Question

Roland Music Company produces and exports musical instruments to Spanish orchestra. The company received an order of 500 violins, 100 pianos and 30 Bass units in December, 2008. The company needs to supply the order in the end of 2009. The order will be recurring for a period of 7 years. The company has decided to finance the production by the issuance of 3 serial bonds with following details:

Bonds	Serial #	Face Value	Coupon Rate	Issued on	Maturity
Bond A	A-356	$500,000	11%	Jan 01, 2009	Dec 31, 2015
Bond B	B-291	$300,000	12.5%	Jan 01, 2009	Dec 31, 2016
Bond C	C-074	$200,000	14%	Jan 01, 2009	Dec 31, 2017

REQUIRED: Calculate the following:

1. The value of each bond 3 years before maturity assuming YTM to be 12%.
2. The total payment to be made by the company on Dec 31, 2015, 2016 and 2017.
3. Brief the benefit of issuing serial bonds.

Answer 1

(i) Calculation of value of each bond 3 years before maturity assuming YTM to be 12%.:

The value of a bond is the present value of -

(a) the coupons to be received throughout the life of a bond

(b) and the repayment of principal at the maturity

For calculating pv of coupons we can use formula of present value of annuity as given below and for calculating pv of principal we shall use normal discounting formula

PV of coupons = Coupons*PV factor of annuity@12% for n periods.
As we have to calculate the value of bond 3years before the maturity so n for each bond shall be 3 years.

PV factor of annuity= [(1+r)^{^n}-1] / [(1+r)^{^n}*r]

Bond A = 1.12^{^3}-1 / 1.12^{^3}*.12

=2.401831

Bond B=1.12^{^3}-1 / 1.12^{^3}*.12

=2.401831

Bond C = 1.12^{^3}-1 / 1.12^{^3}*.12

=2.401831

PV of $1 to be received at maturity= 1/(1+r)^{^n}

Bond A = 1/1.12^{^3}

=.71178

Bond B = 1/1.12^{^3}

=.71178

Bond C = 1/1.12^{^3}

=.71178

Now

Value bond =PV of coupons + PV of Principal

(A) = (2.401831*55000)+(.71178*500000)

=132100.7+355890.1

=487990.8

(B) =2.401831*37500 + 300000*.71178

=90068.67+213534.1

=303602.7

(C) =2.401831*28000 + .71178*200000

= 67251.28+142356

=209607.3

(ii) Calculation of the total payment to be made by the company on Dec 31, 2015, 2016 and 2017.

At the maturity the company is required to repay the principal amount and the coupon due at the date of maturity

Bond A =500000+55000

=555000

Bond B= 300000+37500

=337500

Bond C = 200000+28000

=228000

(iii) Benifits of issuing serial bond:

In case of serial bond instead of issuing a single bond the issuer issues more than one bond with diffrent serial numbers and maturity. The benifit of iisuing such kind of bond is that company has to repay the principal in many installments instead of repaying it lumpsum at single maturity. The company starts earning from the project and gradually it starts the repayment of the bond. In our example we can see that the company is repaying BOND A, BOND B, BOND C at the end of year 6,7,8 respectively.

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