Question

2. Apple issued a 6 year bond with a par value of $2,000. The annual coupon rate is 2.4% and it pays semi-annually. The yield to maturity is 3.15%.

     a) What is the purchase price for this bond?

     b) What is the current yield for this bond?

Answer 1

Semi-annual coupon pament = $$2,000 x 2.4% x (1/2) = $24

Semi-annual yield to maturity = 3.15%/2 = 1.575%

Number of coupon periods = 6 x 2 = 12

(a) Purchase price ($) = Present worth of future coupon payments + Present worth of redemption price (face value)

= 24 x P/A(1.575%, 12) + 2,000 x P/F(1.575%, 12)

= 24 x 10.8567** + 2,000 x 0.8290**

= 260.56 + 1,658.00

= 1,918.56

**P/A(1.575%, 12) = [1 - (1.01575)^-12] / 0.01575 = (1 - 0.8290) / 0.01575 = 0.171 / 0.01575 = 10.8567

**P/F(1.575%, 12) = (1.01575)^-12) = 0.8290

(b) Current yield = Annual coupon payment / Purchase price = $(24 x 2) / $1,918.56 = $0.025 = 2.50%