Reference no: EM132362403

Managerial Finance Assignment - Financial Mathematics and Security Valuation

Outline - You have just started working for Polycorp Pyramid Financial Services, and your supervisor gives you some problems to answer/solve for clients. You should solve the following ten questions showing your full workings and explanations. Each question is worth one mark. You must have the correct answer and show your working and correct explanation to get one mark (very brief or one to two lines of answers are not acceptable). As well as solving the problems manually using the appropriate formulas, you must also solve the problems using Excel functions/calculations. An incorrect answer or an answer without the working receives zero. Include cash flow maps or tables wherever possible. Avoid rounding error. Read the questions carefully, do not assume that they are the same as other questions you have covered in this unit.

Question 1 - Now that they have accumulated a deposit of $50,000, Scott and Helen wish to use the deposit and take out a housing loan to purchase a home. The home costs $600,000. The loan is to be repaid in equal monthly installments over a term of 25 years. Jenny recalls that the interest rate quoted by the bank is an annual nominal rate of 6.0%pa compounded monthly. After 10 years (120th repayment has just been made), the bank announces the interest rate will change to an annual nominal rate of 4.8%pa compounded monthly.

(i) How much is the original monthly repayment?

(ii) Provide Scott and Helen with a repayment schedule based on the original loan using excel.

(iii) How much is the monthly repayment after the interest rate cut, assuming Scott and Helen now wish to repay the loan in 10 years? (Answers should be accurate to the nearest dollar)

Question 2 - Jim is going to establish a University Fund for his daughter Jan, who has just been born. He plans to make the first deposit of $20,000 today and make another 8 annual deposits of $5,000. After this, annual deposits of $10,000 will be made until Jan's 17th birthday. Given the long term nature of the investment, Jim anticipates a 5% pa return. The money is the transferred to an account for Jan and she will then withdraw the money in equal monthly amounts for 5 years starting on her 17th birthday. Jan will only be able to earn 3% pa on her money.

(i) How much will be available on Jan's 17th birthday, before the first withdrawal is made?

(ii) Create a schedule showing the cash inflows and outflows of this fund. How much will Jan be able to spend each month? (Your answers should be accurate to the nearest dollar)

Question 3 - (a) The S&P/ASX200 price index has gone from 6,800 to 6,240 in 3 years. The equivalent accumulation index went from 54,320 to 65,480 over the same period. What is the annual rate of return on each of these indices? Explain the difference.

(b) Using the approach covered in your textbook calculate the geometric average annual rate of return over five years given the following annual rates, year 1 = 2.10%, year 2 = 2.40%, year 3 = 2.80%, year 4 = 3.25% and year 5 = 3.75% . What is the arithmetic average? Explain the difference. (Rates as a percentage accurate to one basis point).

Question 4 - Fran wishes to prepare for her retirement in 15 years' time. Currently she has a house which she estimates will be worth $1,000,000 in 15 years. She anticipates being able to deposit $40,000 at the end of each year until retirement. When she retires, she plans to downsize to a unit worth $800,000. Assume an interest rate of 4% pa and ignore tax in your calculations.

Required - Show how much Fran can expect to live on per year (assuming end-of-year withdrawals) after she retires and if she wishes to maintain her capital to pass on to her heirs. (Accurate to the nearest dollar).

Question 5 - Your supervisor has asked you to do the following calculations:

(a) A bank bill with 180 days to maturity is issued with a yield of 2% pa. Face value is $10,000,000. Calculate the issue price of the bill.

(b) The bill in part (b) is sold after 60 days at a yield of 2.2% pa. Calculate and explain the annual nominal holding period yield. (Accurate to the nearest dollar and rates as a percentage accurate to one basis point).

Question 6 - Wendy buys a bond with a face value of $100, a time to maturity of three years, a coupon of 6% pa with semi-annual payments and a yield of 3% pa. 12 months later (just before the second coupon is to be paid), the Reserve Bank of Australia unexpectedly increases the cash rate. The yield on Wendy's bond increases to 3.3% pa.

Required - Calculate the buying price, the price 12 months later and explain why the price has changed. (Accurate to the nearest cent).

Question 7 - Polycorp has just paid a dividend of $10.00. It is expected to pay a dividend $10.00 at the end of the first year and $11 at the end of the second year. Its dividends will then grow at 3.00%pa for the following ten years. Dividends are then expected to grow at 1.00%pa forever. Shareholders required return on equity is 10.00% pa. What is the current price of Polycorp shares? (Accurate to the nearest cent).

Question 8 - The required rate of return on the shares in the companies identified below is 8% pa. Calculate the current share price (ex-dividend) in each case.

(a) The current earnings per share of Alpha Ltd are $4.20. The company does not reinvest any of its earnings. Earnings are expected to remain constant.

(b) Gamma Ltd is planning to reinvest earnings and not pay dividends until year 6, when a dividend of $8 is expected (D6 = $8). Dividends are expected to grow at 3% pa forever after that. (Accurate to the nearest cent).

Question 9 - Your client wishes to insure their Ferrari. Mooncorp Insurance has quoted an annual premium to insure the car of $20,000. Mooncorp offers a 5% discount if you pay the lump sum immediately. They also offer an alternative payment method. The account can be paid in full by making 12 equal monthly payments of $2,000, rather than the lump sum, with the first payment due in 1 month. What is the effective annual opportunity cost of paying monthly? In other words, what interest rate is being charged if your client decides to use the repayment plan as opposed to the lump sum?

You must provide one complete manual trial calculation of the IRR to demonstrate that you understand the process. Failure to follow this instruction will attract a mark of zero. (Rates as a percentage accurate to one basis point).

Question 10 - You are offered the choice of the following two income streams;-

$10,000 every 2 years in perpetuity with the first receipt immediately.

$2,500 every quarter for 10 years with the first receipt at the end of the first quarter.

The annual interest rate is 6% pa.

Which income stream do you choose? (Answer to the nearest dollar).

Format: Calculation and brief working or short answer with explanation as well as the calculation solved in an Excel spreadsheet. For each calculation you must provide a manual solution and a solution using excel. Typing straight into excel without doing the calculations in excel does not qualify as solving in excel. You have three options:

(a) Do all the assignment with explanations in excel and upload one file. Type your explanation and manual answer in text boxes. This is the preferred method.

(b) Do the assignment in two files, one Word document and one Excel spreadsheet. Then upload both documents.

(c) Do the assignment producing two files, a word document and an Excel spreadsheet. Embed the excel file into the word document and upload one file.

Option (a) is the preferred option.