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Bond pricing using zero coupon bonds

A 7% annual coupon bond (face value $1,000), with three years left till maturity is selling for $986.90. Zero-coupon bonds of 1, 2, 3 years maturity (all with face value of $1,000) sell for $950, $900, $820,respectively. Is this coupon bond properly priced? If not, show an arbitrage transaction to profit $2000 (today) from the mispricing.

I'm not given the market interest rate, and struggling with BA2 plus on this one. Please help.

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Please see the attached file:
A 7% annual coupon bond (face value $1,000), with three years left till maturity is selling for $986.90.Zero-coupon bonds of 1, 2, 3 years maturity (all with face value of $1,000) sell for $950, $900, $820,respectively. Is this coupon bond properly priced? If not, show an arbitrage transaction to profit $2000(today) from the mispricin.

We can price the coupon bond using the discount factor (present value factor) derived from the zero- coupon bonds

Zero coupon bonds
Face Value= $1,000
Present value factor
1 year $950 0.95 =$1,000 / $950
2 year $900 0.90 =$1,000 / $900
3 year $820 0.82 =$1,000 / $820

Now that have got the discount factor we can price the coupon bond

Face Value = $1,000
Coupon = 7% = 7.% x $1,000
Annual interest ...

Solution Summary

Prices a coupon bond using zero-coupon bonds and exploits an arbitrage opportunity because of mispricing.

$2.19