Callaghan Motors' bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity of 9 percent. What is the current market price of these bonds?

N = 10 years to maturity

Going rate, YTM, Rd = 9%

Par value = $1000

Annual payment = 8% = $80

PMT = (0.08)*($1000) = $80

PV?

PVn = PV(rate, Nper, PMT, FV, Type)

PVn = PV(9, 10, 80, 1000, 0)

PVn = $936

1. Nungesser Corporation has issued bonds that have a 9 percent coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 9 percent. What is the price of the bonds?

Annual payment

N = 8 years to maturity

YTM, rd = 9%

Face value, par value = $1000

Annual market interest rate = 9%

Annual coupon payment = 0.09*1000 = $90

Value of the bond: =PV(9%, 8, $90, $1000, 0)

Value of the bond (annual) = $1000

Semiannual payment

Periods to maturity = 8*2 = 16

Semiannual PMT = $90/2 = $45

Periodic rate = 9% / 2 = 4.5%

Value of the bond: =PV(4.5%, 16, $45, $1000, 0)

Value of the bond (semiannual) = $1000

3.The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S a maturity of 1 year (that is, there is only one more interest payment to be made on Bond S).

a. What will be the value of each of these bonds when the going rate of interest is (1) 5 percent, (2) 8 percent, and (3)12 percent?

Bond L:

Years to maturity = 15 years

Annual payment = $100

Par value = $1000

Going rate, rd = 5%, 8%, 12%

Price, value: =PV(5%, 15, $100, $1000, 0) ; =PV(8%, 15, $100, $1000, 0) ; =PV(12%, 15, $100, $1000, 0)

5%: $1518,98

8%: $1171.19

12%: $836.78

Bond S:

Years to maturity = 1 year

Annual payment = $100

Par value = $1000

Going rate, rd = 5%, 8%, 12%

Price, value: =PV(5%, 1, $100, $1000, 0) ; =PV(8%, 1, $100, $1000, 0) ; =PV(12%, 1, $100, $1000, 0)

5%: $1047.62

8%: $1018.52

12%: $982.14

	5%	8%	12%
	Bond L	Bond S	Bond L	Bond S	Bond L	Bond S
Years to maturity	15	1	15	1	15	1
Annual payment, PMT	$100	$100	$100	$100	$100	$100
Par value	$1,000	$1,000	$1,000	$1,000	$1,000	$1,000
Going rate, rd	5%	5%	8%	8%	12%	12%
Value of bond=	$1,518.98	$1,047.62	$1,171.19	$1,018.52	$863.78	$982.14

1. Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1-year)?

As you can see, the price of the bond L (15 years) fluctuates more significantly with a change in interest rates compared to Bond S (1 year). This is because of the concept of duration which represents the average time it takes to receive all the cash flows from a bond. A longer-term bond has a higher duration because you have to wait longer to receive all the payments. When interest rates rise, the present value of future cash flows from a bond decreases. For a long-term bond with a high duration, this decrease in present value is more significant because there are more future cash flows affected. This translates to a larger price decline. On the other hand, when interest rates fall, the present value of future cash flows increases. For a long-term bond, this increase is larger, leading to a bigger price gain. Therefore, bond L with its higher duration experiences more significant price fluctuations due to changes in interest rates compared to bond S which has a lower duration.

______________

4.The HeymanCompany's bonds have 4 years remaining to maturity. Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is 9 percent.

a. What is the yield to maturity at a current market price of (1) $829 and (2) $1,104?

Years to maturity = 4

Coupon rate = 9%

Coupon payment = 9% * $1000 = $90

Par value (FV) = $1000

Current price = $829 OR $1104

YTM, rd: =RATE(4, $90, -$829, $1000) ; =RATE(4, $90, -$1104, $1000)

YTM, rd = 15% (for current value $829), 6% (for current value $1104)

Years to maturity	4	4
Coupon rate	9%	9%
Annual payment	$90	$90
Current price	$829	$1,104
par value, FV	$1,000	$1,000
Going rate, rd, YTM =	15%	6%
	$829	$1,104

b. Would you pay $829 for one of these bonds if you thought that the appropriate rate of interest was 12 percent (that is, if r_d=12%)? Explain your answer.

If your required rate of return was 12%, you should be willing to buy the bond at any price below.

Answer rating: 100% (QA)

To determine if you would pay 829 for the bond when the appropriate rate of interest is 12 rd12 we n... View the full answer