# 11 - FIN 300 Fundamentals of Finance Bonds Pt.2 Chapter 8 1...

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FIN 300 Fundamentals of Finance Bonds Pt.2 Chapter 8 1 FIN 300 - Bonds Pt. 2

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Price vs. Yield FIN 300 - Bonds Pt. 1 2 Bond Trades at: Price: Coupon Rate vs. YTM Premium Price > Par (or, Face) Coupon Rate > YTM Par Price = Par (or, Face) Coupon Rate = YTM Discount Price < Par (or, Face) Coupon Rate < YTM Back to this chart………
Price vs. Yield The price of a bond is just the present value (PV) The yield (YTM) of a bond is, in effect, just the discount rate So, if the yield (discount rate) goes up, the price (PV) goes down And, if the yield goes down, the price goes up Price and yield move in opposite directions Note: This applies to all bonds – not just coupon- paying bonds! FIN 300 - Bonds Pt. 2 3

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Maturity and Price Changes Now, let’s revisit our previous example of the coupon-payer over 3 different YTM’s 10-year, semiannual, 10% coupon, \$1000 face, and YTM=9%, 10%, and 11% FIN 300 - Bonds Pt. 2 4 Price Yield \$1065.04 9% \$1000 10% \$940.25 11%
Maturity and Price Changes Now, let’s re-do the entire example However, the bond’s maturity is now 5 years, instead of 10 years The only change is that the N=10 (5yr. x 2 semi- annual coupon periods/yr.) – all other inputs stay the same FIN 300 - Bonds Pt. 2 5

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Maturity and Price Changes FIN 300 - Bonds Pt. 2 6 𝑌𝑌𝑌 = 11%: 𝑃𝑃𝑃𝑃𝑃 = \$50 0 . 055 1 1 1+0 . 055 10 + \$1000 1+0 . 055 10 = \$962.31 𝑌𝑌𝑌 = 10%: 𝑃𝑃𝑃𝑃𝑃 = \$50 0 . 05 1 1 1+0 . 05 10 + \$1000 1+0 . 05 10 = \$1000 𝑌𝑌𝑌 = 9%: 𝑃𝑃𝑃𝑃𝑃 = \$50 0 . 045 1 1 1+0 . 045 10 + \$1000 1+0 . 045 10 = \$1039.56
Maturity and Price Changes Yield Price (10-year Maturity) Price (5-year Maturity) 9% \$1065.04 \$1039.56 10% \$1000 \$1000 11% \$940.25 \$962.31 FIN 300 - Bonds Pt. 2 7 Semi-annual, 10% coupon, \$1000 face: What does this say about the risk of owning longer maturity bonds? Note the wider price variation at the longer maturity!

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Maturity and Bond Price All else being equal Longer maturity bonds will exhibit a greater change in price for the same change in YTM!
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