Question

Question 1 (10 marks) You can obtain a loan of $100,000 at a rate of 10 percent for two years. You have a choice of (1) paying the interest (10 percent) each year and the total principal at the end of the second year or (ii) amortizing the loan, that is, paying interest (10 percent) and principal in equal payments each year. The loan is priced at par. a. What is the duration of the loan under the first method of payment? [5 marks] b. What is the duration of the loan under the second method of payment? [3 marks] c. Explain the differences and results between method 1 and method 2. [2 marks] Question 2 (8 marks)

Answer 1

a. Duration of Loan for $100,000 at a rate of 10% for 2 years, where interest is paid each year and principal is repaid at the end of second year.

Sr No.	Cashflow	PV of cash flows (1)	Periodic Weight of cashflows (2)	Weighted Cashflows 3= (1 x2)
1	10,000	9,099.18	1	9,099
2	110,000	91,074.61	2	182,149
Total		100,173.79		191,248
Duration = Weighted Cashflows/PV of Cashflows				1.91

b) Duration of Loan for $100,000 at a rate of 10% for 2 years, where interest is paid each year and principal is repaid in equal installments.

Sr No.	Cashflow	PV of cash flows (1)	Periodic Weight of cashflows (2)	Weighted Cashflows 3= (1 x2)
1	60,000	54,595.09	1	54,595
2	55,000	45,537.30	2	91,075
Total		100,132.39		145,670
Duration = Weighted Cashflows/PV of Cashflows				1.45

c) The difference in duration is mainly due to difference in payment on principal amount. In the first case principal is paid at the end of year whereas in the second case principal is paid in equal amounts in each year. The time to repayment is earlier in the second case, which results in lower sensitivity to rate changes and hence lower duration