Question

Complete the below table to calculate the price of a $1.5 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 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%.

Answer 1

Given Information,

Bond= $1.5 million

Calculation of Price of $1.5 million Bond under following 5 assumptions independently

Assumption 1:Maturity 15 years, interest paid annually, stated rate i.e Interest Rate 10%, effective (market) rate i.e Discount Rate12%.

Years	Particulars	Cashflow	Discounting factor@12%	Discounted Cash Flow
1-15 years	Coupon payment @10%	$150,000	6.8108	$1,021,620
15 year	Redemption value	$1,500,000	0.1826	$273,900
	Price of Bond			$1,295,520

Price of Bond under Assumption 1 is  $1,295,520

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

Note: When Interest is payable Semiannually,divide Rate of return /discount & rate of Interest by 2 & multiply number of years by 2.

Years	Particulars	Cashflow	Discounting factor@6%	Discounted Cash Flow
1- 30 year	Coupon payment @10%/2=5%	$75,000	13.7648	$1,032,360
30 year	Redemption value	$1,500,000	0.1741	$261,150
	Price of Bond			$1,293,510

Price of Bond under Assumption 2 is  $1,293,510

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

Note: When Interest is payable Semiannually,divide Rate of return /discount & rate of Interest by 2 & multiply number of years by 2.

Years	Particulars	Cashflow	Discounting factor@5%	Discounted Cash Flow
1- 10 year	Coupon payment @12%/2=6%	$90,000	7.7217	$694,953
10 year	Redemption value	$1,500,000	0.6139	$920,850
	Price of Bond			$1,615,803

Price of Bond under Assumption 3 is  $1,615,803

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

Note: When Interest is payable Semiannually,divide Rate of return /discount & rate of Interest by 2 & multiply number of years by 2.

Years	Particulars	Cashflow	Discounting factor@5%	Discounted Cash Flow
1- 20 year	Coupon payment @12%/2=6%	$90,000	12.4622	$1,121,598
20 year	Redemption value	$1,500,000	0.3768	$565,200
	Price of Bond			$1,686,798

Price of Bond under Assumption 4 is $1,686,798.

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

Note: When Interest is payable Semiannually,divide Rate of return /discount & rate of Interest by 2 & multiply number of years by 2.

Years	Particulars	Cashflow	Discounting factor@6%	Discounted Cash Flow
1- 20 year	Coupon payment @12%/2=6%	$90,000	11.47	$1,032,300
20 year	Redemption value	$1,500,000	0.3118	$467,700
	Price of Bond			$1,500,000

Price of Bond under Assumption 5 is  $1,500,000.

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