Question

Autopia City issues a serial bond of $90,000 to be paid over five years, receiving $89,000. The series of annual payments (including both interest and principal repayment, at the end of each year) is as follows: $15,600; $15,700; $23,900; 22,900; 28,700. Using the TIC approach, what is the effective interest rate?

Answer 1

Effective Int rate is the Rate at which PV of Cash inflows are equal to PV of Cash Outflows

Year	CF	PVF @5%	Disc CF	PVf @6%	Disc CF
0	$ -89,000.00	1.0000	$ -89,000.00	1.0000	$ -89,000.00
1	$ 15,600.00	0.9524	$ 14,857.14	0.9434	$ 14,716.98
2	$ 15,700.00	0.9070	$ 14,240.36	0.8900	$ 13,972.94
3	$ 23,900.00	0.8638	$ 20,645.72	0.8396	$ 20,066.90
4	$ 22,900.00	0.8227	$ 18,839.89	0.7921	$ 18,138.94
5	$ 28,700.00	0.7835	$ 22,487.20	0.7473	$ 21,446.31
NPV			$    2,070.31		$      -657.92

Effective Rate = Rate at which Least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in DIsc rate ] * 1%

= 5% + [ 2070.31 / 2728.23 ] * 1%

= 5% + 0.76%

= 5.76%