Question

1. Roadside Markets has a 6.75 percent coupon bond outstanding that matures in 30 years. The bond pays interest annually. What is the market price per bond if the face value is $1,000 and the yield to maturity is 7.2 percent? (round your answer to two decimal places)

a)How the price of the bond in the question above will change if yield to maturity decreases and everything else stays the same.

Group of answer choices

Price of the bond will increase

Price of the bond will decrease

Price of the bond will stay the same

It can either increase or decrease

Answer 1

The price of the bond is calculated as the present value of of cash flows from Bonds

Cash flow from the bond

Coupon Payment = 1000*6.75%= 67.5 every year

Principal repayment = 1000 after 30 years

The value of bond is compted below:

Time	Coupon Interest	Principal	Total cash flow	Discounting rate at YTM 7.2%	Discounted Cashflow
	6.75% of 1000
N	A	B	C=A+B	D=1/(1+7.2%)^N	E= C*D
1	67.50	-	67.50	0.932835821	62.97
2	67.50	-	67.50	0.870182669	58.74
3	67.50	-	67.50	0.811737564	54.79
4	67.50	-	67.50	0.757217877	51.11
5	67.50	-	67.50	0.70635996	47.68
6	67.50	-	67.50	0.658917873	44.48
7	67.50	-	67.50	0.614662195	41.49
8	67.50	-	67.50	0.573378913	38.70
9	67.50	-	67.50	0.534868389	36.10
10	67.50	-	67.50	0.498944393	33.68
11	67.50	-	67.50	0.465433202	31.42
12	67.50	-	67.50	0.434172763	29.31
13	67.50	-	67.50	0.405011906	27.34
14	67.50	-	67.50	0.377809614	25.50
15	67.50	-	67.50	0.352434341	23.79
16	67.50	-	67.50	0.328763378	22.19
17	67.50	-	67.50	0.306682256	20.70
18	67.50	-	67.50	0.286084194	19.31
19	67.50	-	67.50	0.266869584	18.01
20	67.50	-	67.50	0.248945507	16.80
21	67.50	-	67.50	0.232225287	15.68
22	67.50	-	67.50	0.216628066	14.62
23	67.50	-	67.50	0.20207842	13.64
24	67.50	-	67.50	0.188505988	12.72
25	67.50	-	67.50	0.175845138	11.87
26	67.50	-	67.50	0.164034644	11.07
27	67.50	-	67.50	0.153017392	10.33
28	67.50	-	67.50	0.142740104	9.63
29	67.50	-	67.50	0.133153082	8.99
30	67.50	1,000.00	1,067.50	0.124209965	132.59
				Total	945.26

Value of bond = 945.26

a) There is inverse relation between YTM of the bond and the price of the bond which means the price of the bond increase when YTM decrases and decreases when the YTM increases. As YTM is used to discount the cashflows of the bond hence the lower YTM, the price of the bond increases.

Hence if the YTM decreases Price of the bond increases

correct option is price of the bond increases

(The value of bond at 1% decrease in YTM is calculated below i.e. at 6.2%

Time	Coupon Interest	Principal	Total cash flow	Discounting rate at YTM 6.2%	Discounted Cashflow
	6.75% of 1000
N	A	B	C=A+B	D=1/(1+6.2%)^N	E= C*D
1	67.50	-	67.50	0.941619586	63.56
2	67.50	-	67.50	0.886647444	59.85
3	67.50	-	67.50	0.834884599	56.35
4	67.50	-	67.50	0.78614369	53.06
5	67.50	-	67.50	0.740248296	49.97
6	67.50	-	67.50	0.697032294	47.05
7	67.50	-	67.50	0.65633926	44.30
8	67.50	-	67.50	0.618021902	41.72
9	67.50	-	67.50	0.581941527	39.28
10	67.50	-	67.50	0.54796754	36.99
11	67.50	-	67.50	0.515976968	34.83
12	67.50	-	67.50	0.485854018	32.80
13	67.50	-	67.50	0.45748966	30.88
14	67.50	-	67.50	0.430781224	29.08
15	67.50	-	67.50	0.405632037	27.38
16	67.50	-	67.50	0.381951071	25.78
17	67.50	-	67.50	0.359652609	24.28
18	67.50	-	67.50	0.338655941	22.86
19	67.50	-	67.50	0.318885067	21.52
20	67.50	-	67.50	0.300268424	20.27
21	67.50	-	67.50	0.282738629	19.08
22	67.50	-	67.50	0.266232231	17.97
23	67.50	-	67.50	0.250689483	16.92
24	67.50	-	67.50	0.236054127	15.93
25	67.50	-	67.50	0.222273189	15.00
26	67.50	-	67.50	0.209296789	14.13
27	67.50	-	67.50	0.197077955	13.30
28	67.50	-	67.50	0.185572463	12.53
29	67.50	-	67.50	0.174738665	11.79
30	67.50	1,000.00	1,067.50	0.16453735	175.64
				Total	1074.11

  

Hence the price of the bond increases to 1074.11 when the YTM decreases to 6.2%