Question

Suppose that you invest in a 10-year 8% Treasury Note sold at par and the interest rate drops to 6% after your purchase. What will be the Total Dollar Return and the Realized Yield if you hold the bond (a) for 3 years; (b) for 7 years; (c) to maturity. In each case, decompose the Total Dollar Return into (1) Total Coupon Interest; (2) Interest on Interest; (3) Capital Gain / Loss.

Answer 1

If the bond is held until maturity, it will have 10 years left until maturity. Based on this, the current price of the bond can be computed as the Present value of the bond's cashflows from year 1 until maturity in year 10.
Description	1	2	3	4	5	6	7	8	9	10		Comments
Coupon Receivable	80	80	80	80	80	80	80	80	80	80
Principal receivable	0	0	0	0	0	0	0	0	0	1000
Total receivable	80	80	80	80	80	80	80	80	80	1080
Present Value	75.47169811	71.19972	67.16954	63.36749	59.78065383	56.39684324	53.20457	50.19299	47.35188	603.0664	1147.202	Current Price of Bond (sum of present values)

If the bond is held for 3 years, it will have 7 years left until maturity at year 3. Based on this, the price of the bond can be computed at year 3 as the Present value of the bond's cashflows from year 3 until maturity in year 10.
Description	1	2	3	4	5	6	7		Comments
Coupon Receivable	80	80	80	80	80	80	80
Principal receivable	0	0	0	0	0	0	1000
Total receivable	80	80	80	80	80	80	1080
Present Value	75.47169811	71.19972	67.16954	63.36749	59.78065383	56.39684324	718.2617	1111.648	Price of bond at the end of 3 years

If the bond is held for 7 years, it will have 3 years left until maturity at year 7. Based on this, the price of the bond can be computed at year 7 as the Present value of the bond's cashflows from year 7 until maturity in year 10.
Description	1	2	3		Comments
Coupon Receivable	80	80	80
Principal receivable	0	0	1000
Total receivable	80	80	1080
Present Value	75.47169811	71.19972	906.7888	1053.46	Price of bond at the end of 7 years

If bond is held for 3 years
Price at year 3	1111.647629	3.59%	Price return (annualized) - Capital gain
Purchase price	1000
Interest earned	240	80*3
Income return (HPR)	0.24
Income return (annualized)	7.43%
Total realized Return	11.292%

If bond is held for 7 years
Price at year 7	1053.46	1.75%	Price return (annualized) - Capital gain
Purchase price	1000
Interest earned	560	80*7
Income return (HPR)	0.56
Income return (annualized)	15.98%
Total realized Return	18.009%

If bond is held until maturity
Redemption price	1000	0.00%	Price return (annualized) - Capital gain
Purchase price	1000
Interest earned	800	80*10
Income return (HPR)	0.8
Income return (annualized)	21.64%
Total realized Return	21.644%