Zero-Coupon Bond Valuation

A zero-coupon bond (also known as a discount bond) does not make periodic interest payments during its lifespan. Instead, the issuer of a zero-coupon bond makes a single principal payment to the holder at maturity. Zero-coupon bonds are issued at significant discounts to face value. As a zero-coupon bond reaches maturity, its market value will approach its face value. Below is an example of the payment structure of a zero-coupon with a $10,000 face value:

Although zero-coupon bonds do not make periodic coupon payments, they are valued just like semi-annual coupon bonds. Recall that the value of a coupon bond is equal to the present value of its future cash flows. To calculate present value, an investor must forecast the coupon bond’s future cash flows and discount them at a discount rate. The discounted cash flows can then be summed to derive the value of a bond. Zero-coupon bonds are valued by discounting their single cash flow payment at the proper discount rate. Semi-annual compounding periods are used so that the returns of zero-coupon bonds can be compared to traditional semi-annual coupon bonds.

Consider the following example: An investor wishes to purchase a $1,000 face value zero-coupon bond with seven years remaining until maturity.  The required rate of return on the investment is 6%. Calculate the bond’s value.

The maximum price he should pay for the bond is $661.12 or 66-4. Remember, a zero-coupon bond is valued as if it made semi-annual coupon payments. Thus, a zero-coupon bond with seven years until maturity has 14 periods until maturity. Because the bond has a required rate of return of 6% (considered per annum), its periodic required rate of return is 3%.

Calculate the value of the bond if its required rate of return was reduced to 4%. The bond would be valued as follows:

The decrease in the required rate of return will cause the value of the bond to increase to $757.88 or 75-25.  

Questions:

1.  Calculate the market value of a zero-coupon bond with a $1,000 face value, a 4% required rate of return, and six years remaining until maturity.

2.  Calculate the present value of a zero-coupon bond with a $10,000 face value, a 12.5% discount rate, and four years remaining until maturity.

3.  Calculate the present value of a semi-annual coupon bond with a $1,000 face value, a 9% required rate of return, and one year remaining until maturity.

Answers:

1.  $788.49         N = 12; I = 2; FV = $1,000; PV = Solve

2.  $6,156.99      N = 8; I = 6.25; FV = $10,000; PV = Solve

3.  $915.73         N = 2; I = 4.5; FV = $1,000; PV = Solve

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