Question

On June 19, 2014, Koala, Inc. issued a 10 year bond (with a typical $1000 face value) that had an annual coupon value of $55. Initially, the bond was sold for the premium price of $1,025. On June 20, 2019, this bond was selling for only $955.

1.  What was the nominal yield on this bond on June 20, 2014?

2.  What was the current yield on this bond on June 20, 2014?

3.  What is the nominal yield on this bond on June 20, 2019?

4.  What is the current yield on this bond on June 20, 2019?

5.  What is the yield to maturity for this bond on June 20, 2019?

Answer 1

(1)

Nominal yield = Annual coupon / Face value = $55 / $1000 = 0.055 = 5.5%

(2)

Current yield = Annual coupon / Current bond price = $55 / $1,025 = 0.0537 = 5.37%

(3)

Nominal yield = Annual coupon / Face value = $55 / $1000 = 0.055 = 5.5%

(4)

Current yield = Annual coupon / Current bond price = $55 / $955 = 0.0576 = 5.76%

(5)

Using approximation formula,

YTM = [C + (F - P) / N] / [(F + P)/2] where

C: Annual coupon = $55

F: Face value = $1000

P: Current price = $955

N: Years left to maturity = 10 - 5 = 5

YTM = [55 + (1000 - 955)/5] / [(1000 + 955)/2]

= [55 + (45/5)] / (1955/2)

= (55 + 9) / 977.5

= 64 / 977.5

= 0.0655

= 6.55%