Question

Please help I have the answers but have no idea on how to solve. (These are different numbers than the actual question so I can practice)

1) On February 20, 2015, 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 February 20, 2020, this bond was selling for only $955.

a: What was the nominal yield on this bond on February 20, 2015?

b: What was the current yield on this bond on February 20, 2015?

  c: What is the nominal yield on this bond on February 20, 2020?

d: What is the current yield on this bond on February 20, 2020?

e: What is the yield to maturity for this bond on February 20, 2020?

[For e, use a financial calculator, or excel, or web calculator or trial and error.]

Answer 1

Bond face value = 1000 $

Coupon payment = 55$

Time = 10 years

a. (Nominal Yield is always calculated on Face value of the bond)

Nominal Yield on Feb 20, 2015 = Annual copon payment / Bond Face value * 100

= 55 / 1000 * 100

= 5.5 %

b. (as the bond was purchased at premium of 1025$, current yield will be)

Current Yield on Feb 20, 2015 = Annual copon payment / Bond purchase price * 100

= 55 / 1025 * 100

= 5.3658 %

c. Nominal Yield on Feb 20, 2020 = Annual copon payment / Bond Face value * 100

= 55 / 1000 * 100 = 5.5%

d.(as the bond is selling at discount  of 955$, current yield will be)

Current Yield on Feb 20, 2020 = Annual coupon payment / Bond current price * 100

= 55 / 955 * 100

= 5.7591 %

e. Here we are finding for yield to maturity upto 5 years only from feb 2015 to feb 2020

Yield to Maturity = = (Future Value/Current Bond Purchase Price) ^ (1/Years to Maturity) −1

Future value = face value of bond * (1 + Interest rate)^n

n = Time = 5 years

= 1000 * ( 1 + 5.5%)^5 = 1000 * (1 + 0.055)^5

= 1000 * (1.055)^5 = 1000 *  1.306960006409375

= 1306.96

Now (1306.96 / 1025)^ (1 / 5) - 1

= (1.2750829268292682926829268292683)^0.2 - 1

= 1.0498027017614988954602326180694 - 1

= 0.04980270176149889546023261806937 * 100

= 4.9 %

(in case any doubt do comment)