Question

1.) A 10 year semiannual is selling at par and has a yield to maturity of 7.50 percent. What is the amount of each coupon payment if the face value of the bonds is $1,000? DO NOT USE DOLLAR SIGNS OR COMMAS IN YOUR ANSWER. ROUND ANSWER TO THE NEAREST CENT (2 Decimals). LIST THE NUMBER AS A POSITIVE NUMBER.

2.)A company offers 5.77 percent coupon bonds with semiannual payments and a yield to maturity of 6.49 percent. The bonds mature in 12 years. What is the market price per bond if the face value is $1,000? DO NOT USE DOLLAR SIGNS OR COMMAS IN YOUR ANSWER. ROUND ANSWER TO THE NEAREST CENT (2 Decimals). LIST THE NUMBER AS A POSITIVE NUMBER.

3.)

A $1,000 par value bond sells for $1,020. It matures in 5 years and has an 5% coupon, paid semiannually. What is the bond’s yield to maturity (YTM)? ENTER YOUR ANSWER AS A PERCENTAGE WITH ONE DECIMAL PLACE (e.g., 12.1) AND NOT AS A DECIMAL (e.g., 0.121). ROUND TO THE NEAREST TENTH OF A PERCENT. DO NOT USE THE PERCENT SIGN (%) IN YOUR ANSWER.

Answer 1

1. maturity period = 10 year

Yield to maturity = 7.5%

coupon payment = ?

face value of bond = 1000

interest payment in a year = 2 times

market/selling price of bond = 1000

suppose coupon amount on bond half yearly = x

and we know, market price of bond = coupon rate*PVIFA(7.5%/2,20) + 1000*PVIF(7.5/2,20)

1000 = x*13.8962 + 1000*0.478892

1000 = 13.8962x + 478.892

x = (1000-478.892)/13.8962

= 521.1077/13.8962

= 37.5

full year coupon amount = 37.5*2 = 75

rate of coupon = 75/1000

= 7.5%

2. Rate of coupon = 5.77%

Interest is paid semiannually means 2 times in a year, in that case rate of coupon will be applicable = 5.77/2 = 2.885

yield to maturity = 6.49% semiannually it would be = 6.49/2 = 3.245%

maturity period of bond = 12 years

face value of bond = 1000

market price of bond = ?

market price of bond = coupon rate*PVIFA(6.49%/2,24) + 1000*PVIF(6.49/2,24)

= 1000*2.885%*17.14726 + 1000*0.505301

= 28.85*17.14726 + 505.301

= 494.6985 + 505.301

= 999.999 or 1000

market price of bond should be $ 1000.

3. Face value of bond = 1000

selling price of bond = 1020

maturity period = 5 years

coupon rate = 5%

interest paid semiannually, 2 times in a year

Yield to maturity is that rate where market price of bond = present value of cash inflows (coupon payments + face value of bond at the maturity period)

year	cash flow	Discounting @ 5%		Discounting @ 2%
			Amt.		Amt.
1	25	0.9524	23.8095	0.9901	24.7525
2	25	0.9070	22.6757	0.9803	24.5074
3	25	0.8638	21.5959	0.9706	24.2648
4	25	0.8227	20.5676	0.9610	24.0245
5	25	0.7835	19.5882	0.9515	23.7866
6	25	0.7462	18.6554	0.9420	23.5511
7	25	0.7107	17.7670	0.9327	23.3180
8	25	0.6768	16.9210	0.9235	23.0871
9	25	0.6446	16.1152	0.9143	22.8585
10	1025	0.6139	629.2611	0.9143	937.1983
			806.9566		1151.3488

now by interpolate implicit rate = 5% - (1000-806.9566)/(1151.3488-806.9566)*4%

= 5% - 193.04/344.39*4%

= 5% - 2.24%

= 2.75% it is semiannually rate of yield to maturity

yearly rate = 2.75%*2 = 5.5%

Please check with your answer and let me know.