Question

In: Finance

LeXnews has 15-year bonds outstanding with a face value of $1,000 and a market price of...

LeXnews has 15-year bonds outstanding with a face value of $1,000 and a market price of $974. The bonds pay interest semi-annually and have a yield to maturity of 4.03 percent. What is the coupon rate?
A) 3.80 percent
B) 3.15 percent

C) 4.15 percent

D) 3.60 percent

E) 4.10 percent

32) The 6 percent annual coupon bonds of IPO, Inc., are selling for $1,187. The bonds have a face value of $1,000 and mature in 11 years. What is the yield to maturity?
A) 4.68 percent
B) 3.70 percent

C) 3.88 percent

D) 4.71 percent

E) 4.64 percent

Expert Solution

Given Face value = $ 1000

Market price = $ 974

Let Coupon rate be 2X %

Semi Annual coupon amount = $ 1000*2X%/2

= $ 10X

Duration = 15 years

No.of Coupons received = 15*2=30

YTM = 4.03%

Haly yearly YTM = 4.03% /2

= 2.015%

We know that

At YTM, Sum of the discounted value of future cash inflow is equal to the Market price of the bond

Installment	Coupon amount	Disc @ 2.015 %	Discounted Cash flows
1	10X	0.9802	9.802X
2	10X	0.9609	9.609X
3	10X	0.9419	9.419X
4	10X	0.9233	9.233X
5	10X	0.9051	9.051X
6	10X	0.8872	8.872X
7	10X	0.8697	8.697X
8	10X	0.8525	8.525X
9	10X	0.8356	8.356X
10	10X	0.8191	8.191X
11	10X	0.8030	8.030X
12	10X	0.7871	7.871X
13	10X	0.7716	7.716X
14	10X	0.7563	7.563X
15	10X	0.7414	7.414X
16	10X	0.7267	7.267X
17	10X	0.7124	7.124X
18	10X	0.6983	6.983X
19	10X	0.6845	6.845X
20	10X	0.6710	6.710X
21	10X	0.6577	6.577X
22	10X	0.6447	6.447X
23	10X	0.6320	6.320X
24	10X	0.6195	6.195X
25	10X	0.6073	6.073X
26	10X	0.5953	5.953X
27	10X	0.5835	5.835X
28	10X	0.5720	5.720X
29	10X	0.5607	5.607X
30	10X	0.5496	5.496X
	1000	0.5496	549.6

	Total		223.503X+549.6

By solving the Equation we get

223.503X+549.6 = $ 974

223.503X = $ 974-$ 549.6

223.503X = $ 424.4

X = $ 424.4/223.503

= 1.898855%

2X ( YTM) = 1.898855*2

= 3.79771

Option A) 3.80 % is the correct answer

Part B

We know that

At YTM, Present value of future cash inflows is equal to the market price of the bond

Year	Interest	Disc @ 4.68 %	Disc @ 3.70%	Disc @ 3.88%	Disc @ 4.71%	Disc @ 4.64%
1	60	0.95529	0.96432	0.96265	0.95502	0.95566
2	60	0.91258	0.92991	0.92669	0.91206	0.91328
3	60	0.87178	0.89673	0.89208	0.87103	0.87278
4	60	0.83281	0.86474	0.85876	0.83185	0.83408
5	60	0.79558	0.83389	0.82669	0.79444	0.79710
6	60	0.76001	0.80413	0.79581	0.75870	0.76175
7	60	0.72603	0.77544	0.76608	0.72457	0.72797
8	60	0.69357	0.74777	0.73747	0.69198	0.69569
9	60	0.66256	0.72109	0.70993	0.66086	0.66485
10	60	0.63294	0.69536	0.68341	0.63113	0.63536
11	60	0.60464	0.67055	0.65788	0.60274	0.60719
	Total	8.44780	8.90395	8.81745	8.43439	8.46572

Market price of the bond at various discount rate
Year	Cash Flows	Disc @ 4.68 %	DCF @ 4.68%	Disc @ 3.70%	DCF @ 3.70%
1-11	60	8.44780	506.8677399	8.90395	534.2369515
11	1000	0.60464	604.64	0.67055	670.5538799
			1111.50774		1204.790831

Market price of the bond at various discount rate
Year	Cash Flows	Disc @ 3.88%	DCF @ 3.88%	Disc @ 4.71%	DCF @ 4.71%	Disc @ 4.64%	DCF @ 4.64%
1-11	60	8.81745	529.0469417	8.43439	506.0632864	8.46572	507.9433349
11	1000	0.65788	657.8829777	0.60274	602.7403202	0.60719	607.1904877
			1186.929919		1108.803607		1115.133823

At 3.88% present value of future cash inflows is equal to market price of the bond

So option C ) 3.88% is the correct answer.

jeff jeffy answered 2 years ago

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