Question

A company is issuing a 3-year maturity bond that is expected to pay $40 every six month & a lump sum of $1000 at the end of three years from now. If bond investors require 5% annual nominal interest rate (APR), how much is the price of this bond today? Please show your formula in your answer and explain step-by-step calculation to arrive to your final answer

Answer 1

Answer;

Present value of bond =

=PVAF(RATE, n) +PVF (rate, nth)

=PVAF(2.5%,6period) + PVF (2.5%,6th period)

Rate = 5 % per annum

6 month rate = 2.5% per 6 month

Coupon payment = $40

Redemption price = $1000

PVAF = PMT x (1 - (1+r)^-n /r)

= 40 x ( 1-(1.025)^-6/2.5%)

= 40 x 5.508125

= $220.325

Pvf = redemption amount x (1+r)^-6

= $1000 x. 862296

= $862.30

Present value of bond = 220.32 + 862.30

= $1082.62

Alternatively convert nominam rate in effective rate

= (1.025)^2 - 1

= 5.06%

So, present value of bond=

=40 x 5.5026 + 1000 x. 86078

=220.10 + 860.78

=1080.88

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