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
2. 1. given this market, what are the discount factors and implied zero coupon rates associated with annual terms 1 – 5 years?
   2. What would be the price of a new bond introduced into the market with a $100 notional, 4 year maturity and an annual coupon rate of 3%? ….4 marks

Answer 1

Answer a:

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%

Answer b:

Bond: $100 notional, 4 year maturity and an annual coupon rate of 3%

Annual coupon amount = 100 *3 = 3

Discount factor for 4 year bond as calculated in answer a (iii) above = 2.95%

We will use PV function of excel to get price of the bond:

PV (rate,nper, pmt, fv,type)

PV (2.95%, 4, -3, -100, 0)

= $100.1861

Price = $100.19