Question

One year ago you purchased an 8% coupon rate bond when it was first issued and priced at its face value of $1,000. Yesterday the bond paid its second semi-annual coupon. The bond currently has 7 years left until maturity and has a yield to maturity of 4%. If you sell the bond today, what will your return have been from this investment during the year you held the bond and collected the coupon payments?

		a. -10.6%
		b. -1.9%
		c. 8.0%
		d. 19.3%
		e. 32.2%

Answer 1

The price of a bond can be calculated as the sum of present value of all the future cash flows. The present value of future cash flows can be calculated by discounting with appropriate discount rate.

i.e. = Price = PV(future cash flows)

For the given bond;

The remaining time periods are = 7*2 = 14

coupon paid = 1000*8%/2 = 40

YTM = 4% or semi annual discount rate = 4%/2 = 2%

Drawing the payment schedule for this bond we have,

Time Period	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Cash Flow	40	40	40	40	40	40	40	40	40	40	40	40	40	1040
PF factor	0.980392	0.961169	0.942322	0.923845	0.905731	0.887971	0.87056	0.85349	0.836755	0.820348	0.804263	0.788493	0.773033	0.757875
PV = CF*PF	39.21569	38.44675	37.69289	36.95382	36.22923	35.51886	34.82241	34.13961	33.47021	32.81393	32.17052	31.53973	30.9213	788.19
Price = sum (PV)	1242.125
Discount rate	2.00%

Please note the present value factor is calculate as the 1/(1+2%)^(n), where n is the respective time period having value 1, 2, 3 and so on.

Therefore the current price of the bond would be, 1242.125

total return = (dividend received + current price- buying price)/buying price = (40+40 + 1242.125 -1000)/1000

= 80+242.125/1000 = 322.125/1000 = 0.322 or 32.2%

Hence the option e is the correct answer.