Question

Please give this problem solution:

Problem7: XYZ 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.

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

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%.

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%.

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%.

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%.

Answer 1

a. Dividend in year 1 =Dividend Last year *(1+g) =5*(1+8%) =5.40
Dividend in year 2 =Dividend Last year *(1+g)^2 =5*(1+8%)^2 =5.8320
Dividend in year 3 =Dividend Last year *(1+g)^3 =5*(1+8%)^3 =6.2986
Dividend in year 4 =Dividend Last year *(1+g)^4 =5*(1+8%)^4=6.8024

b. Price in Year 4 =120
Price today =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+D4/(1+r)^4+Price in year 4/(1+r)^4
=5.40/(1+12%)+5.8320/(1+12%)^2+6.2986/(1+12%)^3+6.8024/(1+12%)^4+120/(1+12%)^4=94.54
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c. If the interest rate increases from 12% to 16% the Present value of dividends and price in year 4 will decrease. This is because higher is the required rate more is the risk. Hence lower is the price of bond.
Price today =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+D4/(1+r)^4+Price in year 4/(1+r)^4
=5.40/(1+16%)+5.8320/(1+16%)^2+6.2986/(1+16%)^3+6.8024/(1+16%)^4+120/(1+16%)^4=83.06

d. Price in year 4 =Price today*(1+r)^4-D1*(1+r)^3-D2*(1+r)^2-D3*(1+r)-D4 =90*(1+12%)^4-5.40*(1+12%)^3-5.8320*(1+12%)^2-6.2986*(1+12%)-6.8024=112.86

e. If required Rate decreases the price in year 4 decreases. Lower the interest rate lower is the future price of bond.
Price in year 4 =Price today*(1+r)^4-D1*(1+r)^3-D2*(1+r)^2-D3*(1+r)-D4 =90*(1+8%)^4-5.40*(1+8%)^3-5.8320*(1+8%)^2-6.2986*(1+8%)-6.8024=95.23