Question

6A preferred stock with no stated maturity and a par value of $57 currently sells for $45 and pays a dividend of $7 annually. If it were to establish a sinking fund and a 12-year maturity, what would be the new price of the stock?

A : $45.00

B : $45.98

C : $36.38

D : $84.50

Answer 1

sinking value of fund = par value to be paid off/((1+R)n -1)/R)

if it were to establish sinking fund, then assuming all the principal amount needs to bereak down in equal 12 parts
since, price = dividend/(Rate of interest-growth)
here growth = 0
therefore, Rate of interest = 7/45			15.56%
	n=12
so price	=	Div/1+R    +…	+	… + Div/(1+R)n
		1+R	Dividend	Value
	Year 1	1.1556	7	6.057459
	Year 2	1.335411	7	5.241831
	Year 3	1.543201	7	4.536025
	Year 4	1.783324	7	3.925255
	Year 5	2.060809	7	3.396725
	Year 6	2.38147	7	2.93936
	Year 7	2.752027	7	2.543579
	Year 8	3.180243	7	2.20109
	Year 9	3.675088	7	1.904716
	Year 10	4.246932	7	1.648249
	Year 11	4.907755	7	1.426314
	Year 12	5.671402	7	1.234263
	Total Value			37.05487

Since the total amount is close to option C hence, our answer is Option C.