FIN 300 Bonds Pt 2 16 Example Zero Coupon Price Use lump sum TVM formula 1 1

# Fin 300 bonds pt 2 16 example zero coupon price use

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FIN 300 - Bonds Pt. 2 16
Example – Zero Coupon Price Use lump-sum TVM formula 𝑃𝑃 = 𝐹𝑃 1 + 𝑃 𝑛 𝑃𝑃𝑃𝑃𝑃 = 𝐹𝑎𝑃𝑃 𝑃𝑎𝑉𝑉𝑃 1 + 𝑌𝑌𝑌 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑛 𝑚𝑚𝑦 . FIN 300 - Bonds Pt. 2 17 𝑃𝑃𝑃𝑃𝑃 = \$100,000 1 + 0.10 5 = \$62,092.13
Example – Zero Coupon Yield Given: 10-year maturity Face Value = \$10,000 Observed price = \$7,000 What is the YTM (yield-to-maturity) of this bond? Assume annual compounding FIN 300 - Bonds Pt. 2 18
Example – Zero Coupon Yield Solve for “i” in the lump-sum TVM formula 𝑃𝑃 1 + 𝑃 𝑛 = 𝐹𝑃 \$7,000 1 + 𝑌𝑌𝑌 10 = \$10,000 1 + 𝑌𝑌𝑌 10 = 10,000 7,000 = 1.428571 1 + 𝑌𝑌𝑌 = 1.428571 1 / 10 = 1.036311 𝑌𝑌𝑌 = 0.036311 = 3.6311% FIN 300 - Bonds Pt. 2 19
“Discount” Bonds If yields are positive, then zero-coupon bonds will trade at a discount (below par, or face) Therefore zero-coupon bonds are oft referred to as “deep discount” or “discount” bonds However, there are (granted, rare) exceptions to this – where yields may be negative Recent examples seen in the financial crisis where very short-term T-Bills traded at negative yields Fear causes investors to seek safety of T-Bills, the price is bid-up, and therefore yields go negative If you are desperate for safety – you will accept a guaranteed small loss – to avoid the risk of a greater loss elsewhere in the market FIN 300 - Bonds Pt. 2 20
Another Zero-Coupon Yield Example Given: Bond has a face of \$100 Bond matures in 2 years Bond trades in the market at a price of \$102 What is the YTM, assuming annual compounding? FIN 300 - Bonds Pt. 2 21
Another Zero-Coupon Example \$102 1 + 𝑌𝑌𝑌 2 = \$100 1 + 𝑌𝑌𝑌 2 = 100 102 = 0.980392 1 + 𝑌𝑌𝑌 = 0.980392 1 / 2 = 0.990147 𝑌𝑌𝑌 = 0.990147 1 = 0.009853 = −𝟎 . 𝟗𝟗𝟗𝟗𝟗 FIN 300 - Bonds Pt. 2 22 Note: Price > Face, so the investor expects to lose money, if held to maturity

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