Question

Complete the below table to calculate the price of a $1.2 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)

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

2. Maturity 10 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%.

Table values are based on: Amount Present Value Cash Flow Interest Principal Price of bonds

Answer 1

Solution

Computation of bond issue price for the given different scenarios:

Bond value = $1,200,000

1. Maturity 10 years, interest paid annually, stated rate 10%, effective market rate 12%:

Table Values are based on:
n=	10
i=	12%
Cash Flow	Amount	Present Value
Interest	$120,000	$678,000
Principal	$1,200,000	$386,400
Price of Bonds		$1,064,400

Computations –

Price of bond = PV of principal + PV of interest

PV of principal = $1,200,000 x (P/F, 12%, 10) = 1,200,000 x 0.322 = $386,400

PV of interest = $1,200,000 x 10% x (P/A, 12%, 10) = 120,000 x 5.650 = $678,000

Price of bond = 386,400 + 678,000 = 1,064,400

Discount on bonds payable = 1,200,000 – 1,064,400 = $135,600

2. Maturity 10, interest paid semi-annually, stated rate 10%, effective rate 12%:

Table Values are based on:
n=	20
i=	6%
Cash Flow	Amount	Present Value
Interest	$60,000	$688,200
Principal	$1,200,000	$374,160
Price of Bonds		$1,062,360

Computations –

semiannual periods, n = 10 x 2 = 20

Effective rate for semiannual periods = 12 x ½ = 6%

Price of bond = PV of principal + PV of interest

PV of principal = $1,200,000 x (P/F, 6%, 20) = 1,200,000 x 0.3118 = $374,160

PV of interest = $1,200,000 x 10% x 6/12 x (P/A, 6%, 20) = 60,000 x 11.470 = $688,200

Price of bond = 374,160 + 688,200 = $1,062,360

Discount on bonds payable = 1,200,000 – 1,062,360 = $137,640

3. Maturity 5 years, interest paid semi-annually, stated rate 12%, effective market rate 10%:

Table Values are based on:
n=	10
i=	5%
Cash Flow	Amount	Present Value
Interest	$72,000	$555,984
Principal	$1,200,000	$736,680
Price of Bonds		$1,292,664

Computations –

Price of bond = PV of principal + PV of interest

semiannual periods, n = 5 x 2 = 10

Effective rate for semiannual periods = 10% x ½ = 5%

PV of principal = $1,200,000 x (P/F, 5%, 10) = 1,200,000 x 0.6139 = $736,680

PV of interest = $1,200,000 x 12% x 6/12 (P/A, 5%, 10) = 72,000 x 7.722 = $555,984

Price of bond = 736,680 + 555,984 = 1,292,664

Premium on bonds payable = 1,292,664 - 1,200,000 = $92,664

4. Maturity 10 years, interest paid semiannully, stated rate 12%, effective market rate 10%:

Table Values are based on:
n=	20
i=	5%
Cash Flow	Amount	Present Value
Interest	$72,000	$897,264
Principal	$1,200,000	$452,280
Price of Bonds		$1,349,544

Computations –

Price of bond = PV of principal + PV of interest

semiannual periods, n = 10 x 2 = 20

Effective rate for semiannual periods = 10% x ½ = 5%

PV of principal = $1,200,000 x (P/F, 5%, 20) = 1,200,000 x 0.3769 = $452,280

PV of interest = $1,200,000 x 12% x 6/12 (P/A, 5%, 20) = 72,000 x 12.462 = $897,264

Price of bond = 452,280 + 897,264 = 1,349,544

Premium on bonds payable = 1,349,544 - 1,200,000 = $149,544

5. Maturity 10 years, interest paid semiannully, stated rate 12%, effective market rate 12%:

Table Values are based on:
n=	20
i=	6%
Cash Flow	Amount	Present Value
Interest	$72,000	$825,840
Principal	$1,200,000	$374,160
Price of Bonds		$1,200,000

Computations –

Price of bond = PV of principal + PV of interest

semiannual periods, n = 10 x 2 = 20

Effective rate for semiannual periods = 12% x ½ = 6%

PV of principal = $1,200,000 x (P/F, 6%, 20) = 1,200,000 x 0.3118 = $374,160

PV of interest = $1,200,000 x 12% x 6/12 (P/A, 6%, 20) = 72,000 x 11.470 = $825,840

Price of bond = 374,160 + 825,840 = 1,200,000

bonds payable are at par as maturity value equals issue price, 1,200,000 - 1,200,000 = 0