Question

You are a trader from Fortress Investments, and your boss tells you: “Price this 30 year bond that they are offering us, having an 8.75% coupon rate, and Par Value (i.e. Face Value) of $1,000. The market rate is 3.25%. If the bond offers quarterly coupon payments, what should we pay for this bond today?” – Assume no transaction costs. (Hint: Use Excel’s PV function, and the annuity discounting formula for pricing this bond – please show all steps as

Answer 1

FV = Future Value or Face Value = 1000

R = Rate = Market rate /4 = 3.25% / 4

N = Nper = Total number of coupon periods = 30 years x 4 quarters = 120

PMT = Coupon Payment = 8.75%/4 = 21.875

Bond price today - Using excel PV function > =PV(Rate/4,Nper,-PMT,-FV)

Bond price today - Using excel PV function > =PV(3.25%/4,120,-21.875,-1000) = $2,051.4625

Alternatively, bond price can be calculated as follows:

PV or Price of Bond = (PMT x ((1-((1+R/4)^-N)) / R/4) + (FV/(1+R/4)^N)

Price of the bond = 21.875*((1-((1+3.25%/4)^-120))/(3.25%/4))+(1000/(1+3.25%/4)^120)) = $2,051.4625