Question

Pfender Guitars has a current annual cash dividend policy of $5.00. The price of the stock is set to yield a return of 9​%. What is the price of this stock if the dividend will be paid

a.  for 10 years and then the company repurchases the stock for $30?

b.  for 13 years and then the company repurchases the stock for $30?

c.  for 40 years and then the company repurchases the stock for $30​?

d.  for 60 years and then the company repurchases the stock for $30?

e.  for 100 years and then the company repurchases the stock for $30?

f.   forever with no repurchase of the​ stock?

Answer 1

a) 10 years

As per dividend discount model,

Price = Dividend * PVAF ( r, n ) + Repurchase amount * PVIF ( r, n )

          = 5 * PVAF ( 9%, 10 ) + 30 * PVAF ( 9%, 10 )

          = 5 * [ 1/1.09 + 1/1.092 + ...... + 1/1.0910 ] + 30 * [ 1/1.09 ]10

         = 5 * 6.4177 + 30 * 0.4224

         = $ 44.76 Answer

b) 13 years

As per dividend discount model,

Price = Dividend * PVAF ( r, n ) + Repurchase amount * PVIF ( r, n )

          = 5 * PVAF ( 9%, 13 ) + 30 * PVAF ( 9%, 13 )

          = 5 * [ 1/1.09 + 1/1.092 + ...... + 1/1.0913 ] + 30 * [ 1/1.09 ]13

         = 5 * 7.4869 + 30 * 0.3262

         = $ 47.22 Answer

c) 40 years

As per dividend discount model,

Price = Dividend * PVAF ( r, n ) + Repurchase amount * PVIF ( r, n )

          = 5 * PVAF ( 9%, 40 ) + 30 * PVAF ( 9%, 40 )

          = 5 * [ 1/1.09 + 1/1.092 + ...... + 1/1.0940 ] + 30 * [ 1/1.09 ]40

         = 5 * 10.7574 + 30 * 0.0318

         = $ 54.74 Answer

d) 60 years

As per dividend discount model,

Price = Dividend * PVAF ( r, n ) + Repurchase amount * PVIF ( r, n )

          = 5 * PVAF ( 9%, 60 ) + 30 * PVAF ( 9%, 60 )

          = 5 * [ 1/1.09 + 1/1.092 + ...... + 1/1.0960 ] + 30 * [ 1/1.09 ]60

         = 5 * 11.048 + 30 * 0.0057

         = $ 55.41 Answer

e) 100 years

As per dividend discount model,

Price = Dividend * PVAF ( r, n ) + Repurchase amount * PVIF ( r, n )

          = 5 * PVAF ( 9%, 100 ) + 30 * PVAF ( 9%, 100 )

          = 5 * [ 1/1.09 + 1/1.092 + ...... + 1/1.09100 ] + 30 * [ 1/1.09 ]100

         = 5 * 11.1091 + 30 * 0.0002

         = $ 55.55 Answer

f) Infinite period

As per dividend discount model,

Price = Dividend / Yield

          = 5 / 0.09

          = $ 55.55 Answer

Hope you understand the solution.