Question

5(a) A company is discussing a $0.5 million loan with a bank. The interest rate is 12% compounded annually and the repayment period is 5 years. The bank is offering two options for loan repayment: Option A: Payments are to be received in equal installments at the end of each year Option B: Interest is to be received on a yearly basis and the Principal is to be received at the end All loan repayment items are end-of-year payments Which options is better for the company? For Option A, construct a spreadsheet that shows for each period the following: annual payment, interest received, recovered capital, and unrecovered capital. For Option B, construct a spreadsheet that shows for periods 1 to 4, interest payments, and for the 5th (last) period, interest as well as the principal. 5(b) A bond with a face value of $500,000 pays quarterly interest of 1.5% per each period. Twenty interest payments remain before the bond matures. How much would you be willing to pay for this bond today if the next interest payment is due now and you want earn 8% compounded quarterly on your money?

Answer 1

5A)

Option A)

First of all lets calculate Installment amount

Installment amount = Loan/PVIFA(r%,n)

=500000/PVIFA(12%,5 years)

=500000/3.6047

=138705$

Statement showing repayment schedule

			Towards
Year	Opening balance	Installment	Interest @ 12%	Principal	Closing balance
1	500000	138705	60000	78705	421295
2	421295	138705	50555	88150	333145
3	333145	138705	39977	98728	234418
4	234418	138705	28130	110575	123843
5	123843	138705	14861	123844	0
			193524	500000

Thus total Interest = 193,524$

Option B)

Statement showing repayment of principal and Interest

Year	Interest payments	Principal payment	Total
1	60000		60000
2	60000		60000
3	60000		60000
4	60000		60000
5	60000	500000	560000
Total	300000	500000

Here Interest is 300,000$

Since Interest payment in option A is less than option B. Option A is preferable

5B)

First of all lets find EAR

EAR = (1+ rate/n)^n-1

(1+8%/4)^4-1

=1.02^4-1

=1.08243-1

=8.243%

Means Quarterly rate = 8.243%/4 = 2.0608%

Statement showing PV of interest payment as well as principle

Period	Interest	Principal	Total payment	PVIF @ 2.0608%	Present Value
0	7500		7500	1.0000	7500
1	7500		7500	0.9798	7349
2	7500		7500	0.9600	7200
3	7500		7500	0.9406	7055
4	7500		7500	0.9216	6912
5	7500		7500	0.9030	6773
6	7500		7500	0.8848	6636
7	7500		7500	0.8669	6502
8	7500		7500	0.8494	6371
9	7500		7500	0.8323	6242
10	7500		7500	0.8155	6116
11	7500		7500	0.7990	5993
12	7500		7500	0.7829	5872
13	7500		7500	0.7671	5753
14	7500		7500	0.7516	5637
15	7500		7500	0.7364	5523
16	7500		7500	0.7215	5412
17	7500		7500	0.7070	5302
18	7500		7500	0.6927	5195
19	7500	500000	507500	0.6787	344442
					463783

Thus price of bond that should be paid = 463783$