What is the yield to maturity of a TVA bond that has a 9 1/2 percent coupon, pays interest semiannually, has 12 years to maturity, and sells for $871.50?
A) 11.3%
B) 11.5%
C) 11.8%
D) 12.1%

Question

Quizplus · Accepted Answer

Step 1: Calculate the semiannual coupon payment.

Coupon rate = 9.5% 
Coupon payment = (9.5/2)% * $1000 = $47.50

Step 2: Calculate the total number of semiannual coupon payments.

Semiannual payments = 12 years * 2 = 24

Step 3: Calculate the present value of the bond.

PV = $871.50

Step 4: Determine the yield to maturity using a financial calculator or trial and error.

Using trial and error:

Guess 1: 10% 
PV = ($47.50/0.05)[1 – 1/1.05^24] + $1000/1.05^24 = $901.11 
Guess 2: 11% 
PV = ($47.50/0.055)[1 – 1/1.055^24] + $1000/1.055^24 = $882.64 
Guess 3: 11.5% 
PV = ($47.50/0.0575)[1 – 1/1.0575^24] + $1000/1.0575^24 = $872.48 
Guess 4: 11.8% 
PV = ($47.50/0.058)[1 – 1/1.058^24] + $1000/1.058^24 = $871.78 
Guess 5: 12% 
PV = ($47.50/0.06)[1 – 1/1.06^24] + $1000/1.06^24 = $871.64

The yield to maturity is between 11.5% and 11.8%.

Therefore, the answer is B) 11.5%.

What Is the Yield to Maturity of a TVA Bond