Question

What is the price of a bond with a coupon of 6%, a maturity of 15 years, and a yield (annual) of 9.1% if the bond is an annual pay bond? What if the bond is a semi-annual pay bond and the yield is a semi-annually compounded 9.1%? If the bonds are otherwise identical, which one is a better deal?

Answer 1

Case 1: Receiving annual intrest

Let us assume that Bond par value is $ 100

Coupon Rate = 6%

Coupon amount = $ 100*6%= $ 6

Term to maturity = 15 Years

YTM = 9.1% P.A

We know that at YTM , Present value of cash inflows is equal to the market price of a Bond

S.No	Cash flow	Disc @ 9.1%	Discounted Cash flows
1	$6	0.9166	$5.50
2	$6	0.8401	$5.04
3	$6	0.7701	$4.62
4	$6	0.7058	$4.23
5	$6	0.6470	$3.88
6	$6	0.5930	$3.56
7	$6	0.5435	$3.26
8	$6	0.4982	$2.99
9	$6	0.4566	$2.74
10	$6	0.4186	$2.51
11	$6	0.3836	$2.30
12	$6	0.3516	$2.11
13	$6	0.3223	$1.93
14	$6	0.2954	$1.77
15	$106	0.2708	$28.70
		Total	$75.16

Therefore Market Price of the Bond is $ 75.16 .

Case 2: Receiving Semi Annual Coupon payment.

Coupon Amount = $ 100*6%/2 =$ 3 ( Payable Semi Annually)

YTM is 9.1% for annum

YTM for 6 monts = 9.1%/2= 4.55%

No.of Payments = 15*2=30

S.No	Cash flow	Disc @ 4.55%	Discounted Cash flows
1	$3	0.9565	$2.87
2	$3	0.9149	$2.74
3	$3	0.8750	$2.63
4	$3	0.8370	$2.51
5	$3	0.8005	$2.40
6	$3	0.7657	$2.30
7	$3	0.7324	$2.20
8	$3	0.7005	$2.10
9	$3	0.6700	$2.01
10	$3	0.6409	$1.92
11	$3	0.6130	$1.84
12	$3	0.5863	$1.76
13	$3	0.5608	$1.68
14	$3	0.5364	$1.61
15	$3	0.5130	$1.54
16	$3	0.4907	$1.47
17	$3	0.4693	$1.41
18	$3	0.4489	$1.35
19	$3	0.4294	$1.29
20	$3	0.4107	$1.23
21	$3	0.3928	$1.18
22	$3	0.3757	$1.13
23	$3	0.3594	$1.08
24	$3	0.3437	$1.03
25	$3	0.3288	$0.99
26	$3	0.3145	$0.94
27	$3	0.3008	$0.90
28	$3	0.2877	$0.86
29	$3	0.2752	$0.83
30	$103	0.2632	$27.11
	Total		$74.90

Therefore Market Price of a Bond is $ 74.90 ..

The market price of a bond receiving coupons annually is $ 75.16 and for semi annual coupon bond is $ 74.90

Since market price for a semi Annual Coupon bond is cheaper, investor will go with semi Annual Coupon Bond.

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