Question

ABC private limited as given the dividend of $5 last year and has promised to increase the dividend by 8% each year for the next four years.

1. Find out the dividend of each of the next four years.
2. If the stocks are selling at $120 at the end of fourth year, find out the price of stock today, assuming expected return as 12%.
3. Write a detailed comment on what will happen to the today’s selling price of the stock if the expected return is increased from 12% to 16%.
4. If the stocks are selling at $90 today, find out the price of stock at the end of fourth year, assuming expected return as 12%.         
5. Write a detailed comment on what will happen to the selling price of the stock at the end of fourth year if the expected return is decreased from 12% to 8%.

Answer 1

a.Find out the dividend of each of the next four years.

Growth Rate =g=8%=0.08

D0=Last dividend=$5.00

Dividend in year 1=D1=5.00*(1+g)=5.00*1.08=$5.40

Dividend in year 2=D2=5.40*(1+g)=5.40*1.08=$5.83

Dividend in year 3=D3=5.83*(1+g)=5.83*1.08=$6.30

Dividend in year 4=D4=6.30*(1+g)=6.30*1.08=$6.80

b.If the stocks are selling at $120 at the end of fourth year, find out the price of stock today, assuming expected return as 12%.

Expected Return =12%=0.12

Price of stock today=Present Value of future cash flows discounted at 12%

Price of stock today=(D1/1.12)+(D2/(1.12^2))+(D3/(1.12^3))+(D4/(1.12^4))+(120/(1.12^4))

Price of stock today=(5.40/1.12)+(5.83/(1.12^2))+(6.30/(1.12^3))+(6.80/(1.12^4))+(120/(1.12^4))=$94.54

c.Write a detailed comment on what will happen to the today’s selling price of the stock if the expected return is increased from 12% to 16%.

If Expected return is increased to 16%, the cash flows will be discounted at 16%. The Present Value will decrease.

Today's selling price will reduce.

Price of stock today=(5.40/1.16)+(5.83/(1.16^2))+(6.30/(1.16^3))+(6.80/(1.16^4))+(120/(1.16^4))=$83.05

d.If the stocks are selling at $90 today, find out the price of stock at the end of fourth year, assuming expected return as 12%.

Present Value of dividends=(5.40/1.12)+(5.83/(1.12^2))+(6.30/(1.12^3))+(6.80/(1.12^4))=$18.27

Price of stock at the end of fourth year=(90-18.27)*(1.08^4)=$112.86

e.Write a detailed comment on what will happen to the selling price of the stock at the end of fourth year if the expected return is decreased from 12% to 8%.

Present Value of dividends=(5.40/1.08)+(5.83/(1.08^2))+(6.30/(1.08^3))+(6.80/(1.08^4))=$20.00

Price of stock at the end of fourth year=(90-20)*(1.08^4)=$95.23