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The 6.3 percent, semi-annual coupon bonds of PE Engineers mature in 13 years and have a price quote of 99.2. These bonds have a current yield of _____ percent, a yield to maturity of _____ percent, and an effective annual yield of ______ percent
A) 6.23; 6.36; 6.42
B) 6.23; 6.20; 6.16
C) 6.12; 6.36; 6.42
D) 6.35; 6.39; 6.49
E) 6.35; 6.32; 6.29

Respuesta :

Answer:

Hi, the answer is D) current yield=6.35% ; YTM=6.39% ; Effective annual rate=6.49%

Explanation:

In order to decide, we need to use 3 formulas with the information given, let´s start to solve this.

Current yield

[tex]Current Yield=\frac{Coupon}{Current Price}[/tex]

Now, our bond is its face value times the coupon, (for all bonds, its face value is 100)

Therefore, 100x6.3% = 6.3

[tex]Current Yield=\frac{6.3}{99.2} =6.35[/tex]

Yield to Maturity (YTM)

We should only follow this formula.

[tex]YTM=\frac{C+\frac{F-P}{N} }{\frac{F+P}{2} }[/tex]

Where:

C = Coupon (6.3)

F= Face Value (remember, 100)

P= Price (99.2)

n= years to maturity

Therefore

[tex]YTM=\frac{6.3+\frac{100-99.2}{13} }{\frac{100+99.2}{2} }=6.39[/tex]

Finally, we have to find the effective annual rate, for that, we have to use the YTM as our nominal rate, since it is semi-annual, the number of compounding periods is 2 (two semesters in a year).

The formula goes as follows.

[tex]Effective Annual Rate=((1+\frac{YTM}{Compounding Periods}) ^{Compounding Periods}-1)x100[/tex]

Therefore.

[tex]Effective Annual Rate=((1+\frac{0.0639}{2}) ^{2} -1)x100=6.49[/tex]

Best of luck.

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