What is yield of the bond (problems and solutions)

What is yield of the bond?
The yield of a bond is inverse to its price: as bond prices increase, bond yields fall. For example, assume that an investor purchases a bond with a 10% annual coupon and a par value of $1,000. The yield on this bond would be its par value divided by the interest it pays.
(Definition by investopedia)


Problem#1

Consider a bond with 10% coupon and YTM=8%. If the bond’s YTM is constant, then in one year, will bond prices be higher or lower or unchanged?

 

Ans.The bond price will be lower. As time passes, the bond price, which is now above par value, will approach par.

Problem#2

A 20-yr bond with $1000 par makes semi-annual coupon payments at a coupon rate of 8%. Find the BEY and EA YTM of the bond if the price 

(a) 950 

(b) 1000 

(c) 1050.

(Solution for a)

Use the following inputs: 

n = 40, 

FV = 1000, 

PV = –950, 

PMT = 40,

You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity of: 4.26% x2 = 8.52%

(Note:Effective annual yield to maturity = (1.0426)2 – 1 = 0.0870 = 8.70%)

(Solution for b)

Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon, 4%. The bond equivalent yield to maturity is 8%.

(Note: Effective annual yield to maturity = (1.04)2–1 = 0.0816 = 8.16%)

(Solution for c)

Keeping other inputs unchanged but setting PV = –1050, 

we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis.

(Note:Effective annual yield to maturity = (1.0376)2–1 = 0.0766 = 7.66%)

Problem#3

A Zero-coupon bond with par of $1000 and maturity of 5 years sells for 746.22. what is YTM? 

Using a financial calculator, 

PV =-746.22, 

FV = 1,000, 

t=5, PMT = 0

The YTM is 6.0295%.
 

What is new YTM if price falls to $730?
Using a financial calculator, PV =-730.00, FV = 1,000, t=5, pmt = 0. The YTM is 6.4965%.
(Note that the YTM increases as the bond price falls)

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I m moly aneglina and doing blogging since 2 years when i found my deep interest in writing and searching. I try to make good article for my readers and visitors.