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:
Pn = D(n+1) / Ke
Where,
Pn = Price of the stock at time ‘ n ‘ ; D(n + 1 ) = Next Year dividend payment
Ke = Required Return ;
Thus Price of share in Year 16
P16 = D17 / Ke
As per the information given in the question we have
D17 = $ 12 ; Ke = 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 = Cn / (1 + r )n
PV = Present Value ; Cn : 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
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