Question

Ashes Divide Corporation has bonds on the market with 13 years to maturity, a YTM of 7.4 percent, and a current price of $1,186.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

rev: 09_18_2012

Multiple Choice

• 9.66%

• 19.36%

• 9.76%

• 16.32%

• 8.14%

Grohl Co. issued 17-year bonds a year ago at a coupon rate of 12 percent. The bonds make semiannual payments. If the YTM on these bonds is 11 percent, what is the current bond price?

rev: 09_18_2012

Multiple Choice

• $1,084.52

• $1,074.52

• $1,059.32

• $574.82

• $1,823.73

Answer 1

Answer to Question 1:

Face Value = $1,000
Current Price = $1,186.50

Time to Maturity = 13 years
Semiannual Period = 26

Annual YTM = 7.40%
Semiannual YTM = 3.70%

Let semiannual coupon be $x

$1,186.50 = $x * PVIFA(3.70%, 26) + $1,000 * PVIF(3.70%, 26)
$1,186.50 = $x * (1 - (1/1.0370)^26) / 0.0370 + $1,000 * (1/1.0370)^26
$1,186.50 = $x * 16.518288 + $388.823347
$797.676653 = $x * 16.518288
$x = $48.29

Semiannual Coupon = $48.29

Annual Coupon = 2 * Semiannual Coupon
Annual Coupon = 2 * $48.29
Annual Coupon = $96.58

Coupon Rate = Annual Coupon / Face Value
Coupon Rate = $96.58 / $1,000
Coupon Rate = 0.0966 or 9.66%

Answer to Question 2:

Face Value = $1,000

Annual Coupon Rate = 12.00%
Semiannual Coupon Rate = 6.00%
Semiannual Coupon = 6.00% * $1,000
Semiannual Coupon = $60

Time to Maturity = 16 years
Semiannual Period = 32

Annual YTM = 11.00%
Semiannual YTM = 5.50%

Current Price = $60 * PVIFA(5.50%, 32) + $1,000 * PVIF(5.50%, 32)
Current Price = $60 * (1 - (1/1.055)^32) / 0.055 + $1,000 * (1/1.055)^32
Current Price = $60 * 14.904198 + $1,000 * 0.180269
Current Price = $1,074.52