Question

you have purchased a 4-year upon bond paying a coupon rate of 10% per year semiannually with a yield to maturity of 8% and a Face value of $1000.

What would your rate of return if you sell the bond 30 days after receiving the first coupon? The reinvestment rate is 3% for these 30 days (not annualized). Assume that bonds bid and ask prices on the market at the time are Bid: $1013.96 and ask: $1019.03. the coupon periods has 182 days.

Answer 1

Return on the Bond = (Ending value of bond + coupon + reinvestment income ) / Beginning value - 1

We need to calculate the beginning value with the help of the discounting future cash flows @yield to maturity

Years	Coupons	Principal	Total cash flows	Discounting Factor	Present Value
0.50	50		50	0.961538462	48.08
1.00	50		50	0.924556213	46.23
1.50	50		50	0.888996359	44.45
2.00	50		50	0.854804191	42.74
2.50	50		50	0.821927107	41.10
3.00	50		50	0.790314526	39.52
3.50	50		50	0.759917813	38.00
4.00	50	1000	1050	0.730690205	767.22
			Price of bond		1067.33

Beginning value of the bond =$ 1067.33

Coupon Amount received = $ 50

Reinvestment income on coupon = 50 * 3% = 1.5

Ending value of the bond is the $1013.96 ie the bid rate

Rate of return on the bond = (1013.96 + 50 + 1.5 ) / 1067.33 - 1

= (1065.46 / 1067.33) - 1

= - 0.1752%

Holding period return = -0.1752%

Annual return = (1065.46 / 1067.33 )^365/182 - 1

= (1065.46 / 1067.33 ) ^ 1.72 - 1

= -0.3012%

Return on the bond =