Question

Staton-Smith Software is a new​ start-up company and will not pay dividends for the first five years of operation. It will then institute an annual cash dividend policy of $3.75 with a constant growth rate of 6​%, with the first dividend at the end of year six. The company will be in business for 25 years total. What is the​ stock's price if an investor wants

a.  a return of 10​%?

b.  a return of 15​%?

c.  a return of 23​%?

d.  a return of 35​%?

Answer 1

Answer:

Dividend in Year 6 = $3.75
Growth Rate = 6%
Number of Payments = 20

Answer a.

Required Return = 10%

Current Price = $3.75/1.10^6 + $3.75*1.06/1.10^7 + …. + $3.75*1.06^19/1.10^25
Current Price = $3.75 * (1/1.10)^5 * [1 - (1.06/1.10)^20] / [0.10 - 0.06]
Current Price = $3.75 * 8.122889
Current Price = $30.46

Answer b.

Required Return = 15%

Current Price = $3.75/1.15^6 + $3.75*1.06/1.15^7 + …. + $3.75*1.06^19/1.15^25
Current Price = $3.75 * (1/1.15)^5 * [1 - (1.06/1.15)^20] / [0.15 - 0.06]
Current Price = $3.75 * 4.441684
Current Price = $16.66

Answer c.

Required Return = 23%

Current Price = $3.75/1.23^6 + $3.75*1.06/1.23^7 + …. + $3.75*1.06^19/1.23^25
Current Price = $3.75 * (1/1.23)^5 * [1 - (1.06/1.23)^20] / [0.23 - 0.06]
Current Price = $3.75 * 1.982749
Current Price = $7.44

Answer d.

Required Return = 35%

Current Price = $3.75/1.35^6 + $3.75*1.06/1.35^7 + …. + $3.75*1.06^19/1.35^25
Current Price = $3.75 * (1/1.35)^5 * [1 - (1.06/1.35)^20] / [0.35 - 0.06]
Current Price = $3.75 * 0.762911
Current Price = $2.86