Question

Problem 5-1 Valuing Bonds

What is the dollar price of a zero coupon bond with 18 years to maturity, semiannual compounding, and a par value of $1,000, if the YTM is: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

		Bond Price
a.	3 percent	$
b.	6 percent	$
c.	9 percent	$

Answer 1

Solution

Let assemble the given information

Zero coupon bond Par value = $1000

Maturity = 18 Years

Compounding semi annually

As the Bond is zero coupon bond hence no interest is payable on bond and question has also mentioned it is also Semi-annually compounding

In such as a case where semi-annually compounding is given we need to multiple Maturity term by 2 and divide Interest rate by 2.

It means maturity term will be twice of 18 i.e. 36 semi-annually and given interest rate will be half

Question has asked to calculate the price of bond if YTM are as follow

1)3.00% or 2) 6.00% or 3)9.00%

Part (1)

If YTM is 3.00%,

Semi-annually rate will be = 3/2 i.e. 1.50%

Maturity is 18 year, semi-annually maturity = 18 *2 = 36

Po = Fo/(1+R)^T

Here,

Po is present value

Fo is future value

R is YTM

T is no of year for maturity,

Now put the given value in the formula

Po = Fo/(1+R)^T

=1000/(1+0.015)^36

=1000/1.7094

=$585

Part (2)

If YTM is 6.00%,

Semi-annually rate will be = 6/2 i.e. 3.00%

Maturity is 18 year, semi-annually maturity = 18 *2 = 36

Now put the given value in the formula

Po = Fo/(1+R)^T

=1000/(1+0.30)^36

=1000/2.8983

=$345.03

Part (3)

If YTM is 9.00%,

Semi-annually rate will be = 9/2 i.e. 4.50%

Maturity is 18 year, semi-annually maturity = 18 *2 = 36

Now put the given value in the formula

Po = Fo/(1+R)^T

=1000/(1+0.45)^36

=1000/4.8774

=$205.03