Question

Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years. The last dividend paid was $7. The discount rate is 15% and the steady growth rate after 3 years is 2%.

a. What is the capital gain in stock price from year 0 to year 1? (Do not round intermediate calculations. Enter your answer as a dollar amount rounded to 2 decimal places.)

b. Calculate the expected rate of return.

Answer 1

a. Dividend Year 1 =D0*(1+20%) =7*1.20
Dividend Year 2 =D0*(1+20%)^2=7*1.20^2
Dividend Year 3 =D0*(1+20%)^3=7*1.20^3
Dividend Year 4 =D0*(1+20%)^3*(1+2%)=7*1.20^3*1.02
Terminal Value =Dividend Year 4 /(R-g) =7*1.20^3*1.02/(15%-2%) =94.907077

a. Price in Year 0 =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+Terminal Value/(1+r)^3
=7*1.20/1.15+7*1.20^2/1.15^2+7*1.20^3/1.15^3+94.907077/1.15^3 =85.2825
Price in Year 1 =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+Terminal Value/(1+r)^3
=7*1.20^2/1.15^1+7*1.20^3/1.15^2+94.907077/1.15^2 =89.6749
Capital Gain =(Price 1-Price 0)/Price 0 =(89.6749-85.2825)/85.2825=5.15%

b. Expected Rate of Return =(Price 1-Price 0+Dividend)/Price 0 =(89.6749-85.2825+7*1.20)/85.2825=15%