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 ?$4.75 with a constant growth rate of 4?%, 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 12?%?
b. a return of 13?%?
c. a return of 24?%?
d. a return of 35?%?

Answer 1

annual dividend after 6 years, D6 = $4.75

growth rate, g = 4% = 0.04

No. of years for which co. will pay dividends,n = 25 - 5 = 20

a) return, R = 12% = 0.12

stock price at the end of 5th year, P5 = D6*[(1-[(1+g)/(1+R)]ⁿ)/(R- g)] = 4.75*[(1-[(1.04/1.12)]²⁰)/(0.12-0.04)]

= 4.75*[0.772853/0.08] = $45.88817  

current stock price , P0 = P5/(1+R)⁵ = 45.88817  /(1.12)⁵ = $26.03818 or $26.04( rounding off to 2 decimal places) or $26.0 ( rounding off to 1 decimal place) or $26 ( rounding off to nearest dollar value)

b)

b) return, R = 13% = 0.13

stock price at the end of 5th year, P5 = D6*[(1-[(1+g)/(1+R)]ⁿ)/(R- g)] = 4.75*[(1-[(1.04/1.13)]²⁰)/(0.13-0.04)]

= 4.75*[0.809849/0.09] = $42.7420467

current stock price , P0 = P5/(1+R)⁵ = 42.7420467 /(1.13)⁵ = $23.1986705 or $23.20( rounding off to 2 decimal places) or $23.2 ( rounding off to 1 decimal place) or $23 ( rounding off to nearest dollar value)

c)

return, R = 24% = 0.24

stock price at the end of 5th year, P5 = D6*[(1-[(1+g)/(1+R)]ⁿ)/(R- g)] = 4.75*[(1-[(1.04/1.24)]²⁰)/(0.24-0.04)]

= 4.75*[0.97033577/0.2] = $23.0454745

current stock price , P0 = P5/(1+R)⁵ = 23.0454745 /(1.24)⁵ = $7.86098973 or $7.86( rounding off to 2 decimal places) or $7.9 ( rounding off to 1 decimal place) or $8 ( rounding off to nearest dollar value)

d)

return, R = 35% = 0.35

stock price at the end of 5th year, P5 = D6*[(1-[(1+g)/(1+R)]ⁿ)/(R- g)] = 4.75*[(1-[(1.04/1.35)]²⁰)/(0.35-0.04)]

= 4.75*[0.9945801/0.31] = $15.2395338

current stock price , P0 = P5/(1+R)⁵ = 15.2395338 /(1.35)⁵ = $3.3986217 or $3.40( rounding off to 2 decimal places) or $3.40 ( rounding off to 1 decimal place) or $3 ( rounding off to nearest dollar value)