Question

Calculate the price of the following semi-annual bond: The bond pays a 10% coupon rate, has an annual yield to maturity of 7%, matures in 20 years and has a face value of $1,000.

Answer 1

• Price of a bond is the present value of all future cash flows from it discounted at a required rate of return. This required rate of return is the YTM.
• YTM is the yield the bond-holder earns when the bond is held till its maturity.
• The cash flows from a bond are periodic coupon payments and the redemption of face value on maturity.
• Interest is always paid on par value: $1,000 × 5% = $50
  • Annual coupon rate = 10%. Since coupon payment is semi-annual, rate per period of 6 months = 10% ÷ 2 = 5%
• When cash flows are non-annual convert the years to maturity into periods.
• Therefore, there are 40 periods (20 years × 2 periods of 6 months)
• The YTM of the bond is the required rate of return or market rate of interest ‘i’ = 3.5%
  • Annual YTM = 7%; YTM for 6 months = 7% ÷ 2 = 3.5%
• Bond cash flows are discounted using this discount rate.
• Bond interest payments are in the form of annuities. So PVAF for 3.5%, 40 time periods is used to discount interest cash flows.
• Principal should be discounted using PV factor for 40^th period, 3.5%
  • 

Time period	Description	Cash flow ($)	×	PV Factor or PVAF	=	Present Value ($)
1 – 40	Interest	50.00	×	21.355072	=	1,067.7536
40	Principal	1,000.00	×	0.252572	=	252.572
PRICE OF THE BOND						1,320.33