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FINM 1001: Money Markets and Finance

Valuing Debt Instruments: Solutions to Practice Questions

Question One

What is the price of a $100 zero-coupon bond that matures in
2 years given the required return is 6% p.a.?

To calculate the price of the zero-coupon bond, simply use the formula for the present value of a single sum:

Question Two

What is the price of a Commonwealth Government 14.5% Treasury Bond with 6 years until expiry given it is reported to have a yield of 8% p.a?

In calculating the price of this instrument, recall the bond conventions discussed in lectures.  More specifically, given that virtually all coupon-paying bonds pay coupons every six-months, both coupon rates and yields are quoted as nominal rates compounding semi-annually.  Given this, the price of the bond can simply be calculated as the sum of the present value of the coupons (an annuity) and the present value of the face value:

Given the fact that the coupon rate exceeds the yield, it is unsurprising that price of the bond is greater than its face value.

Question Three

What is the price of a 10-year, 12% Government bond if the yield to maturity is 6% p.a?

The price of the Government bond can be calculated using a methodology identical to that described in the solution to Question Two:

As in Question 2, given the fact that the coupon rate exceeds the yield, it is unsurprising that the price of this instrument exceeds its face value.

Question Four

A 180-day bank accepted bill is quoted as having a yield of 7% p.a. What is the price of the bill?

Recalling the quotation conventions for bank accepted bills, the price of this bill is calculated as follows:

Question Five

Find the price of a 12%, $100 Commonwealth Government bond with exactly four and a quarter years to maturity if the bondholders required return is 10% p.a.

The instrument matures in 4.25 years, but we know that coupons are paid semi-annually.  This means that there is 3 months until the next coupon is paid.  With this in mind, it is easiest to calculate the present value of all cash flows in 3 months’ time and discount this figure back the last 3 months to get today’s price.  Again, recalling the quotation conventions for coupon-paying bonds, the price of this bond is calculated as follows: