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The 5.3 percent bond of Dan's Auto Parts has a face value o

Homewroklib Q&A #1268 - The 5.3 percent bond of Dan's Auto Parts has a face value o

The 5.3 percent bond of Dan's Auto Parts has a face value o

The 5.3 percent bond of Dan's Auto Parts has a face value of $1,000, a maturity of 12 years, semiannual interest payments, and a yield to maturity of 6.12 percent. What is the current market price of the bond? $945.08 5959.33 $931.01 $1,072.13 $912.40
 
The 5.3 percent bond of Dan's Auto Parts has a face value o

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Homeworklib: Your Answer

Current market price of the bond: $931.01
The 5.3 percent bond of Dan's Auto Parts has a face value o
  • The 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 he holds the bond till maturity.
  • The cash flows from a bond are periodic coupon payments and the redemption of face value on maturity.
  • In this question, cash flows are: semi-annual coupon payments & redemption value on maturity.
    • Coupon is always paid on par value: $1,000 × 2.65% = $26.5.
    • Annual coupon rate = 5.3%. Since coupon payment is semiannual, rate per period of 6 months = 5.3% ÷ 2 = 2.65%. (Conventionally, coupon rates for bonds are always expressed in per annum basis)
  • When Cash flows are non-annual convert the entire problem data into periods.
  • Thus, there are 24 periods (12 years × 2) (note: 2 periods per year, since coupon payments are semi-annual)
  • YTM for each period = 6.12% ÷ 2 = 3.06%
Instead of doing a lengthy calculation, this can be easily solved by finding the present value of annuity. (annuity being semi-annual coupon payments)
The 5.3 percent bond of Dan's Auto Parts has a face value o
PVAF = (1-(1.0306)-24)÷0.0306 = 16.8266
Now present value of semi annual coupon payments = $26.50 × 16.8266 = 445.9049
Present value of maturity value = $1,000 × PVF (24 periods, 3.06%) = $1,000 × 0.48511 = $485.11
Present value of all cash flows from the bond = $445.9049 + $485.11 = $931.01

Homeworklib: Your Answer #2

The 5.3 percent bond of Dan's Auto Parts has a face value o

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