Asset Valuation: Bonds

Chapter 8

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.

Example:

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.

For example:

coupon =
.08 •
$1,000 = $80

The
Bond Valuation equation:

P_{bond} = coup (PVIFAK_{d,
N}) + Mat (PVIFF_{d, N})

K_{d} = the required
return on the bond

N = number of periods until
maturity

Example

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%.

Solution

P_{bond}
= $70 (PVIFA_{5, 10%}) + $1000 (PVIF_{5, 10%})

P_{bond}
= $70 (3.7908) + $1000 (.6209)

P_{bond
}= $886.27

Double
the number of periods, divide the required return and interest payment by 2.

Example

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%?

Solution

P_{bond}
= $35 (PVIFA_{10, 5%}) + $1000 (PVIF_{10, 5%})

P_{bond
}= $35 (7.7217) + $1000 (.6139)

P_{bond
}= $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.

TABLE
8.2 Price of $1,000 Par,

10% Coupon Bond with Different Maturities and Market Interest Rates

Market Rate

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 - P___{0}__)/N__

(Par + 2(P_{0})/3

Example

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?

Solution

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?

Solution

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.