Question

You buy a bond issued by Terlingua Oil & Gas Exploration Corp. The coupon rate is 8%, and coupons are paid semi-annually. Par of your bond is $10,000. The bond matures in 12 years. Your price today on the bond is $11,000. In six months, the YTM on the bond has fallen by 1%. You collect the coupon payment and sell the bond. What is your effective annual rate of return?

-1.00%

24.14%

6.88%

11.42%

8.00%

Answer 1

Given Conditions:

Face Value = 10,000

Tenure = 12 Years

Price = 11000

Coupon Rate = 8%

Frequency = Semi - Annually

Steps to Solve:

1. Calculate Yield Till Maturity (YTM)

2. Derive YTM @ 6 months from now.

3. Calculate Price of Bond @ 6 months from now

4. Calculate total Inflow of payments to bondholder after selling the bond

5. Calculate Effective annual rate of return.

STEP 1 : Calculate Yield Till Maturity (YTM)

Coupon = (8% x 10,000 ) / 2 = 400

Face Value = 10,000

Price = 11,000

No of coupon payments (N) = 12 x 2 = 24

This will give you YTM = 3.384787 %

Annualt YTM = 3.384787 x 2 = 6.769 %

STEP 2: Derive YTM @ 6 months from now.

New YTM = Old YTM - 1%

New YTM = 6.679% - 1 = 5.679%

STEP 3 : Calculate Price of Bond @ 6 months from now

No of Coupons Remaing (N) = 24 - 1 = 23

Coupon = 400

Face Value = 10,000

YTM = 5.679%

This will give you Price = 10,972.32

STEP 4 : Calculate total Inflow of payments to bondholder after selling the bond

Inflow from Coupon: 400

Inflow from Selling of bond at price determined in step 4 = 10,972.32

Total Inflow = 400 + 10,972.32 = 11372.325

STEP 5 : Calculate Effective annual rate of return.

Investment Value = 11,000

Value Realized in 6 months = 11372.325

Annual Rate of Return = (11372.325 / 11000)² - 1

= 0.0688

= 6.88%

And this is you answer.