Question

Question 1 [6 marks]
a. [1 mark ] Find the price (per $100 face value, rounded to 3 decimal
places) of a 12% Treasury bond, 145 days before maturity, at a yield
of 6.26% p.a. 1
b. [2 marks] Suppose another student sees your answer to a., and says
“You’re wrong! Your answer is more than $100. The price
of a short term financial instrument should be always less
than its face value!”
Explain to this student why the price of the Treasury bond in a. is
greater than its face value of $100.
c. [3 marks] Consider the bond in a., but rather price it 187 days before
maturity at a yield of 6.24% p.a. Here, a coupon payment is made
on the fifth day and the last day. Draw a cash flow diagram that
represents this scenario to accompany your answer.

Answer 1

Part (a)

Price of the bond = PV of all the pending coupon + PV of repayment

Only one semi annual coupon is pending = 12% / 2 x 100 = 6

Semi annual yield = 6.26% / 2 = 3.13%

Hence, price of the bond = (6 + 100) / (1 + 3.13%)^145/(365/2) = $  103.436

Part (b)

If a bond trades at yield > coupon rate, then bond trades in premium. Because of this it's market value or trading price or current price will be higher than the face value or par value.

Part (c)

Pending payments = A semi annual coupon in 5 days = $ 6 and last coupon and principal on the last day

Semi annual yield = 6.24% / 2 = 3.12%

hence, Price = 6 / (1 + 3.12%)^{(5 x 2 / 365)} + 106 / (1 + 3.12%)^{(187 x 2 / 365)} = $  108.710