Question

17/18

Cinqua Terra Incorporated issued 10-year bonds three years ago with a coupon rate of 6.75% APR. The bonds pay semi- annual coupons, have a face value of $1,000 each and were issued at par value. Cinqua Terra bonds currently trade at $1,074.00 Given your answer to the 6-month return, what is the yield to maturity (as an EAR) for holding the bond? Submit Answer format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924)) Leonard Cooper is looking to invest in a two-year bond from Big Bang Productions Corporation. The company makes semi-annual coupon payments of $67.00 (every 6 months) with a face value of $1,000. If the market price of the bonds is $1,063.00, what yield to maturity will Leonard earn (express as an EAR)? Submit Answer format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Answer 1

Answer to Question 17:

Face Value = $1,000.00
Current Price = $1,074.00

Annual Coupon Rate = 6.75%
Semiannual Coupon Rate = 3.375%
Semiannual Coupon = 3.375% * $1,000
Semiannual Coupon = $33.75

Time to Maturity = 7 years
Semiannual Period = 14

Let Semiannual YTM be i%

$1,074.00 = $33.75 * PVIFA(i%, 14) + $1,000.00 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -1074
PMT = 33.75
FV = 1000

I = 2.732%

Semiannual YTM = 2.732%

Effective Annual Rate = (1 + Semiannual YTM)^2 - 1
Effective Annual Rate = (1 + 0.02732)^2 - 1
Effective Annual Rate = 1.0554 - 1
Effective Annual Rate = 0.0554 or 5.54%

Answer to Question 18:

Face Value = $1,000.00
Current Price = $1,063.00
Semiannual Coupon = $67.00

Time to Maturity = 2 years
Semiannual Period = 4

Let Semiannual YTM be i%

$1,063.00 = $67.00 * PVIFA(i%, 4) + $1,000.00 * PVIF(i%, 4)

Using financial calculator:
N = 4
PV = -1063
PMT = 67
FV = 1000

I = 4.926%

Semiannual YTM = 4.926%

Effective Annual Rate = (1 + Semiannual YTM)^2 - 1
Effective Annual Rate = (1 + 0.04926)^2 - 1
Effective Annual Rate = 1.1009 - 1
Effective Annual Rate = 0.1009 or 10.09%