Question

Please do not use excel and use financial formulas

1. Consider the following five bonds, all with notional amounts of $100.00, that are trading in a liquid market on September 30th 2018

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

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

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

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

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

a. How would you characterize the market that these bonds are trading in? What does this imply with respect to pricing a new bond that is just introduced into the market, with cashflow dates that align with the exiting bonds?

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

c. 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%?

d. Suppose another T-bill is introduced into the market with a $100 notional (no coupon) and a maturity date of 1.5 years. What is the challenge here and how might you address it? What would be a good price for this T-bill?

Answer 1

Ans a) The market currently is not yielding (YTM) more than 3% on 5 year 8% coupon bond. This signifies that some bonds are priced at a premium with respect to YTM percentages eventually leading to a loss in overall return at maturity when compared to annual coupon rate. YTM for first two bonds can be calculated as (Face Vale/Market Price)^1/Year to Maturity -1 which gives YTM as 1.00% for (i) T Bill and 2.50% for (ii) T Bill respectively. The other bonds can be calculated as Coupon Paid on Bond + (Face Value-Current Price)/Term this whole will be divided by (Face Value+Current Price)/2 this will give YTM for all Coupon rated bonds which will come as (iii) 2.96%; (iv) 2.96% and (v) 3.00%.

Pricing of new Bonds with Coupon rate more than 3.00% should be at a premium otherwise it can be Zero Coupon Bond where Market will price it effectively at 2.50% YTM. The market is highly liquid which means too much cash in the market but too few takers.

Ans b) The answer to this Question is already provided above with Year 1 T Bill yielding 1.00%, Year 3 T Bill yielding 2.50% and Year 4 to Year 5 Bonds yields ranging from 2.96% to 3.00%.

Ans c) Cash flows for this bond will be Year 1 $3.00 coupon payment, Year 2 $3 coupon payment, Year 3 $3 coupon payment, Year 4 $3 and $100 notional price so $103.00. If we use YTM of 2.96% as our discount rate then Price of the Bond should be PV of Cash Flow 1: $3*(1/(1+0.0296)^1)=2.914, likewise PV of Cash Flow 2:$3*(1/1+0.0296)^2)=2.830, PV of Cash Flow 3: $3*(1/1+0.0296)^3)=2.749 and Cash Flow 4: $103*(1/1+0.0296)^4)=91.656 thus total Value of all Cash Flows or Price of Bond= $100.149.

Ans d) The challenge in the T Bill for 1.5 years maturity date is that we know the annualized yield to maturity of 1.00% and semi annual rate is not available. Thus what we can do to price the T Bill is to use annualized YTM rate and get the payment semi annually thus we can discount at the rate 0.50% for 3 cash flows. Thus the formula would be PV Cash Flows 1= 0.50*DF@ the price of T Bill will be $100.00 only