Investments: Analysis and Behavior. Chapter 15- Bond Valuation. ©2008 McGraw-Hill/Irwin. Learning Objectives. Calculate the value of a bond Compute the yield offered by various bonds Measure the interest rate risk of bonds using duration and convexity
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Chapter 15- Bond Valuation
PV of Annuity (pmt, I, N) + PV (FV, I, N)
Where N = time to maturity
i= market interest rate
PMT = semiannual interest payment
FV = face value
When the market interest rate is less than the bond’s coupon rate, price is greater
than the face value (Sold at premium, bonds 2,4).
When the market interest rate greater than coupon rate, bond is sold at discount
(bonds 1, 3, 5).
N = 2 x 3 1/12 = 6.167 yrs
I/Y = 6% /2 = 3%
PMT = 25
FV = $1,000
PV = $972.23
Bond price = PV of Annuity (pmt, I, N) + PV (FV , I, N)
The bond pays $25 every six months.
The bond matures in 3 years and one month.
Price of the bond is $972.23.
What is the bond’s yield to maturity?
Using financial calculator
N= 6.167 PV = -972.23 PMT= 25 FV=1,000
i 3% (or 6% annually)
Example: Calculate duration for a 7.5% bond with 5 years to maturity and a yield of 6.75%.
% change in bond price = – 1 × % Yield change × modified duration
Example: given that duration is 4.3 yrs, if interest rates fall by 0.5% what is the change in the bond price?
Modified duration = 4.3 / (1.0337) = 4.16
% change in price= -1× (–0.5%)×4.16 = 2.08%
Compute the convexity for the 7.5% bond with 5 years to maturity and a yield of 6.75%.
– (–0.005)×4.16 + ½×21.49×(–0.005)2 = 2.11%.
(% change approximation using only duration was 2.08%)
A common stock pays a 35¢ dividend and has a price of $55/share.
The company also has 6% convertible bond selling at 118% of the par value, convertible into common at $50/share.
What is the conversion ratio, conversion value, and premium to convert?
The conversion ratio is $1,000/$50 = 20:1.
The conversion value is 20$55 = $1,100.
The premium to convert is $1,180 - $1,100 = $80.