Question

You want to buy a $1000 face value US treasury bond with a maturity of three years. The coupon rate is 7% (with annual interest payments). The yield to maturity is 6%.

A. What is the basic cash flow formula for calculating the present value of any generic three year bond?

B. Using the answer to above part A, insert the specific bond information above into it and calculate its present value.

C. What are the bond valuation formulas you would use to value a generic three year bond if you wanted to utilize an annuity formula?

D. Using the answer to above part C, insert the specific bond information from part C and calculate present value.

Answer 1

A. Yearly Interest payment=1000*7%=$70, yield=6%, face value=$1000, nper=3

Hence, present value of any three year generic bond= 1st year interest/(1+yield)+2nd year interest/(1+yield)^2+3rd year interest/(1+yield)^3+Face Value/(1+Yield)^3

B. Using the above formula Present Value= 70/(1+6%)+70/(1+6%)^2+70/(1+6%)^3+1000/(1+6%)^3=$1026.73

C. In terms of annuity formula for bond= C×[1−(1+i)^(-n)​]/i +FV/(1+i)^n (Here C= Annual interest,i =yield, n=tenure)

D. Using the above formula present value of bond= 70*((1-(1+6%)^(-3))/6%+1000/(1+6%)^3=$1026.73