Present value of annuity problem?
A year 6, $ 1.000 IBM bond pays interest of $ 80 per year and currently sells for $ 950. What are its coupon rate, current yield and yield to maturity?
coupon rate = 80/1000 = 8% current yield = 80/950 = 8.42% YTM – use mortgage calculator, n = 8 = pv-950-PMT = 80-vf = 1000-I / Y (YTM) =? = 8.9% proof that YTM = 8.9% 80/1.089 ^ 1 + 80/1.089 ^ 2 + 80/1.089 ^ 3 + 80/1.089 ^ 4 + 80/1.089 ^ 5 + 80/1.089 ^ 6 + 80/1.089 ^ 7 + 1080/1.089 ^ 8 = 950 yield to maturity is the discount rate at which all flows future cash flows are discounted to arrive at the current value. In this case, if you discount all future cash flows at 8.9% in the number of years that are out in the future, we arrive at a present value of $ 950. Please note the payment in year 8 (1080/1.089 ^ 8). This amounts to $ 1.080 because you get your payment of $ 80 of interest the nominal value of $ 1000 back.
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