Question

Fifth National Bank just issued some new preferred stock. The issue will pay an annual dividend of $12 in perpetuity, beginning 17 years from now. If the market requires a return of 4.2 percent on this investment, how much does a share of preferred stock cost today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Stock price

Answer 1

Solution:

As per the information given in the question, dividend will be received beginning 17 years from now I.e., in Year 16.

Calculation of Price of the share in Year 16:

The price of preferred stock at Year “n” can be calculated using the following formula:

P_n = D_(n+1) / K_e

Where,

P_n = Price of the stock at time ‘ n ‘ ; D_{(n + 1 )} = Next Year dividend payment

K_e = Required Return    ;

Thus Price of share in Year 16

P₁₆ = D₁₇ / K_e

As per the information given in the question we have

D₁₇ = $ 12   ; K_e = 4.2 % = 0.042

Applying the above information in the formula we have

= $ 12 / 0.042

= $ 12 / 0.042

= $ 285.714286

Thus price of the share in Year 16 = $ 285.714286

Calculation of Current price of the share :

The current price of the share is obtained by discounting the price of the share at Year 16 to its Present value

The present value of price of share or stock at period 'n' is calculated using the following formula:

PV = C_n / (1 + r )ⁿ

PV = Present Value   ; C_n : Price of share at period n ;

r = discount rate ; n = Number of periods or years

As per the information given in the question we have

r = 4.2 % ; n = 16 year   ; C₁₆ = $ 285.714286 ;

Applying the above values in the formula we have

PV = $ 285.714286 / ( 1 + 0.042 ) ¹⁶

= $ 285.714286 / ( 1.042 ) ¹⁶

= $ 285.714286 / 1.931450

= $ 147.927341

= $ 147.93 ( when rounded off to two decimals )

Thus the current price of the preferred stock is = $ 147.93

Note: The value of ( 1.042 ) ¹⁶   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.042,16) = 1.931450