ACCA Applied Skills · Financial Management · The valuation of debt and other financial assets
A bond pays a single redemption payment of $1,000 in three years and no coupons. The spot yield curve is: 1 year 3%, 2 years 4%, 3 years 5%. What is the bond's market value, to the nearest dollar?
The bond is worth $864. Because it pays only $1,000 in three years, it should be discounted at the three-year spot rate of 5%: 1,000 divided by 1.05 cubed, which is 1.157625, gives $863.84. Shorter-maturity rates would overstate its value.
- A$864Correct
- B$889
- C$926
- D$905
Explanation
A zero-coupon bond is discounted using the 3-year spot rate: 1,000 / 1.05^3 = 1,000 / 1.157625 = $863.84, which is $864. Using the 1-year rate gives 971; using the 2-year rate gives 925 (close to $926 option via 4%, 1,000/1.04^2). The $889 option uses 4% for three years (1,000/1.04^3 = 889).
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