Question

Assume that one-year discount rate is 3.8%, two-year discount rate is 4%, and three-year discount rate is 4.5% (all in annual terms). What is a fair market price of a bond that matures in three years, and pays annual coupons at the rate of 5.25%?

Answer 1

Note: Face Value is taken as $1000

Coupon = Face Value*Coupon Rate = 1000*5.25% = $52.5

Yield = 3 year Interest Rate = 4.5%

Period	Cash Flow	Discounting Factor [1/(1.045^year)]	PV of Cash Flows (cash flows*discounting factor)
1	52.5	0.956937799	50.23923445
2	52.5	0.915729951	48.07582244
3	52.5	0.876296604	46.00557171
3	1000	0.876296604	876.2966041
		Price of the Bond = Sum of PVs	1020.617233

Therefore, Fair Market Price = $1020.62 or 102.062% of Face Value