Question

I need to show work, and mainly understand what I'm doing

1) Harrison Co. issued 15-year bonds five years ago at a coupon rate of 6 percent. The bonds make semiannual payments. If the YTM on these bonds is 5 percent, what is the current dollar price assuming a $1,000 par value? A. $ 750.76 B. $ 845.56 C. $ 1077.95 D. $ 451.66

2)  The Timberlake-Jackson Wardrobe Co. has 5 percent coupon bonds on the market with 7 years left to maturity. The bonds make annual payments and have a par value of $1,000. If the bonds currently sell for $990.00, what is the YTM? A. 5.17% B. 4.88% C. 5.00% D. 5.71%

3)  Stein Co. issued 10-year bonds two years ago at a coupon rate of 5 percent. The bonds make semiannual payments. If these bonds currently sell for 90 percent of par value, what is the YTM? A. 3.32% B. 6.63% C. 3.18% D. 6.36%

Answer 1

Answer to Question 1:

Par Value = $1,000

Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
Semiannual Coupon = 3% * $1,000
Semiannual Coupon = $30

Time to Maturity 10 years
Semiannual Period = 20

Annual YTM = 5.00%
Semiannual YTM = 2.50%

Current Price = $30 * PVIFA(2.50%, 20) + $1,000 * PVIF(2.50%, 20)
Current Price = $30 * (1 - (1/1.025)^20) / 0.025 + $1,000 * (1/1.025)^20
Current Price = $30 * 15.589162 + $1,000 * 0.610271
Current Price = $1,077.95

Answer to Question 2:

Face Value = $1,000
Current Price = $990

Annual Coupon Rate = 5%
Annual Coupon = 5% * $1,000
Annual Coupon = $50

Time to Maturity = 7 years

Let Annual YTM be i%

$990 = $50 * PVIFA(i%, 7) + $1,000 * PVIF(i%, 7)

Using financial calculator:
N = 7
PV = -990
PMT = 50
FV = 1000

I = 5.17%

Annual YTM = 5.17%

Answer to Question 3:

Face Value = $1,000

Current Price = 90% * $1,000
Current Price = $900

Annual Coupon Rate = 5%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $1,000
Semiannual Coupon = $25

Time to Maturity = 8 years
Semiannual Period = 16

Let Semiannual YTM be i%

$900 = $25 * PVIFA(i%, 16) + $1,000 * PVIF(i%, 16)

Using financial calculator:
N = 16
PV = -900
PMT = 25
FV = 1000

I = 3.315%

Semiannual YTM = 3.315%

Annual YTM = 2 * 3.315%
Annual YTM = 6.63%