# PV of Bond Interest Payment & Principal Payment

Seems everyone is now busy commenting on the latest test results… I’ll need some real help here. Can someone refresh me of this? \$10,000 2006 bond due in 2021 with 10% coupon rate will pay \$500 every six months for its 15-yr life. PV of interest payment? PV of principal payment? Please show me the formula. I can’t recall it now. Thx much.

Is the PV of the interest payment 4713? And the PV of the principal payment I get -573… hrmmmm.

Interest: N=30 (twice a year for 15 years, from 2006 to 2021) I/Y=10%/2=5% PMT=500 FV=0 CPT PV = 7,686.23 Principal: 10,000- 7,686.23 = 2,313.77 Alternate for principal PV: N=30 I/Y=5% PMT=0 FV=10,000 CPT PV=2,313.77

I’ve calculated the same as map 1.

Thx map1 to show me the calculator steps and thx topher to verify the answer. What about to express in formulas? Is the below correct? PV (PMT) = PMT1/(1+i/2) + PMT2/(1+i/2) ^2 + PMT3/(1+i/2) ^3 + … + PMT30/(1+i/2) ^30 where PMT is the stream of interest payment and i is the coupon rate. And PV(PMT) is the price of the bond? What’s the formula for PV(Principal)?

Ah crap… i always forget to divide the interest rate!!!

Yes the formula is correct for the present value of the coupon payments. But no, PV (PMT) is not the price of the bond. The bond price will be the present value of all future cash flows which includes both coupon and principal payments. PV(Principal) = FV/(1+i/2)^30 = 10000/(1.05)^30 = 2313

I see. Feel much clearer now, thx topher. So Price of Bond = PV (PMT) + PV(Principal) ?

Yes, try for yourself: Remember map1’s answers. PV (pmt) = 7686.23 PV (principal) = 2313.77 Add them together and they equal \$10,000 exactly. This makes intuitive sense because if the bond is brand new and issued at par, it will cost \$10,000.

Cool!

hyang, where did u got this problem from , i mean q bank or end of reading

No. I decided to focus on the CFAI textbooks on my first round and then go to the supplement materials provided I can manage my time efficiently The problem actually appeared at Vol. 5 p. 172 Chapter of “Valuation of Alternative Investments”. The book did not go to details so I tried to refresh my mind in that little piece… By the way, regarding map1’s steps, I tried this morning and found I need to input negative value of PMT or FV to get the results. See below. Interest: N=30 (twice a year for 15 years, from 2006 to 2021) I/Y=10%/2=5% PMT=500 --> PMT=-500 FV=0 CPT PV = 7,686.23 Principal: 10,000- 7,686.23 = 2,313.77 Alternate for principal PV: N=30 I/Y=5% PMT=0 FV=10,000 --> FV=-10,000 CPT PV=2,313.77

i havent got calultor here and performed calculation on excel and got the same answer, however f.v cannot be -ve unless the there is an investment in future;in case of bond quite unlikely and payment too. what you will get negative is p.v

it’s a little hard to understand what you’re saying but i think you’re saying PV should be negative in the calculations. yes, it should but we are ignoring it.

got me right

You consider PMT and FV as distribution to bondholders. So from the standpoint of bond issuers, they are negative values.

you could say that . however when performing bond calculation you are looking from the view point of bond holder , who is buying the security( p.v is -ve, as it is a cash out flow) to get interest payments annually or semi annually (most cases unless zero coupon bond) and principal at the end of maturity

True. The direction is one way or the other. Cash inflow or cash outflow depending on where you stand.

i dont if my concern is unnecessary here. i think we assumed it is a par bond here, hence the calculation is pretty straightforward. otherwise, we need to get the price of the bond first. or is it just me thinking about this?

yes we assumed the bond is trading at par (coupon=yield) and yes the calculation is straight forward ; if you like to call it that way. basically discounted all the cash flow( coupons here) to thier present value i.e 500/1.05 … 500/(1.05) x ^y30= 7686.226. then obviously bond value is price - accumalated interest , i.e, 10000-7686.226= 2313