Answer :
cost of debit is 4.64 %
Explanation:
given data
sold = $1,000
time t = 20 year
rate r = 7 %
bond currently sells = $925
tax rate = 40%
to find out
component cost
solution
we will find first YTM by given formula that is
bond currently sells = [tex]\sum_{1}^{2t}[/tex] ( semi annual coupon / [tex](1+YTM/2)^{t}[/tex] ) + sold / (1+YTM/2)^{2t}[/tex] )
put here all value
so we get
925 = [tex]\sum_{1}^{40}[/tex] ( (1000×7/100×7) / [tex](1+YTM/2)^{20}[/tex] ) + sold / (1+YTM/2)^{40}[/tex] )
so here solve and we get
YTM = 3.87 %
and
cost of debit = 3.87 % × 2 = 7.74%
we know that cost of debit after tax is equal cost of debit ( 1 - tax rate )
put here value
cost of debit = cost of debit ( 1 - tax rate )
cost of debit = 7.74% ( 1 - 40% )
cost of debit is 4.64 %
