An investor gathered the following information on three zero-coupon bonds: 1-year, $600 par, zero-coupon bond valued at $571 2-year, $600 par, zero-coupon bond valued at $544 3-year, $10,600 par, zero-coupon bond valued at $8,901 Given the above information, how much should an investor pay for a $10,000 par, 3-year, 6 percent, annual-pay coupon bond? A) $10,016. B) $10,000. C) $10,600. D) Cannot be determined by the information provided.

B

It’s A. I Simply calculated this by putting : PMT : 600 I/Y = 6% N = 3 FV =10,000 CPT->PV But what i got is just not in given options. How you calculated B? What am missing?

I believe the value of a 3 year bond will be the sum of the individual zero coupon bonds - so 8901 + 571 + 544 = 10016. CP

You need to calculate each spot rate and then discount each cash flow according to the spot rate curve. Spot 1: 600/(1+r1) = 571 Spot 2: 600/(1+r2)^2 = 544 Spot 3: 10,000/(1+r3)^3 = 8,901 Solve for each r Then discount each of the bond’s cashflows at the appropriate spot rate 6 / (1+r1) 6 / (1+r2)^2 106 / (1+r3)^3 Add the present values of each CF and you have the value of your bond.

cpk123 Wrote: ------------------------------------------------------- > I believe the value of a 3 year bond will be the > sum of the individual zero coupon bonds - so 8901 > + 571 + 544 = 10016. > > CP Thats right, since each coupon payment is $600. The last bond is equal to par + last coupon payment on the 10k bond. So in this case you don’t even need to do the calculation.

mcleod 600/571 = 1+r1 so 6/1+r1 = 5.71 similarly 600/(1+r2)^2 = 544 so 6/(1+r2)^2 = 5.44 and same way for the 3rd piece – it will be 89.01 so sum of the zeros = value of the bond so it will be 571 + 544 + 8901 = 10016 — choice A CP

Yeah, I was doing a quick calculation per $100 par and rounded down. Definitely A.

RDX Wrote: ------------------------------------------------------- > It’s A. > > I Simply calculated this by putting : > > PMT : 600 I/Y = 6% N = 3 FV =10,000 CPT->PV > > > But what i got is just not in given options. > Financial calculators are evil. Learn how to do all TVM questions without the old BAII Plus and it will make everything more intuitive.

Got it ! As YTM is missing, i need to get Spot Rate from the given data. McLeod81, “Thats right, since each coupon payment is $600. The last bond is equal to par + last coupon payment on the 10k bond. So in this case you don’t even need to do the calculation.” I didn’t get this. Can you please explain? thanks.

The bond in question is a 10,000 par bond. The coupon rate is 6%, meaning that each payment is $600. The bond itself is a series of cashflows: 3 coupon payments and one return of principle at maturity. Each individual cashflow is equivalent to a zero coupon bond with the same par value and the same maturity. So are cash flows are as follows: Year 1: 600 (coupon) Year 2: 600 (coupon) Year 3: 600 (coupon) + 10,000 (principle) You know that the price of a 600 cashflow one year from now (571), a 600 cashflow 2 years from now (544), and a 10,600 cashflow 3 years from now (8901) given the current spot rate curve. All you have to do in is add the value of each cash flow. The value of the 10,000 bond is just the sum of its individual cashflows (571 + 544 + 8901 = 10,016).

If they didn’t give you the market prices for bonds with par values equal to your cashflows, you would have to calculate each spot rate and use it to discount the cashflows.

thanks McLeod81 for explanation. The question was tricky indeed.

To see why CPK’s approach works, realize that the discount factor for each zero is just current price/par value. Then expand it out: (571/600)(600) + (544/600)(600) + (8901/10600)(10,000 + 600) there’s canceling for each component, so this becomes 571 + 544 + 8901 = 10,016