Question

Bond valuation Nesmith Corporation's outstanding bonds have a $1,000 par value, a 8% semiannual coupon, 7 years to maturity, and an 9% YTM. What is the bond's price? Round your answer to the nearest cent. $ ______________

Answer 1

Bond price is the present value of :

(a)the coupons to be received throughout the life time of the bond and

(b) the principal of bond to be received at the maturity of the bond

Hence,

PV of coupons=Coupon amount* PV factor of annuity @ r rate for n periods

Where r= rate of interest per period.( 4.4031% per half year see calculation below)

n= number of periods(14 i.e. 7*2)

How to arrive at semiannual rate if annual rate is given.

We know @9% per annum $1 shall become 1.09 after one year.

In other words we can say that at r% semiannual rate $1 shall become $1.09.

so,

(1+r)^{^2}=1.09

(1+r)=1.09^{^1/2}

(1+r)=√1.09

(1+r)=1.044031

r=1.044031-1

=.044031 or 4.403065% semi-annual.

Calculation of PV factor of annuity:

PV factor of annuity= [(1+r)^{^n}-1] / [(1+r)^{^n}*r]

= [(1+.044031)^{^14}-1] / [(1+.044031)^{^14}*.044031]

=(1.828048-1)/(1.828048*.044031)

=10.28749

Calculation of PV factor of $1 receivable after 7 years:

PV factor =1/(1+r)^{^n}

=1/(1+.09)^{^7}

=.547034

Coupon amount= 1000*8%

=80

Now, Price of bond= PV of coupons+PV of Principal

=80*10.28794 + 1000*.547034

=823+547.034

=1370.034

Hence value of bond shall be 1370.034.

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