It seems a few steps are missing in these notes making it difficult to understand. Where did 13.5903 come from? Why are there different bond issue prices for different market prices when the bond was issued at a specific rate. How did we get 86,411 as the issue price etc etc?

A Firm issues bond of $100,000 for 10 years, the stated interest is 6%. The bond is due in ten years and interest is paid semiannually.

• The term bond has two parts: interest and face amount.

Issuing Price = Present value of the interest + Present value of the Face Value

Present value of the interest= Interest paid each time x Annuity Present Value Factor

Present value of the Face Value = Face Value x Present Value Factor

If interest paid semiannually

The interest rate the half of the stated rate(6% /2=3%)

The period is double the number of years(10x 2 = 20)

• If the market rate is 8%

Interest Payment is$100,000 * 6% /2= 3,000

Because it is semiannual bond, paid for 20 times

Market Rate is 8% , the half year rate is 4%

Present value of the interest= Interest paid each time x Annuity Present Value Factor

= 3,000 x 13.5903= 40,771(4%, 20 terms Annuity Present Value Factor is 13.5903)

Present value of the Face Value = Face Value x Present Value Factor

=100,000 x 0.4564= 45,640(4%, 20 terms Present Value Factor is 0.4564)

Issuing Price = Present value of the interest + Present value of the Face Value

=40,771+45,640=86,411

• If the market rate is 8%(Look up tables with 4%, 20 terms)

Issuing Price = Present value of the interest + Present value of the Face Value

= 3,000 x 13.5903+ 100,000 x 0.4564

= 86411

• If the market rate is 6%(Look up tables with 3%, 20 terms)

Issuing Price = Present value of the interest + Present value of the Face Value

= 3,000 x 14.8775+ 100,000 x 0.5537

= 100,000

• If the market rate is 4%(Look up tables with 2%, 20 terms)

Issuing Price = Present value of the interest + Present value of the Face Value

= 3,000 x 16.3514+ 100,000 x 0.6730

= 116354