Question

1. Consider the following five bonds, all with notional amounts of $100.00, that are trading in a liquid market on September 30^th 2018
   1. T-bill 1: 1 year maturity, no annual coupon, market price = $99.01
   2. T-bill 1: 3 year maturity, no annual coupon, market price = $92.86
   3. Bond 1: 4 year maturity, 4% annual coupon, market price = $103.92
   4. Bond 2: 5 year maturity, 2% annual coupon, market price = $95.52
   5. Bond 3: 5 year maturity, 8% annual coupon, market price = $123.31

Assume that all coupon and maturity dates align with all cashflows (coupons and notional amounts) paying at September 30^th of each year.

Given this market, what are the discount factors and implied zero coupon rates associated with annual terms 1 – 5 years? (show all your work) …10 marks

Answer 1

Answer:

zero coupon rates:

i. T-bill 1: 1 year maturity, no annual coupon, market price = $99.01

We will use excel function RATE to get zero coupon rates:

RATE (nper, pmt, pv, fv, 0)

=RATE (1, 0, 99.01, -100, 0)

=1.00%

Zero coupon rates = 1.00%

ii. T-bill 1: 3 year maturity, no annual coupon, market price = $92.86

= RATE (3, 0, 92.86, -100, 0)

=2.50%

Zero coupon rates = 2.50%

Bonds:

iii. Bond 1: 4 year maturity, 4% annual coupon, market price = $103.92

Annual coupon = 100 * 4% = 4

Discount factor = RATE (4, 4, -103.92, 100, 0)

=2.95%

Discount factor = 2.95%

iv. Bond 2: 5 year maturity, 2% annual coupon, market price = $95.52

Annual coupon = 100 * 2% = 2

Discount factor = RATE (5, 2, -95.52, 100, 0) = 2.98%

Discount factor = 2.98%

v. Bond 3: 5 year maturity, 8% annual coupon, market price = $123.31

Annual coupon = 100 * 8% = 8

Discount factor = RATE (5, 8, -123.31, 100, 0) = 2.92%

Discount factor = 2.92%