Question: Compute the price of a preferred stock which is callable after 7 years

Question

Question:

Compute the price of a preferred stock which is callable after 7 years at 104 par value, has a yield of 4% and pays a quarterly dividend of $2. If the firm does not buy the preferred back, what will its price be at that time?

Please identify which numbers are I (coupon or interest rate), par value, price of the bond, n (number of periods), ytm (yield to maturity) or ytc (yield to call) if there are any.

Please provide the formula that you used to solve the problem and please show work (step by step). The more detailed, clear, and organized your work is, it will help me understand the problem a lot better. It is important for me because I need to solve this problem for a take home test. Thanks in advance.

Explanation / Answer

The Price of the preferred stock if called after 7 years= PV of all dividends+PV of the called value

Present Value of an annuity=PV= A*[ (1+r)^n -1]/[(1+r)^n * r] Here A=2 , r=4/4=1% , n=7*4=28 PV of dividends=2*(1.01^28-1)/(1.01^28*(0.01))=48.63 PV of the called value=104/(1.01^28)=78.71 Price of the preferred stock=48.63+78.71=127.34 If the Preferred stock is not called , the Price will be the PV in dividend in perpetuity=A/r=2/0.01=200

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