OT: Need help from all you accounting/finance majors

shazbot

Senior member
Jul 25, 2001
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Ok, I've been looking at this stupid bonds problem for the past hour, and I can't figure out how the book is coming up w/ these figures. Say you have a $100,000 5 yr. bond w/ a contract rate of 8%, but the market rate is 10%. Therefore the bond has to sell at a discount. Now the book is saying the price is $97,277. My question is, HOW THE HELL did they come up w/ that number? Same thing goes for this premium question. $100k 5 yr. bond w/ a contract of 12%, but the market rate is 10%. The book says the issue price for these bonds is $107,720. How in gods name did they come up w/ these #'s? Nowhere did the book explain how to determine issue prices to account for the different b/t market & contract rates.
 

mithrandir2001

Diamond Member
May 1, 2001
6,545
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I can't duplicate their numbers but the formula goes like this:

Bond price = monthly coupon * PA(market rate/12, periods) + principle amount * PF(market rate/12, periods)

where PA = present value of a level annuity, PF = present value of a one-time cash flow

So in your first case:

Bond price = 667 * PA(0.83%, 60) + 100000 * PF(0.83%, 60)
Bond price = 31421.7 + 60899.53
Bond price = 92321.33

I'm assuming monthly interest payment and anything different would change the values.

For simplicity, if you want to assume annual interest payment only:

Bond price = 8000 * PA(10%, 5) + 100000 * PF(10%, 5)
Bond price = 30326.29 + 62092.13
Bond price = 92418.42

8000: 100000 * 8% contract rate
PA(10%, 5): 10% for the market rate, 5 for the number of payments (one a year, 5 years)
100000: bond principle
PF(10%, 5): same as for PA

I took an investment class in college about 8 years ago, so this is still a little rusty to me.
 

AaronP

Diamond Member
Feb 27, 2000
4,359
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gimme a few min's to get my brain working, I just woke up and still have some benadryl in my system
 

AaronP

Diamond Member
Feb 27, 2000
4,359
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I am using the TI BA II + calc and also gettin gthe 92,418 figure:

N = 5
I = 10
PMT = 8000
FV = 100,000

Compute PV and it spits out 92,418

and on the second question:

N=5
I=10
PMT = 12,000
FV = 100,000

compute PV and it comes up with 107,581.57
 

mithrandir2001

Diamond Member
May 1, 2001
6,545
1
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The bond is probably in the middle of its "term", hence the higher price. The pricing formulas above are only valid when the bond is first written.
 

NeoV

Diamond Member
Apr 18, 2000
9,504
2
81
present value calc's will get you straightened out.....

pay attention in class!
 

PeeluckyDuckee

Diamond Member
Feb 21, 2001
4,464
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oh, what do we have here, good 'ol accounting here eh. Now those questions sure look familiar, too bad they don't click no more :(

I remember doing the calculations by hand, to the whatever decimal place, awhile ago. No calculators :(