Question

Question 8

The Australian Treasury has issued 9.0-year zero coupon bonds with a face value of $1,000. Assume that coupon payments are normally semiannual. What will be the current market price of these bonds if the yield for similar investments in the market is 5.3 percent p.a.? (Round to the nearest dollar; do not use $ sign or commas))

Answer 1

A zero coupon bond is a bond that is issued at a deep discount to its face value but pays no interest. A zero-coupon bond is a bond where the face value is repaid at the time of maturity. It does not make periodic interest payments or coupon payments, hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par value.

In the given case of Australian Treasury has issued 9-year zero coupon bonds with a face value of 1000 with semi annual coupon payments which tends to be zero since the bond is a zero coupon bond. The yield from similar investments in the market is 5.3% annually or 2.65% semi annual.

Now on applying the market yield rate of 2.65% or 0.0265 (in decimal) on the zero coupon bond for 18 semi annual periods after which the zero coupon bond is repaid, we can get the current market price of the zero coupon bond.

Current Market Price of the Bond = Face value of the bond * Present value factor

Where-

Face value of the bond is 1000

Present value factor = 1/ (1 + 0.0265)¹⁸

Present value factor = 1 / (1.0265)¹⁸

Present value factor = 0.62451

On putting these figures in the above formula, we get

Current Market Price of the Bond = Face value of the bond * Present value factor

Current Market Price of the Bond = 1000 * 0.62451

Current Market Price of the Bond = 624.51

Current Market Price of the Bond = 625 (Rounded to the nearest dollar)