Assignment Title - Financial Mathematics Calculations and Decision-Making
QUESTION 1: In February 2020 Ink Joy Ltd reported net profits after tax of $500,000 for the year 2019 and announced that it will pay the annual dividend on 20 May 2020. Ink Joy expects the net profits after tax for 2020 to be 20% higher and it will maintain its current dividend payout ratio of 60%. Ink Joy will pay the annual dividend for 2020 in 20 May, 2021.
Amy Aldan owns 10% of the ordinary share capital of Ink Joy Ltd. She has no savings and her sole income comes from Ink Joy Ltd. If Amy wishes to buy household goods worth $5000 in May 2020 and pays all her other bills totalling $35,000, calculate how much can she consume in May 2021? Assume the market rate of interest is 8% per annum compounded annually.
QUESTION 2: Discuss if "maximising shareholder's wealth" is the most appropriate goal of financial management.
QUESTION 3: North Ltd is entering into an interstate expansion phase and requires $10,000,000 to fund this project. North Ltd does not have the funding for this investment today and need to borrow the funds. Income from new branches will fund operation and borrowing costs over the 10 year term of the loan.
The company is considering the options below, with repayments consisting of principal and interest:
1. Global Banking Corp (GBC). Quarterly repayments due at the end of each quarter. The interest rate will be 4.1% p.a. compounding quarterly.
2. International Financing Group (IFG): Annual repayments due at the end of each year. The interest rate will be 4% p.a. compounding annually.
3. Worldwide Wholesale Banking Services (WWBS): Repayments to be made at the end of each 2 year period, across the 10 year term. The interest rate will be 4.05% p.a. compounding annually.
a. Calculate the repayments for each of these options.
b. Identify which would be the best option for North, showing all calculations.
QUESTION 4: Scott Larimore bought a house three years ago that cost $750,000. Scott put up 20% deposit and borrowed the rest from Suncorp Bank at a rate of 7.2% per annum, compounded monthly, for 10 years. The loan will be repaid by equal monthly repayments, consisting of principal and interest.
Three months ago, Suncorp Bank notified Scott that after the last monthly repayment for the third year, the interest rate on his loan will increase to 9.6% per annum, compounded monthly, in line with market rates. Also, from the fourth year of his loan Scott can either increase the monthly repayment (so as to pay off the loan by the originally agreed date), or he can keep paying the same original monthly repayment and extend the term of the loan.
a. Calculate the new monthly repayment if Scott pays off the loan by the originally agreed date.
b. If Scott keeps on paying the original repayment, calculate the extra period added to the term of the loan.
QUESTION 5: You are a Financial Planner and you have been provided details for a new client Rose Tran. Rose is 35 and she plans to retire when she is 65 years old.
Rose has $80,000 in a balanced managed fund. She will not add any further savings to this fund however it will remain in place until retirement. This fund earns 6% p.a. compounded annually after tax. Rose's superannuation fund has a balance of $85,000, to which she contributes $1,500 per month. The superannuation fund earns 7% p.a. compounded monthly.
When Rose retires, she will add both her super and investment balances together and purchase an annuity, which will provide her with a regular income stream throughout retirement.
Her life expectancy is 83 years old, but she is concerned that if she reaches life expectancy and has spent all of her savings she will have nothing left to fund further lifestyle comforts she may need in her advanced years. To ensure she has some money left over to supplement her aged pension, she would like to have a balance of $200,000 remaining in the fund at age 83.
Rose's retirement annuity will earn 7% p.a. which will be compounded monthly.
a. Calculate the total value of Rose's financial assets when she retires at age 65.
b. Calculate the monthly pension amount that Rose will receive in retirement to age 83.
QUESTION 6: On 1 October 2019 Jack Deed bought two $100,000 Australian Government bonds at par, at the date of the last coupon payment. Both bonds pay 8% per annum coupon paid semi-annually. The first bond will mature on 1 April 2023 and the second bond will mature on1 April 2027.
Since then, the yields on both bonds have risen by 2% per annum, compounded semi-annually. If Jack now intends to sell the bonds, calculate the price he will receive from each bond if he sells on 1 April 2020 at the new yield, immediately after receiving the coupon interest payments due that day.
QUESTION 7: SN Thomson Ltd produces solar panels for the Australian residential market. Due to high demand for solar panels, the company has decided to extend its installation services to include batteries which store the energy captured by the panels. They have just conducted a market study costing $20,000 which provided them positive customer response regarding the demand for the batteries.
The company expects to sell 5,000 units of batteries in the first year. The number of units sold is then expected to grow at 15% per annum. The price for each unit in the first year will be AU$12,000. It is expected that this price will then grow by 5% each year. The variable costs will be 70% of the sale price per year. The fixed costs are expected to be $3,000,000 for the first year and then will increase by 2% per annum every year. The project will also require $1,500,000 working capital.
This project will require an initial investment of $56,000,000, which will be depreciated straight line to zero over its four year life. The company believes it can sell the equipment at the termination of the project for $8,000,000.
Assume that all cash flows after the initial outlay occur at the end of each year. The company tax rate is 30%. SN Thomson's required payback is 3 years and required rate of return is 10%.
a. Calculate the incremental cash flows for each year (Y0 to Y4 inclusive).
b. Calculate the payback period of the project.
c. Calculate the net present value, that is, the net benefit or net loss in present value terms of the project.
d. Calculate the present value index of the project.
e. Calculate the discounted payback period of the project.
f. Calculate the internal rate of return of the project.
g. Identify and explain what other factors SN Thomson should consider. Explain if the company should accept the project or not.
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