Workman Software has 8.4 percent coupon bonds on the market with 20 years to maturity. The bonds make semiannual payments and currently sell for 107 percent of par.

a. What is the current yield on the bonds?

b. What is the YTM?

c. What is the effective annual yield?

a.

7.85%

b.

7.78%

c.

8.58%

Explanation:

a.

Current yield is the ratio of coupon payment of a bond to its current market price.  It is calculated by using coupon payment and the current market value of the bond.

Coupon payment = $1,000 x 8.4% = $84 annually

Market Price = $1,000 x 107% = $1,070

Formula for Current yield is as follow

Current Yield = Annual Coupon Payment / Current Market Price

Current Yield = $84 / $1,070

Current Yield =7.85%

b.

The actual return that an investor earn on a bond until its maturity is called the Yield to maturity. It is a long term return which is expressed in annual rate.

Assuming the face value of the bond is $1,000.

Coupon payment = $1,000 x 8.4% = $84 annually = $42 semiannually

Market Price = $1,000 x 107% = $1,070

Yield to maturity = [ C + ( F - P ) / n ] / [ (F + P ) / 2 ]

Yield to maturity = [ 42 + ( $1,000 - $1070 ) / 40 ] / [ ( $1,000 + $1,070 ) / 2 ]

Yield to maturity = 40.25 / $1,035 = 0.0389 = 3.89% Semiannually = 7.78% annually

c.

Formula for effective yield is as follow

Effective yield = [1 + (r/n)]^n – 1

Effective yield = [1 + (8.4%/2)]^2 – 1

Effective yield = 8.58%

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