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# Bond pricing using zero coupon bonds

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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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#### Solution Preview

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