Calculate the annualised discount rates and prices

Reference no: EM131359694

Assignment: Presentation

Tasks

Task 1

a) On Friday 11th November 2016, the UK government held its weekly auction of government Treasury bills. The table below outlines results for the one-, three- and six-month bills.

Maturity Date	Average Price	Average Discount
12^th December 2016	99.988998	0.141452%
13^th February 2017	99.963433	0.144662%
15^th May 2017	99.887269	0.222985%

Show that the prices and discount rates for the three bills are consistent by working out the terms to maturity and incorporating them into price calculations. You must show the price using an appropriate mathematical formulation.

b) The table below lists the principal amounts of each bill auctioned and the scale of bidding on 11th November.

Maturity Date	Principal Amount Sold	Aggregate Scale of Bids
12^th December 2016	£500 million	£2449.5 million
13^th February 2017	£1500 million	£6300.5 million
15^th May 2017	£2500 million	£7511.4 million

Calculate and comment on the significance of the bid-to-cover ratios given the size of the yields. The word-count for this element should be 200-300 words.

c) Discuss the scale of the discount rates prevailing on 11th November 2016, contrasting them with another Debt Management Office treasury bill auction of your choice that took place between 2005 and 2007. The discussion should focus on the difference between the earlier and recent discount rates, and provide reasons why they are so different. Make sure that you clearly record and reference the earlier data. The word count for this element should be 300-400 words.

Task 2

A company operates a commercial paper programme to finance its short-term borrowing requirements. On 11th November 2016, the company sold paper with terms to maturity of 30 days, 182 days and 270 days. The table below lists treasury bill rates and the basis point premiums over treasury bills offered by each issue of commercial paper.

Days to Maturity	Treasury Bill Discount Rate	Basis Point Premium
30 days	0.1572%	50 basis points
182 days	0.2385%	77 basis points
270 days	0.3246%	88 basis points

a) Calculate the annualised discount rates and prices for the three commercial paper issues. Your mathematical workings should be clearly outlined in your written presentation. For valuation purposes, assume a 365-day year.

b) The commercial paper was given a P-2 rating by Moody's and an A-2 rating by Standard & Poor. Outline the ratings systems used by Moody's and Standard & Poor for grading short-term debt securities and explain the significance of the ratings given to the company's commercial paper. The word-count for this element should be 300-400 words.

c) With reference to the data on the company's commercial paper yields, discuss the following questions:

1. Why do short-term debt securities issued by private companies generally offer higher yields than treasury bills issued by central governments?

2. Why is the size of the basis point premium larger the longer the term to maturity?

The word count for this element should be 200-300 words.

Task 3

A company is obliged to pay a bill of $2,700,000 to one of its suppliers two-months from today but will not have sufficient funds to do so. It intends to borrow the funds but will be unable to repay the loan until three-months after the bill is paid.

The money market interests rate spreads for short-term dollar transactions are presented in the table below.

Money Market Dollar Interest Rate Spreads (%)
1 month	2 months	3 months	4 months	5 months	6 months
0.50 - 0.60	0.66- 0.76	0.80 - 0.90	0.93 - 1.03	1.05 - 1.15	1.15 - 1.25

a) Assume that the company wishes to undertake a money market hedge to fix the future borrowing rate. Explain the character of the company's interest rate risk exposure and calculate the annualised forward interest rate that it can achieve using the current interest rates. Base calculations on months rather than days and clearly outline the mathematical workings in your written presentation. The word-count for this element should be 150-250 words.

b) A bank is willing to offer the company a forward rate agreement (FRA), incorporating a forward rate fixed at the level calculated in part a). When the bill is due to be paid, the relevant $LIBOR rate is 3.25%. Calculate and explain the terms on which the FRA is settled. Clearly outline the mathematical workings in your written presentation.

c) Given the forward rate available to the company, discuss the factors that it should consider at the outset when deciding whether to fix the future interest rate. The word count for this element should be 200-300 words.

Task 4

The table below Lists the terms to maturity, the coupon rates, coupon payment dates and yields to maturity for three UK government bonds at the close of business on 26th October 2016.

Gilts Prices Close of Business 26^th October 2016
Maturity Date	Coupon Rate	Coupon Payment Dates	Yield to Maturity
07/09/2020	3.75%	7^th September, 7^th March	0.684735
22/07/2026	1.50%	22^nd January, 22^nd July	1.296943
07/03/2036	4.25%	7^th September, 7^th March	1.928408

The coupon rates are quoted as annual rates. But UK government bonds divide the annual coupon into two equal instalments payable every six months.

a) Work out the time periods to maturity, the periodic coupons and the periodic yields for each of the three bonds. Use the information to calculate the clean price of each bond. Your mathematical workings should be clearly outlined in your written presentation.

b) Calculate the accrued interest and dirty prices for each bond at the close of business on 26th October 2016. Your mathematical workings should be clearly outlined in your written presentation.

c) UK government bonds are widely considered to be risk-free investments. Explain what is meant by ‘risk-free' in this context and discuss the notion that they are, nevertheless, exposed to market risk. The word count for this element should be 250-350 words.

Task 5

a) A company has issued $140 million (face value) of bonds with three-years to maturity. They offer an annual coupon of 3.2% above the sixth-month $LIBOR. Interest is paid every six months and the $LIBOR is currently 0.85%. Assume that the $LIBORs for the subsequent five interest set dates are as stated in the table below.

$LIBOR Rates
0.5 years	1 year	1.5 years	2 years	2.5 years
1.47%	2.68%	3.45%	3.68%	5.02%

Calculate the coupon rate and the amount of interest that the company pays each six-month period. Your mathematical workings should be clearly outlined in your written presentation.

b) A company has issued five-year bonds with the annual coupon and the repayment of principal linked to an index of inflation. The coupon rate is 4.75% and the principal is £100. The index of inflation is currently set at 100. Assume annual inflation rates for the next five years in the table below.

Inflation Rate
Year 1	Year 2	Year 3	Year 4	Year 5
1.47%	2.68%	3.45%	3.68%	5.02%

Calculate the level of the inflation index for each year and use it to determine the coupon payment per bond for each of the five years. In addition, calculate the amount that the company pays bondholders when the debt matures after five years. Your mathematical workings should be clearly outlined in your written presentation.

c) Explain the main characteristics of variable coupon and index-linked bonds. Discuss how they help to off-set some of the risks faced by investors in fixed interest securities. The discussion should include an assessment of the limitations of variable coupon and index-linked securities as assets offering protection against certain types of risk. The word count for this element should be 350-450 words.

Reference no: EM131359694

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