Question

Can someone explain me how to calculate this on a TI-83 PLUS financial calculator...

What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this relationship exist?

Answer 1

		Bond Duration = Present value of (cash flows multiplied by length of time to receipt) / (the  current market value)
		Semi-annual Coupon =(1000*10%)/2	$50
		Annual Yield to maturity =12%=0.12
		Semi annual yield to maturity =(12/2)%=6%=0.06
		Present Value (PV)=(Cash flow)/(1.06^N)
		N=Period of cash flow
			N	CF	A=CF/(1.06^N)	B=CF/(1.07^N)	C=CF/(1.05^N)	D=CF/(1.04^N)	E=N*CF	F=E/(1.06^N)	G=E/(1.07^N)	H=E/(1.05^N)	I=E/(04^N)
			Semi annual Period	Cash Flow	Present Value at 12%	Present Value at 14%	Present Value at 10%	Present Value at 8%	Period*Cash Flow	Present Value at 12%	Present Value at 14%	Present Value at 10%	Present Value at 8%
			1	$50	$47.17	$46.73	$47.62	$48.08	$50	$47.17	$46.73	$47.62	$48.08
			2	$50	$44.50	$43.67	$45.35	$46.23	$100	$89.00	$87.34	$90.70	$92.46
			3	$50	$41.98	$40.81	$43.19	$44.45	$150	$125.94	$122.44	$129.58	$133.35
			4	$50	$39.60	$38.14	$41.14	$42.74	$200	$158.42	$152.58	$164.54	$170.96
			5	$50	$37.36	$35.65	$39.18	$41.10	$250	$186.81	$178.25	$195.88	$205.48
			6	$50	$35.25	$33.32	$37.31	$39.52	$300	$211.49	$199.90	$223.86	$237.09
			7	$50	$33.25	$31.14	$35.53	$38.00	$350	$232.77	$217.96	$248.74	$265.97
			8	$50	$31.37	$29.10	$33.84	$36.53	$400	$250.96	$232.80	$270.74	$292.28
			9	$50	$29.59	$27.20	$32.23	$35.13	$450	$266.35	$244.77	$290.07	$316.16
		(1000+50)	10	$1,050	$586.31	$533.77	$644.61	$709.34	$10,500	$5,863.15	$5,337.67	$6,446.09	$7,093.42
				SUM	$926.40	$859.53	$1,000.00	$1,081.11		$7,432.07	$6,820.45	$8,107.82	$8,855.25
	SA=Sum of A	Current Market Price at 12% Yield	$926.40
	SB=Sum of B	Current Market Price at 14% Yield	$859.53
	SC=Sum of C	Current Market Price at 10% Yield	$1,000.00
	SD=Sum of D	Current Market Price at 8% Yield	$1,081.11
	SF=Sum of F	PV of Cash Flow*Period at 12% Yield	$7,432.07
	SG=Sum of G	PV of Cash Flow*Period at 14% Yield	$6,820.45
	SH=Sum of H	PV of Cash Flow*Period at 10% Yield	$8,107.82
	SI=Sum of I	PV of Cash Flow*Period at 8% Yield	$8,855.25
	(SF/SA)/2	Bond Duration at 12% Yield in Years	4.0112668	Years
	(SG/SB)/2	Bond Duration at 14% Yield in Years	3.9675535	Years
	(SH/SC)/2	Bond Duration at 10% Yield in Years	4.0539108	Years
	(SI/SD)/2	Bond Duration at 8% Yield in Years	4.0954494	Years
		As Yield increases, Bond Duration decreases
		Yield	Duration
		8%	4.0954494
		10%	4.0539108
		12%	4.0112668
		14%	3.9675535