Question

Singing Fish Fine Foods has a current annual cash dividend policy of ​$3.50. The price of the stock is set to yield a return of 10%. What is the price of this stock if the dividend will be paid

a. for 10 ​years?

b.  for 16 ​years?

c.  for 41 ​years?

d.  for 60 ​years?

e.  for 100 ​years?

f.  ​forever?

Answer 1

Here we have to calculate PV of Annuity for corresponding years.

Formula for PV of Annuity

a. for 10 years

Price = 3.5 * { [ 1 - {1 / (1+0.1)^10 } ] / 0.1}

= 3.5 * { [1 - {1 / 2.5937} ] / 0.1}

= 3.5 * { [ 1- 0.3855 ] / 0.1 }

= 3.5 * { 6.144}

Price = $ 21.50

b. for 16 years

Price = 3.5 * { [ 1 - {1 / (1+0.1)^16 } ] / 0.1}

= 3.5 * { [1 - {1 / 4.59497} ] / 0.1}

= 3.5 * { [ 1- 0.2176 ] / 0.1 }

= 3.5 * { 7.824}

Price = $ 27.38

c. for 41 years

Price = 3.5 * { [ 1 - {1 / (1+0.1)^41 } ] / 0.1}

= 3.5 * { [1 - {1 / 49.7852} ] / 0.1}

= 3.5 * { [ 1- 0.020086 ] / 0.1 }

= 3.5 * {9.8}

Price = $ 34.3

d. for 60 years

Price = 3.5 * { [ 1 - {1 / (1+0.1)^60 } ] / 0.1}

= 3.5 * { [1 - {1 / 304.4816} ] / 0.1}

= 3.5 * { [ 1- 0.0033 ] / 0.1 }

= 3.5 * {9.967}

Price = $ 34.89