Class 11 Completed

# K the market interest rate is 6 for similar bonds k

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K The market interest rate is 6% for similar bonds K The price of the bond is \$957.88 (see earlier example). K Now suppose that one year later, the yield-to-maturity for similar bonds has increased to 8%. K If an investor bought the bond one year ago at \$957.88 and sells it now, what is his realized rate of return (ROR)? 64 . 900 \$ ) 08 . 1 ( 000 , 1 08 . 0 ) 08 . 1 ( 1 50 4 4 1 = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = PV ROR ! = 50 957.88 + 900.64 " 957.88 957.88 = 5.22% + ( " 5.98%) = " 0.76% current yield+ %capital loss What happened? Interest rate risk! * Computing the ROR like this only works for one time period. See next slide for more.

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16 Converting ROR Formula for a one Period Investment K FYI: This is for those who are curious how I got from the one definition of the ROR to the other one. K The general formula for calculating the ROR is PV*(1+ROR) n = FV. For a one-period investment, where all cash inflows occur at the end of the period, we can use algebra to get the equation that says the ROR is equal to the current yield +/- %capital gain/loss. Using the numbers from the previous example, this is the math that gets you from the general formula to the one-period formula. PV ! (1 + ROR ) n = FV 957.88(1 + ROR ) = 50 + 900.64 957.88 + 957.88 ! ROR = 50 + 900.64 957.88 ! ROR = 50 + 900.64 " 957.88 ROR = 50 957.88 + 900.64 " 957.88 957.88 = 5.22% + ( " 5.98%) = " 0.76%
17 Example: ROR on Bond Investment (1) K You buy a corporate bond with 5 years to maturity. K The bond makes semi-annual coupon payments at a coupon rate of 8%. K You pay \$852.80 for the bond, implying a ytm of 12% K You hold the bond to maturity while re-investing the coupon payments in a savings account that pays 2% per year compounded semi-annually. K What is your realized rate of return (ROR)? K Hint: Need something that looks like PV*(1+r) n = FV Or P B *(1+ROR) n = FV(all cash flows associated with holding bond)

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18 Example: ROR on Bond Investment (2) K Timeline: 0 1 2 3 4 5 6 7 8 9 10 Periods K ----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|----- 40 40 40 40 40 40 40 40 40 40 1,000 K Want something that looks like K PV(1+ROR) n = FV K Or P B *(1+ROR) n = FV(all cash flows associated with holding bond) K What is the future value of the investment? Need FV of coupon payments using the re-investment rate of r semi = 1%: 4885 . 418 , 1 000 , 1 4885 . 418 000 , 1 01 . 0
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