Financial Modelling

Take Home Quiz

1. Today is 1 January 2018. Mary is 40 years old today and she is planning to set up a university education fund for her 12 year old daughter Emily. The fund should be enough to cover Emily's university tuition fee costs (35 marks).

a. Assume that Emily will attend university at age 18 to complete a three-year bachelor degree. Mary estimates that current average university tuition fees are $25,000 per person per year and are growing at a rate of 3% p.a. (e.g., the estimated tuition fee for 2019 is $25, 000 × (1 + 3%)).

Find Emily's first year, second and third year tuition fee amount. Calculate the amount that Mary needs to deposit into the fund today. Assume the fund yield rate is j1 = 3.6% p.a. and the tuition fee is paid on an annual basis at the beginning of each study year. Round your answer to three decimal places.

b. Mary has a portfolio which consists of three securities (henceforth referred to as security A, security B and security C).

• Security A is a 180-day $50,000 bank bill which is purchased on its issue date 15 November 2017. The purchase yield rate is 4.1% p.a. (simple interest rate).

• Security B is a Treasury bond which matures on 1 January 2025. This Treasury bond has a coupon rate of j2 = 3.25% p.a. and a face value of $100. Mary purchased this Treasury bond on 23 September 2017. The purchase yield rate was j2 = 3.7% p.a.

• Security C is a Treasury bond which matures on 1 January 2023. This Treasury bond has a coupon rate of j2 = 4.75% p.a. and a face value of $100. Mary purchased this treasury bond on 28 December 2016. The purchase yield rate was j2 = 4.1% p.a.

Calculate the purchase price of security A, security B and security C. Round your answer to three decimal places. The price of both security B and security C should be calculated using the RBA method.

c. Mary decides to sell all three securities today to pay the required deposit for the education fund. Security A can be sold at a yield rate of 3.9% p.a. (simple interest rate). Security B and security C can be sold at a yield rate of j2 = 3.75% p.a. Calculate the sale price of security A, security B and  security C. Round your answer to three decimal places. Note that the sale of security B and security C occurs after the coupon payment.

d. Based on Mary's perspective, draw three carefully labelled cash flow diagrams to represent the above financial transactions of security A, security B and security C, respectively.