Today is 1 July 2019. John is 30 years old today. He is planningto purchase an apartment with the price of $800,000 on 1 January2024. John believes that, at the time of purchasing the house, heshould have savings to cover 20% of the house price (i.e.,$160,000) on 1 January 2024. John has a portfolio which consists oftwo Treasury bonds and a bank bill (henceforth referred to as bondA, bond B and bank bill C). There are 200 units of bond A, 300units of bond B and 400 units of bank bill C.
a)
• Bond A is a Treasury bond which matures on 1 July 2030. Oneunit of bond A has a coupon rate of j2 = 3.95% p.a. and a facevalue of $100. John purchased this Treasury bond on 15 February2017. The purchase yield rate was j2 = 3.85% p.a.
• Bond B is a Treasury bond which matures on 1 January 2026. Oneunit of bond B has a coupon rate of j2 = 3.7% p.a. and a face valueof $100. John purchased this Treasury bond on 1 July 2016. Thepurchase yield rate was j2 = 4.1% p.a.
• Bank bill C is a 180-day bank bill which matures on 1September 2019. One unit of bank bill C has a face value of $100.John purchased this bank bill on 15 April 2019. The purchase yieldrate was 3.05% p.a. (simple interest rate).
Calculate:
• The purchase price of one unit of bond A
• The purchase price of one unit of bond B
• The purchase price of one unit of bank bill C
b. John decides to sell each of the three security types today.Both the bonds are sold at a yield rate of j2 = 3.2% p.a. and thebank bill is sold at 3% p.a. (simple interest rate).
Calculate • The sale price of one unit of bond A
• The sale price of one unit of bond B
• The sale price of one unit of bank bill C
Round your answer to three decimal places. Then calculate thetotal sale price of the portfolio (round your answer to the nearestdollar). Note that the sale of each bond occurs after a couponpayment.
c. John plans to use $80,000 of the sale proceeds calculated inpart b to invest into a fund today. John predicts that the returnrate of this fund will be 1 July 2019 to 30 June 2021 j2 = 5.1%, 1July 2021 to 31 December 2023 j2 = 5.3%. Calculate the accumulatedvalue of John’s fund investment on 1 January 2024.
d. To save for remaining required amount on 1 January 2024 (thedifference between the 20% of the house price and the accumulatedvalue from part c), John plans to deposit z% of his annualafter-tax salary into a saving account on 1 July of each year from2019 to 2023 (5 deposits in total). The saving account rates areassumed to be 0.2% per month. Assume that John’s after-tax salaryis $90,000 p.a. Find the value of z (expressed as a percentage androunded to two decimal places).
e. From John’s perspective, draw a carefully labelled cash flowdiagram to represent the above financial transactions of parts cand d.
