Question

	(1)	(2)	(3)	(4)
Face value	$190,000	(d)	$280,000	$1,950,000
Stated rate	12%	4%	6%	(i)
Interest payment period	Quarterly	Semiannually	Quarterly	Quarterly
Interest payment	(a)	$10,400	$4,200	$19,500
Maturity (in years)	10 years	3 years	6 years	4 years
Market rate	8%	(e)	16%	8%
Bond issue price	(b)	(f)	(g)	(j)
(Discount)/premium	(c)	$(60,837)	(h)	(k)

Fill in the missing items for each of the cases​ below:

Answer 1

Ans 1.

a) Interest Payment = $ 190,000 * 3% = $ 5,700

b) Bond Issue Price = $5,700 * PVAF(2%,40) + $190,000 PVIF(2% ,40)

= $5,700 * 27.3554 +$190,000* 0.4529

= $155,926.23 +$86,051 = $241,977.23

c) Premium = 241,977.23 - $190,000 =$ 51,977.23

2.

d) Face Value = $10,400/2% = $ 520,000

f) Bond Issue Price = 520,000 - 60,837 = $459,163

e) Market Rate = 4.25 * 2 = 8.5% exactally (By hit and trial method)

or we can calculate it by formula r = ( I + ( F-P )/ n )/ {(F + P)/2}

Where,

I = Periodic Interest Amount

F = Redemption Amount

P = Current Market Price

n = Remaining Period to maturity

r = Periodic market Interest rate to be converted into annual

r = {$10,400 + ( $520,000- $459,163 )/ 6 }/ {($520,000 + $ 459,163)/2} = ($10,400+$10,139.5)/$4,89,581.5 =

$ 20,539.5/$ 4,89,581.5 = 0.041953 or 4.2% (approx.) and annual rate is 4.2 * 2 =8.4%

3.

g) Bond Issue Price =$ 4200 * PVAF (4%,24) + $ 280,000 * PVIF (4%,24)

= $ 4,200 * 15.24696 + $ 280,000*0.39012

=$ 64,037.23 + $ 109,233.6

=$ 173,270.83

h) Discount = $173,270.83 - $ 280,000 = - $106,729.17

4.

i) Stated Rate =( $ 19,500/ $ 1,950,000 )* 100 = 1% (for 1 Quarter)

Yearly Stated rate = 4 * 1% = 4%

j) Bond Issue Price = $ 19500 * PVAF (2%,16)+$ 1,950,000* PVIF (2%,16)

= $ 19,500 * 13.57771 +1,950,000 * 0.72845

=$ 264,765.345 + $ 1,420,477.5

= $ 1,685,242.845

k) Discount =$ 1,685,242.845 - $ 1,950,000 = - $ 264,757.155