value of bond

CFA Level I Fixed Income
#1

In an example in SS15 - Fixed Income, it says -

the yield on a 6%, 20yr $1000 bond has declined from 6% at issuance to 4% on Jun 22, 2017 (first call option date). If there was no call option, the bond would trade at $1224. The issue date is Jun 22, 2012.

How did they arrive at $1224? Even if a bond is expected to yield 4%, the Present value 15 years of coupons at 4% will be – 40/(1.04) + 40/(1.04^2) + 40/(1.04^3) + … + 40/(1.04^15) = $444.74

So I was expecting the value of bond to be $1444.74. I am new to finance so bear with me if I am getting the concept of “bond value” totally wrong. I know “something” is wrong as the bond should trade at lower value than the PV of all coupons+principal for buyer to make any money but not sure how to determine the value

#2

I believe that you need the present value of the principal payment, not the future value.

#3

Hi Singh.

To get the trade value, you need to know how much is this bond worth today, ie to calculate PV of the bond.

The PV is the sum of every future discounted cash flows.

Since the bond was issued in 2012 and is a 20-years long bond, it still has 15 payments to go in 2017 considering the payment is annual.

Now, considering the bond was issued at par (ie coupon rate = yield at issuance), the annual coupons are worth $60 (6% * $1000) each.

The future payments will then be 60/1.04 + 60/(1.04)^2 + … + 1060/(1.04)^15 = 1224

Note that the last payment on the 15th year includes both coupon and reimbursement ($1000)

The reimbursement must be discounted because it will only be received in 15 years and naturally suffers from the concept of time value of money as any other future cash-flow.

Get used to the calculator once you have understood the concepts.

On a BAII calculator, you should type: N=15 I/Y=4 PMT=60 FV=1000 and CPT->PV

#4

Thanks…I now realize I was getting two things wrong -

  1. I changed the coupon value to $40 instead of $60 based on the expected rerun. I now understand I should only change the rate to 4% while calculating PV and coupon value should remain the same

  2. I was adding 1000 at the end without realizing I need to convert the final payment at the end of term to PV too

#5

You’re quite welcome.