Question

a) [3 marks] Draw a carefully labelled cash flow diagram to represent the above financial transaction. Draw your cash flow diagram from Luke’s perspective.

b) [4 marks] Calculate the purchase price of the 180-day bank bill on 1 January 2019 (rounded to three decimal places) and the sale price of the 180-day bank bill on 15 April 2019 (rounded to three decimal places).

c) [2 marks] Calculate Luke’s holding period yield (expressed as a percentage and rounded to two decimal places).

d) [4 marks] Calculate the capital gain/loss component of the dollar return on the investment. (The “dollar return on the investment” means the difference between the sale price and the purchase price). Make sure you identify whether a capital gain or capital loss has been made. Round your answer to two decimal places. Please also explain why capital gain or loss has occurred.

e) [2 marks] Assume that Luke borrowed money to purchase the bill at the price of $495, 000 at a interest rate of 3.3% and decided to sell the bank bill after 100 days. What price must the bill be sold after 100 days for Luke to break even on his investment (rounded to 2 decimal places)?

Answer 1

a) The cash flow diagram as per the given situation in the question can be prepared as follows:-

b) 

By extracting the information:

Par value of 180- day bank bill=$5,00,000

Yield rate p.a=3.18%

So, the Yield rate for 180 days=1.59%

Therefore, the purchase price can be calculated by using the following formula:-

Purchase Price of 180-day bank bill on 1 January 2019=Par value of 180-day bank bill/(1+180 day yield rate)

By substituting the values:

=$500,000/(1+0.0159)

=$500,000/1.0159

=$492,174

Now, the sale price of the 180-day bank bill as of 15 April 2019 can be calculated by using the following formula:-

Sale Price of the 180-day bank bill=Par value of 180-day bank bill/(1+75 days yield rate)

Here, the Par value of a 180-day bank bill=$500,000

Yield rate at the time of sale=3.06%

Balance days are from January to 15 April

So 75 days yield rate=0.6375%

By substituting the values:

Sale Price of the 180-day bank bill=$5,00,000/(1+0.006375)

=$500,000/1.006375

=$496,833

c) 

The formula for calculating holding period yield is as follows:-

Holding Period Yield=(Sale Price of 180-day bank bill- Purchase Price of 180-day bank bill)/Purchase Price of the 180-day bank bill*105/360*100

Here, the Sale price of a 180-day bank bill=$496,833

Purchase price of 180-day bank bill=$492,174

By substituting the values:

Holding period yield=($496,833-$492,174)/$492,174*105/360*100

=($4,659/$492,174)*105/360*100

=3.245% p.a

d)

There will be a capital gain which can be calculated by using the following formula:-

Capital gain=Sale Price of the 180-day bank bill- Purchase Price of the 180 -day bank bill

=$496,833-$492,174

=$4,659

Answer 2

Note : 1/1 - 15/4 is 76 days and ausie use 365 day a year, holding term = 104 days