>> There are two values of a bond we need to be aware of and being able to calculate.
The first is the book value of bonds.
This is the amount reported on a balance sheet
and is based on the face value of bonds.
The second is the market value of bonds,
this amount is based on the market price of bonds.
You're going to learn how to calculate both.
The book value of bond is easy to determine.
It's the number of bonds times the face value per bond.
For example, the Smiths issued 10,000 bonds.
The face value is $1,000 per bond,
thus the total book value is then $10 million,
which is 10,000 bonds times $1,000 dollars per bond.
The market value is less simple to calculate.
The market value is the present value of expected cash flows
discounted at the market rate of interest.
Bonds have to cash flow streams that must be discounted.
The first is the principal amount that is repaid to investors when the bond matures.
The other is the periodic interest payments.
Thus the market value is affected by three things:
the amount and timing of future cash flows,
the risk and uncertainty of those cash flows,
and the rate of return investors require to buy the bonds.
In order to calculate the present value of the bonds,
let's revisit the present value formula in Excel.
It is equals PV(rate,nper,-pmt,-fv).
Let's apply the bond information to this formula.
Rate is the market rate,
nper is the number of interest periods until maturity,
PMT is the amount of a semi-annual interest payment,
and FV is the face value of the bond at maturity.
Let's look at an example.
The Smiths issue 10,000 bonds with a face value of $1,000 per bond.
When the market rate for bonds of similar risk is six percent,
the stated rate of the bonds is five percent,
the bonds are issued for 10 years.
So we're going to use the Excel formula for present value.
To start with, what is the rate?
The annual market rate of interest is six percent.
Since the bonds pay interest semi-annually,
we need to divide this rate in half.
So the rate is three percent.
Next, let's determine the number of interest payment periods.
The term of the bond is 10 years,
But since bonds pay interest semi-annually,
we need to double the years,
so nper is 20.
The interest payment is based on the stated rate,
it's the stated rate times the face value.
In this example, that's 5 percent times $1,000 equals $50 per year, per bond.
Since the bonds pay interest semi-annually,
we need to half this amount.
So PMT equals $25,
and this needs to be a negative amount.
Finally, the future value is the face value of the bond at maturity.
In this example, it is $1,000.
So FV is 1,000,
and this needs to be a negative amount when solving for present value.
So the price of the bond is $925.61 per bond.
This means the total market value of 10,000 bonds times $925.61 per bond
equals $9,256,100.
You might recall from accounting that since this amount is less than the book value,
we say that these bonds were issued at a discount.