Bond X is a premium bond making annual payments. The bond pays a 13
percent coupon, has a YTM of 8 percent, and has 22 years to maturity.
Bond Y is a discount bond making annual payments. This bond pays a 8
percent coupon, has a YTM of 13 percent, and also has 22 years to
maturity. If interest rates remain unchanged, you would expect that 4
years from now, Bonds X and Y will be priced at $____ and $____ ,
respectively. And in 11 years: $___ and $____  .

Hi!!

I will assume face values of $1000 for both bonds.

Bond Price (BP) = present value of coupon + present value of face value

At year i of n of maturity:
PV coupons = Coupon/YTM * [(1 - (1 / (1+YTM)^(n-i)))] 
PV of face = Face Value / (1+YTM)^(n-i) 


4 years from now:

-Bond X:
PV coupons = 130/0.08 * [(1 - (1/(1.08)^18] =
           = 130/0.08 * 0.74975 =
           = 1218.35

PV of face = 1000 / (1.08)^18 =
           = 1000 / 3.996 =
           = 250.25

BPX = 1218.35 + 250.25 = $1,468.60


-Bond Y:
PV coupons = 80/0.13 * [(1 - (1/1.13)^18] =
           = 80/0.13 * 0.8892 =
           = 547.20

PV of face = 1000 / (1.13)^18 =
           = 1000 / 9.024 =
           = 110.81

BPY = 547.20 + 110.81 = $658.01


-11 years from now:

-Bond X:
PV coupons = 130/0.08 * [(1 - (1/(1.08)^11] =
           = 130/0.08 * 0.5711 =
           = 928.04

PV of face = 1000 / (1.08)^11 =
           = 1000 / 2.332 =
           = 428.82

BPX = 928.04 + 428.82 = $1,356.86


-Bond Y:
PV coupons = 80/0.13 * [(1 - (1/1.13)^11] =
           = 80/0.13 * 0.7393 =
           = 454.95

PV of face = 1000 / (1.13)^11 =
           = 1000 / 3.8359 =
           = 260.70

BPY = 454.95 + 260.70 = $715.65


You must note that every year the bonds matures, the distance between
their face value and their price get closer and closer together, the
premium one approximates the face value from above and the discount
bond approximates it from below.


For references see:
"Bond Valuation, Calculation, Finance Basics":
http://www.moneyinstructor.com/art/bondvaluation.asp

"Bond Valuation":
http://teachmefinance.com/bondvaluation.html

"Bond valuation":
http://wise.fau.edu/~ppeter/fin3403/module4/bondval.pdf


Search strategy for references:
"bond valuation"


Hope that this helps you. Feel free to request for a clarification if
you find something unclear or in the case of a miscalculation
(sometimes we type the wrong number on the calculator), I will be glad
to give you further assistance on this question if you need it.


Regards,
livioflores-ga

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Request for Answer Clarification by i_dont_even_care-ga on 11 Oct 2005 10:01 PDT

This is great stuff livioflores-ga - if only my professor explained it
so clearly...
One other thing, do you know if there is an online calculator where I
could get similar results?

---

Clarification of Answer by livioflores-ga on 11 Oct 2005 11:08 PDT

Hi!!

Thank you for the good comments and rating.
Regarding to your request, I think that you will find the following
Excel file very useful:
"Bond Valuation":
http://www.studyfinance.com/templates/bondvaluation.xls


An useful online calculator is the following:
"Bond Price Calculator":
http://www.investopedia.com/calculator/BondPrice.aspx

For example you can calculate the Bond X price 4 years from now, use
the following inputs:
Par Value: 1000   
Settlement Date: today date
Maturity Date: same day 18 years from today date (remember that you
need to use the number of periods to maturity, in this case is
22-4=18)
Annual Rate: 13%  --> coupon rate
Yield: 8%
Redemption Value: 1000 (usually it is the same as par value)
Payments: check Annually

Result --> Price: $1,468.59 (the same figure that we found).

Hope this helps you.

Regards,
livioflores-ga

very through and clear