Question

Complete the below table to calculate the price of a $1.4 million bond issue under each of the following independent assumptions (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.):

1. Maturity 15 years, interest paid annually, stated rate 10%, effective (market) rate 12%
2. Maturity 15 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%
3. Maturity 5 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%
4. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%
5. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%

n= i=
interest(ampunt & present value)
Principal (amount & present value)

=price of bonds

Answer 1

Note :

Price of bonds (Annually) = Stated Int Amt * [ PVIFA _{i , n}] + Principal  * [ PVIF_{i , n}]

Price of bonds ( Semi Annually) = Semi-Stated Int Amt * [ PVIFA _{i /2 , n*2}] + Principal  * [ PVIFi /2 , n*2]

Answer 1 :  Maturity 15 years, interest paid annually, stated rate 10%, effective (market) rate 12%

Particular	Present Value ($)
n= 15 years i=12 %
Interest : Amount = $1400,000 * 10 % = $140,000 PV = $140,000 * PVIFA 12 % ,15 years =  $140,000 * 6.8109	953,526
Principal : Amount =  $1400,000 , PV = $140,000 * PVIF12 % ,15 years =  $1,400,000 * 0.1827	255,780
Price of bonds	1,209,306

Answer 2 :  Maturity 15 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%

Particular	Present Value ($)
n= 30 years i=6 %
Interest : Amount = $1400,000 * 5 % = $70,000 PV = $140,000 * PVIFA 6 % ,30 years =  $70,000 * 13.7648	963,536
Principal : Amount =  $1400,000 , PV =$1400,000 * PVIF 6 % ,30 years =  $1400,000 * 0.1741	243,740
Price of bonds	1,207,276

Answer 3 :  Maturity 5 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%

Particular	Present Value ($)
n= 10years i=5 %
Interest : Amount = $1400,000 * 6% = $84,000 PV = $140,000 * PVIFA5 % ,10 years =  $84,000 * 7.7217	648,622.80
Principal : Amount =  $1400,000 , PV =$1400,000 * PVIF 5 % ,10 years =  $1400,000 * 0.6139	859,460
Price of bonds	150,5082.80 or 150,5083

Answer 4 :  Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%

Particular	Present Value ($)
n= 20 years , i = 5 %
Interest : Amount = $1400,000 * 6% = $84,000 PV = $140,000 * PVIFA5 % ,20years =  $84,000 * 12.4622	1,046,824.80
Principal : Amount =  $1400,000 , PV =$1400,000 * PVIF 5 % ,20 years =  $1400,000 * 0.3769	527,660
Price of bonds	1,574,484.80 or 1,574,485

Answer 5 :   Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%

Particular	Present Value ($)
n= 20 years , i = 6 %
Interest : Amount = $1400,000 * 6% = $84,000 PV = $140,000 * PVIFA6 % ,20years =  $84,000 * 11.4699	963,471.60
Principal : Amount =  $1400,000 , PV =$1400,000 * PVIF6 % ,20years =  $1400,000 * 0.3118	436,520
Price of bonds	1,399,991.60 or 1400,000 (aaprox)