Question

4% 6. Suppose that you are given the following information: Bond T (maturity) Coupon rate Price A 0.5 99.0291 B 1 2% 95.2555 C 1.5 97.3620 All bonds have a $100 face value. Calculate zero-coupon yields for 0.5, 1, and 1.5-year maturities. 7%

Answer 1

As the above is zero coupon bonds , the coupon rate would not be applicable over here.

The above equation can be solved with helped of below formula :-

Yield to maturity = (Face Value of bond/Current Bond Value)^(1/Year of maturity)-1

Where

Face value in the initial value of bond

Current Bond value is market value of bond

^ represent the highest power

maturity is the expiry on bond

So Taking into consideration all the above scenario, will solve it one by one as below

Face value of Bond for all the three scenario would be $100

1. First Bond yield for 0.5 years

Current Bond value = 99.0291

Maturity 0.5 year

Applying the above numbers on the given formula

=(100/99.0291)^(1/0.5)-1

=0.0197044

You can have this rounded up to % value which would be 1.9704 %

2. Second Bond yield for 1 year

Current Bond Value - 95.2555

Maturity = 1 year

Applying the above formula

=(100/95.2555)^(1/1)-1

=0.049808

You can have this rounded up to % value which would be 4.9808 %

3. Third Bond yield for 1.5 year

Current Bond value - 97.3620

Maturity - 1.5 year

Applying the above formula

=(100/97.362)^(1/1.5)-1

=0.0179825

You can have this rounded up to % value which would be 1.7982 %

So Solving the above equation below are the yields as per the maturity

For 0.5 year = 1.9704 %

For 1 year = 4.9808 %

For 1.5 year = 1.7982 %

Please let me know if you found this answers relevant or else need more clarification on this.