Question

All of the bonds listed below are $1000 par bonds. To keep things simple, assume all are annual coupon bonds. In the table see bonds of maturity 1 through 4, with their prices and coupons (in percent) listed. (Remember prices are presented as a percentage of par.) I want you to find each bond's yield to maturity. That should be easy. But I also want you to bootstrap the zero coupon yield curve. That is, find the four zero-coupon yields that you can: 011, 02, 03, and 014. Thus your job is to fill in the table below. Please enter answers in % form to three decimal places. Avoid rounding too much when calculating your answer. You MUST show me your work. Maturity Coupon Price (% Yield (%) Zero- (%) of par) coupon yield (%) optio ایم این 7.50 103 7.30 101 7.00 6.2090

Answer 1

We model the cash flows arising out of the bond. We sum them up for each year, and then use the IRR function to calculate yield.

Following tables show the calculations for the coupon paying bonds

Bond 1
Par value	$        1,000
Maturity	1
Coupon	7.50%
Price	103%
Year	0	1
Bond proceeds	$        1,030
Coupon		$ (75.00)
Principal repayment		$ (1,000)
Net cash flows	$        1,030	$ (1,075)
IRR	4.369%

Bond 2
Par value	$    1,000
Maturity	2
Coupon	7.30%
Price	101%
Year	0	1	2
Bond proceeds	$    1,010
Coupon		$ (73.00)	$ (73.00)
Principal repayment			$ (1,000)
Net cash flows	$    1,010	$        (73)	$ (1,073)
IRR	6.749%

Bond 3
Par value	$    1,000
Maturity	3
Coupon	7.00%
Price	98%
Year	0	1	2	3
Bond proceeds	$        980
Coupon		$ (70.00)	$ (70.00)	$ (70.00)
Principal repayment				$ (1,000)
Net cash flows	$        980	$        (70)	$        (70)	$ (1,070)
IRR	7.773%

Bond 4
Par value	$    1,000
Maturity	4
Coupon	6.20%
Price	90%
Year	0	1	2	3	4
Bond proceeds	$        900
Coupon		$ (62.00)	$ (62.00)	$ (62.00)	$ (62.00)
Principal repayment					$ (1,000)
Net cash flows	$        900	$        (62)	$        (62)	$        (62)	$ (1,062)
IRR	9.308%

For the zero coupon bonds, we simply make coupon payments equal to 0 in the same model get following calculations

Bond 1
Par value	$        1,000
Maturity	1
Coupon	0.00%
Price	103%
Year	0	1
Bond proceeds	$        1,030
Coupon		$           -
Principal repayment		$ (1,000)
Net cash flows	$        1,030	$ (1,000)
IRR	-2.913%

Bond 2
Par value	$    1,000
Maturity	2
Coupon	0.00%
Price	101%
Year	0	1	2
Bond proceeds	$    1,010
Coupon		$           -	$           -
Principal repayment			$ (1,000)
Net cash flows	$    1,010	$           -	$ (1,000)
IRR	-0.496%

Bond 3
Par value	$    1,000
Maturity	3
Coupon	0.00%
Price	98%
Year	0	1	2	3
Bond proceeds	$        980
Coupon		$           -	$           -	$           -
Principal repayment				$ (1,000)
Net cash flows	$        980	$           -	$           -	$ (1,000)
IRR	0.676%

Bond 4
Par value	$    1,000
Maturity	4
Coupon	0.00%
Price	90%
Year	0	1	2	3	4
Bond proceeds	$        900
Coupon		$           -	$           -	$           -	$           -
Principal repayment					$ (1,000)
Net cash flows	$        900	$           -	$           -	$           -	$ (1,000)
IRR	2.669%

Hence completing the table in the question,

Maturity	Coupon (%)	Price (% of par)	Yield (%)	Zero coupon yield (%)
1	7.5	103	4.369	-2.913
2	7.3	101	6.749	-0.496
3	7	98	7.773	0.676
4	6.2	90	9.308	2.669