Question

On1 july 2018 bmw ltd issues $2 million in 10 year debentures that pay interest each six month at coupon rate of 10%.at the time of issuing the securities, the market requires a rate of return of 12 per cent.interest expense is determined using the effective interest method.

Formula for PV of $1in n periods =1/(1+k)n

Formula for present value of annuity of $1 per period for n periods =1-1/(1+k)n

Where k is the discount rate expressed in decimal

Required:

1. Determine the issue price of the debentures.

2.provide the journal entries at 1 july 2018 and 30 june 2019.

Answer 1

1) Issue price of bond=Present Value of Face value+Present value of Coupon payments

Present Value of Face Value:

Present Value (P)=C/{[(1+r)^n]}

Where,

C=Future Value= 2000000

r=ROI= 0.06

n=No. of periods= 20

Now putting values in formula,

= 2000000/{[(1+ 0.06)^20 ]}

= 2000000/{[( 1.06)^20 ]}

= 2000000/{[ 3.20714 ]}

= 623609.4538

Present Value of coupons:

Present Value of Annuity Factor(P)=A{1-[(1+r)^-n]/r}

Where,

A=Annuity Amount= 100000

r=ROI= 0.06

n=No. of periods= 20

Now putting values in formula,

= 100000{1-[(1+ 0.06)^-20 ]/ 0.06}

= 100000{1-[( 1.06)^-20 ]/ 0.06}

= 100000{1-[ 0.3118 ]/ 0.06}

= 100000{ 0.6882 / 0.06}

= 100000{ 11.46992}

= 1146992.12186

Thus Value of bond=623609.453+1146992.122=$1,770,601.575

2)

In the books of M/s BMW Ltd	Journal	.	.
Date	Particulars	Dr($)	Cr($)
1 Jul 2018	Cash	1,770,601.58
	Discount on bonds payable		229,398.42
	To Bonds Payable		2,000,000
	(being bonds issued at discount)
30 Jun 2019	Interest Expense	106,236
	To discount on bonds payable		6,236
	To cash		100,000
	(Being Interest on bonds paid and discount amortised)

A	B	C	D	E	F	G
DATE	INT PAYMENT(FACE VAL*4%)	INTEREST EXPENSE(PREVIOUS BOOK VAL IN G*5%)	AMORTISATION(C-B)	BALANCE IN DISCOUNT(PREV VALUE-D)	FACE VALUE	BOOK VALUE(PREV VALUE+D)
Coupon Payment				229398	2000000	1770602
1	100000	106236	6236	223162	2000000	1776838
2	100000	106610	6610	216552	2000000	1783448
3	100000	107007	7007	209545	2000000	1790455
4	100000	107427	7427	202118	2000000	1797882
5	100000	107873	7873	194245	2000000	1805755
6	100000	108345	8345	185900	2000000	1814100
7	100000	108846	8846	177054	2000000	1822946
8	100000	109377	9377	167677	2000000	1832323
9	100000	109939	9939	157737	2000000	1842263
10	100000	110536	10536	147202	2000000	1852798
11	100000	111168	11168	136034	2000000	1863966
12	100000	111838	11838	124196	2000000	1875804
13	100000	112548	12548	111648	2000000	1888352
14	100000	113301	13301	98346	2000000	1901654
15	100000	114099	14099	84247	2000000	1915753
16	100000	114945	14945	69302	2000000	1930698
17	100000	115842	15842	53460	2000000	1946540
18	100000	116792	16792	36668	2000000	1963332
19	100000	117800	17800	18868	2000000	1981132
20	100000	118868	18868	0	2000000	2000000

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