Asset Valuation: Bonds
The value of any investment: Is the present value of all future cash flows discounted at an interest rate that reflects the risk of the investment.
How would you find the value of a commercial building?
By computing the PV of the rental receipts net of expenses.
Bonds are valued like any other asset
Find the PV of the cash flows
The cash flows from a bond:
The equal annual interest payments (an annuity)
And the final lump sum payment at maturity.
The interest payment is found by:
Multipling the coupon interest rate by the bond’s face value.
coupon = .08 • $1,000 = $80
The Bond Valuation equation:
Pbond = coup (PVIFAKd, N) + Mat (PVIFFd, N)
Kd = the required return on the bond
N = number of periods until maturity
What is the value of a bond with 5 years to maturity if the coupon interest rate is 7% and it has a $1000 maturity value? Assume annual interest payments are made and the required return is 10%.
Pbond = $70 (PVIFA5, 10%) + $1000 (PVIF5, 10%)
Pbond = $70 (3.7908) + $1000 (.6209)
Pbond = $886.27
Double the number of periods, divide the required return and interest payment by 2.
What is the price of a bond if it pays interest semi-annually on a 7% coupon and if it has 5 years to maturity, a $1000 face amount and a required return of 10%?
Pbond = $35 (PVIFA10, 5%) + $1000 (PVIF10, 5%)
Pbond = $35 (7.7217) + $1000 (.6139)
Pbond = $884.18
As market interest rates rise and fall:
The value of the bond changes.
If interest rates increase, the value of the bond falls.
8.2 Price of $1,000 Par,
10% Coupon Bond with Different Maturities and Market Interest Rates
Term 9% 10% 11%
1 $1,009.17 $1,000.00 $991.00
10 1,064.18 1,000.00 941.11
20 1,091.28 1,000.00 920.37
As the time to maturity nears:
The value of the bond approaches par.
If the coupon rate on a bond is 8% and the market rate is 10%, the price of the bond must increase 2% to give the investor a fair return.
Yield to maturity:
Is the return an investor will earn if the bond is held until it matures
Solving for YTM:
Is difficult without a financial calculator
But can be estimated using the estimation equation
YTM = Coup + (Par - P0)/N
(Par + 2(P0)/3
What is the YTM for a bond with 5 years to maturity, an 8% coupon, $1000 par, and a current market price of $900.00?
YTM = 80 + (1000 - 900) / 5
[1000 + 2(900)] / 3
YTM = 10.71%
Calculator solution = 10.68%
Current Yield = coupon payment / market price
If the current market price is $900, and the coupon payment is $80, then what is the current yield?
CY = $80 / $900 = .0889 = 8.89%
The current yield:
The percentage return earned in a year from interest payments. The YTM also includes changes in the value of the bond.
Even though bonds are called “fixed income securities,” They are subject to significant price changes when interest rates are volatile.