00 dividend next year. If investors believe that the expected rate of return on XYZ is 14%, what constant growth rate in dividends must be expected?

Answer 5

Stock price = Expected dividend / (Rate-Growth rate)

P0 = D1/(r-g)

50 = 4 / (14%-g)

14% - g = 4/50

• g = 8% - 14%
• g = - 6%

g = Growth rate = 6.00%

Question 6

Cougar Software, a fast-growing clothier, just paid a dividend of $1.64. Analysts project annual dividend growth to be 20% for the next 4 years, and then 5% thereafter. If investors’ required rate of return is 8%, what should the price of the stock be?

Answer 6

Solution: As per question dividend growth rate would 20% in year 1-4 and 5% in year 5 and thereafter.

Now, D1 = 1.64(1.20) = $1.968

D2 = $1.968(1.20) = $2.362

D3 = $2.362(1.20) = $2.834

D4 = $2.834(1.20) = $3.401 and,

D5 = $3.401(1.05)= $3.571

Now, here we can calculate P4 with the help of above D5:

P4 = D5 / r-g = $3.571 /(0.08-0.05) = $119.033

so, P4 = $119.033

Thus, Price of stock (P0) = Present value of all future benefits

P0 = Present value of D1, D2, D3, D4 and P4

= $1.968/1.08^1 + 2.362/(1.08)^2 + 2.834(1.08)^3 + 3.401(1.08)^4 + 119.033(1.08)^4

= $ 96.0896

Question 7

Cougar Auto is expecting its earnings and dividends to grow at a rate of 19% over the next 5 years. After the period, the firm is expecting to grow at the industry average of 5% indefinitely. If the firm recently paid a dividend of $1.25, and the required rate of return is 12%, what is the most you should pay for this company’s stock?

Answer 7

Step-1, Dividend for the next 5 years

Dividend per share Year 1 (D1) = $1.49 per share ($1.25 x 119%)

Dividend per share Year 2 (D2) = $1.77 per share ($1.49 x 119%)

Dividend per share Year 3 (D3) = $2.11 per share ($1.77 x 119%)

Dividend per share Year 4 (D4) = $2.51 per share ($2.11 x 119%)

Dividend per share Year 5 (D5) = $2.98 per share ($2.51 x 119%)

Step-2, Share Price in Year 5

Share Price in Year 5 (P5) = D5(1 + g) / (Ke – g)

= $2.98(1 + 0.05) / (0.12 – 0.05)

= $3.13 / 0.07

= $44.74 per share

Step-3, The Price of the company’s Stock

The Price of the company’s Stock is the Present Value of the Future Dividend plus the present value of the share price in year 5

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

= [$1.49 / (1 + 0.12)1] + [$1.77 / (1 + 0.12)2] + [$2.11 / (1 + 0.12)3] + [$2.51 / (1 + 0.12)4] + [$2.98 / (1 + 0.12)5] + [$44.74 / (1 + 0.12)5]

= $1.33 + $1.41 + $1.50 + $1.59 + $1.69 + $25.39

= $32.91 per share