Introduction to Corporate Finance

Valuing BondsYTMDiscount rate that explains bond price i.e. the rate of interest when PV of cash flows becomes equal to priceConvenient way of summarizing bond characteristics

Ques 1 & 5A 10 year bond FV = 1,000 paying interest = 60 a year; if interest rates in market increase coupon rates will be same; price will fall ; YTM will rise3b. Bond Yield > Coupon means price < face value in comparing Coupon Amt / Price vs Coupon Amt / Face Value3c. Price more than 100 , so yield is lesserQues 2 Bond is selling at a discount i.e. Price < FV, YTM > Current Yield > Coupon Rate

Bond is selling at a premium i.e Price > FV,YTM < Current Yield < Coupon Rate

Bond is selling at par YTM = Current Yield = Coupon Rate

Spot Rates & Forward RatesSpot rate is the rate of interest between today and a point in future.

Forward rate is the rate of interest between a future date and another date beyond. It is markets best guess today about what future spot rate will be. It is a forecast of future spot rate between t-1 and t. It is observed today.

Future Spot Rates What actually they ; dont know ; dont observe How to calculate Forward Rates if Spot rates are givenExample :1 year spot rate is 5%2 year spot rate is 6%3 year spot rate is 7%4 year spot rate is 6%So, expected one year interest in one years time is (1.06)(1.06) / 1.05 1 Expected one year interest in two years time = (1.07)(1.07)(1.07) / (1.06)(1.06) -1Expected one year interest in three years time = (1.06)(1.06)(1.06)(1.06) / (1.07)(1.07)(1.07) - 1 Expected two year interest in one years time (1.07)(1.07)(1.07) = (1.05)(1+f) (1+f)Expected two year interest in two years time = (1.06)(1.06)(1.06)(1.06) = (1.06)(1.06)(1+f)(1+f) IN EQUILIBRIUM, investment in a series of short-maturity bonds must offer the same expected return as an investment in a single long maturity bond.

1 year spot rate = 2%2 year spot rate = 4%3 year spot rate = 3%4 year spot rate = 3%5 year spot rate = 4%Calculate 2 year rate in 3 years time,So: (1.04)(1.04)(1.04)(1.04)(1.04) = (1.03)(1.03)(1.03)(1+f)(1+f)Ans: 5.5%

If 6 months, 1 year, 18 months rates are given on annual basis, first divide by 2 to get semi annual rates. Multiply f by 2 to get final rateExample: 6 months: 2%1 year : 3%18 months : 3.5%2 years : 3.7%Calculate 18 month forward starting 6 months from today ? 4.26%

(1.085)(1.085)(1.085)(1.085) = (1.01)(1+f)(1+f)(1+f)Term Structure of Interest RatesPlot of r as a function of time you get a sense of future R are going to lie . This graph gives you yield curveUpward sloping i.e. the geometric average of all R increaseDownward sloping decrease in future

Yield Curve as of Oct 01, 2015

81.067.5471781.12367.11997281.1910166.71695481.2624776.3367491081.33822680.70388Price today108.4247One year hence:81.067.5471781.12367.11997281.1910166.7169541081.26247785.54612106.9302