Question

Pricing bonds with spot rates: A four-year default-free annual-pay coupon bond is priced at 100 percent of par. What is its coupon (in percent of par) if annual spot rates are as follows: r1 = 1.86%, r2 = 2.33%, r3 = 2.58%, r4 = 2.53% Carry intermediate calcs. to four decimals. Answer to two decimals.

Answer 1

Price=Sum of Present value of all cash flows

Let par be 100

=>Price=100

Let coupon rate be c
=>Coupon=c

100=c/1.0186+c/1.0233^2+c/1.0258^3+c/1.0253^4+100/1.0253^4

=>c=(100-100/1.0253^4)/(1/1.0186+1/1.0233^2+1/1.0258^3+1/1.0253^4)

=>c=2.524103872

So, coupon rate is 2.524103872% of par