Question

A company issued 6%, 10-year bonds with a face amount of $65 million. The market yield for bonds of similar risk and maturity is 7% Interest is paid semiannually. At what price did the bonds sell? (FV of $1. PV of $1. FVA of $1. PVA of $1. FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Enter your answers in whole dollars. Round final answers to the nearest whole dollar.) Table values are based on: Amount Present Value Cash Flow Interest Principal Price of bonds

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 provided 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 rates are conventionally stated per annum. Therefore, the given interest rate is 6% per annum.
• Interest is always paid on face value: $65,000,000 × 3% = $1,950,000
  • Annual coupon rate = 6%. Since coupon payment is semi-annual, rate per period of 6 months = 6% ÷ 2 = 3%
• When Cash flows are non-annual convert the entire problem data into periods.
• Thus, there are 20 periods (10 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 an annuity. So PVAF i = 3.5%, n = 20 can be used to discount interest cash flows.
• Principal should be discounted using PV factor: n =  20; i = 3.5%
• 
  1-(1 + i)- Present Value Annuity Factor PVAF = — • . i = interest rate per period = 3.5% n = number of periods = 20 PVAF – 1-(1+0.035)-20 = 14.2124033 0.035 1 PV factor = (1 + i)n i = interest rate per period = 3.5% n = number of periods = 20 PVF = (1+0.035)20 = 0.50256588
  
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  Present Value Time period 1-20 ($) Cash flow Description ($) Interest 1,950,000 Principal 65,000,000 PRICE OF THE BOND PV Factor or PVAF 14.2124033 0.50256588 20 x 27,714,186 32,666,782 60,380,968