Question

what is the solution to 7-21?

conroy consulting corporation has been growing at a rate of 30% per year in recent years. this same nonconstant growth rate is expected to last for another 2 years.

a. If D₀ = $2.50 (r_s= 12%) and g_t = 7% then what is conroy consulting's stock worth today? what is its expected dividend yield for the first year? what is the expected capital gains yield for the first year?

b. Now assume Conroy consulting's period of nonconstant growth is to last another 5 years rather than 2 years. How would this affect its price, dividend yield, and capital gains yield? (no calculations required)

c. What will conroy consulting's dividend yield and capital gains yield be once its period of nonconstant growth ends?

d. Of what interest do investors is the relationship over time between dividend yield and capital gains yield?

Answer 1

As per rules I will answer the first 4 subparts of the question

D0=$2.5

Rs=12%

Gt=7%

D1=D0*(1+g)^1 = 2.5*130% = $3.25

D2= D0*(1+g)^2 = 2.5*(1+30%)^2 = $4.225

D3= D0*(1+g)^3 = 2.5*(1+30%)^3= $5.4925

1)P2= D3/(Rs-g)

= 5.4925/(12%-7%)

= $109.85

Value of stock = D1/(1+Rs) + D2/(1+Rs)^2 + P2/(1+Rs)^2

= 3.25/(1+12%) + 4.225/(1+12%)^2 + 109.85/(1+12%)^2

P0=$93.84

2)Dividend yield in year 1= Dividend/P0

=3.25/ 93.84

= 3.46%

3)P1= D2/(1+Rs)^1 + P2/(1+Rs)^1

= 4.225/(1+12%)^1 + 109.85/(1+12%)^1

=101.8527

Capital gain yield =(P1-P0)/P0

=8.54%

OR CGY= Required rate – Dividend yield

= 12%-3.46%

=8.54%

4:If the non constant growth continues for another 5 years, the price will increase since there is greater dividend received at high growth. Dividend yield will also increase since there are more dividends. Capital gains will remain the same since terminal value will be the same.