Question

1. Grohl Co. issued 13-year bonds a year ago at a coupon rate of 11 percent. The bonds make semiannual payments. If the YTM on these bonds is 11 percent, what is the current bond price?

$630.76

$1,727.34

$1,010.00

$1,000.00

$1,005.00

2.

Ngata Corp. issued 16-year bonds 2 years ago at a coupon rate of 9.7 percent. The bonds make semiannual payments. If these bonds currently sell for 96 percent of par value, what is the YTM?

11.27%

5.12%

9.22%

10.24%

12.29%

3.

Ashes Divide Corporation has bonds on the market with 17 years to maturity, a YTM of 6.4 percent, and a current price of $1,326.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

9.58%

14.48%

19.21%

7.22%

9.68%

Answer 1

Solution 1:

As coupon rate and YTM on bond are same, therefore current price of bond will be equal to its face value i.e. $1,000

Hence 4th option is correct.

Solution 2:

Let YTM of bond is i

Now at YTM present value of interest and principal will be equal to current price.

Current price of bond = $1000*96% = $960

Remaining maturity period = 14 years, 28 semiannual period

Now lets calculate Present value of interest and principal at 10% and 11%

Present value of interest and principal at 10% = ($1000*9.7%*6/12) * Cumulative PV factor at 5% for 28 periods + $1,000 * PV Factor at 5% for 28th period

= $48.50 * 14.89813 + $1,000 * 0.255094 = $977.65

Present value of interest and principal at 11% = ($1000*9.7%*6/12) * Cumulative PV factor at 5.50% for 28 periods + $1,000 * PV Factor at 5.50% for 28th period

= $48.50 * 14.12142 + $1,000 * 0.223322 = $908.21

Semi annual YTM = 5% + ($977.65 - $960) / ($977.65 - $908.21) * 0.5 = 5.12%

Annual YTM = 5.12%*2 = 10.24%

Hence 4th option is correct.

Solution 3:

Let semiannual coupon rate in i

Now YTM = 6.4%, 3.2% semiannual

now

($1000 * i%) * Cumulative PV Factor at 3.2% for 34 periods + $1,000 * Cumulative PV Factor for 34th period = $1,326.50

= ($1,000*i%) * 20.54121 + $1,000 * 0.342681 = $1,326.50

= $20,541.21*i% = $983.82

i = 4.79%

Annual coupon rate= 4.79*2 = 9.58%

Hence first option is correct.