FINANCIAL MATHS AND SECURITY VALUATION

QUESTION

Figure 1: Excel Table Formatting Example

Table Formatting:

• Top row of table headings ‘Bold’ and ‘Centred’, may left justify left most cell of column headings – refer figure above
• Try to only use horizontal lines – in design less is more, but don’t confuse this with the basic economic premise that more is more….
• For column headings, use a single line on top and double line at the bottom
• Last row ends with single line on the bottom
• Where appropriate use other horizontal lines
• May use double lines to indicate sum

Graph Formatting:

• Use the right graph for the particular form of analysis
• Include meaningful Headings and Axis Titles (note I haven’t included y-axis label in Figure 2 because values are self explanatory)
• Ensure that headings, plots and other information don’t overlap each other.
• Choose an appropriate font

Figure 2: Comparative Graph of Share Price

Finally, complete the table below and add it to your assignment.

Outline

Each question is worth one mark and you must get the question correct to be awarded the mark, which means that there are no part marks for incorrect answers. The remaining two marks are awarded for your ability to use and format your Excel document as per the Finance 1 Excel formatting document.

Question 1

Estella, who has an exceptional credit record, has just purchased $10,000 worth of goods on invoice. The invoice has trade terms of 2/10 n30. Your task is to provide Estella with a graph that demonstrates how the cost of credit related to this invoice declines the longer she delays payment of the invoice. As well, your graph must indicate the point at which the cost of credit drops below 10% p.a.

Question 2

Pip recently contacted his bank about purchasing a Bank Bill with a maturity of six months. He was provided with the following options:

Option 1:        Purchase 180-day Bank Bill with a specified purchase price of $100,000.00 and an interest rate of 6.40% p.a.

Option 2:        Purchase 90-day Bank Bill with a specified purchase price of $100,000.00 and an interest rate of 6.30% p.a. On maturity of this Bill, roll the maturing funds into another 90-day Bank Bill but at an interest rate of 6.50% p.a.

Provide calculations to demonstrate Pip’s preferred option.

Hint: when I say purchase price, I mean purchase price not face value. So think of this problem as a deposit/s into an account rather than a Bank Bill.

Question 3

An anonymous benefactor will provide you with six annual payments of $100,000 with the first payment being made today. Assuming that the appropriate discount rate is J₂ = 10%, what is the present value of these cash flows?

Question 4

Mr Jaggers wants to retire 25 years from now.  One year after retiring, he will draw down the first of 30 annual payments of $40,000.  Assuming he currently has no savings and will earn a constant rate of 10% p.a. on all future savings, what constant amount must he save at the end of each year until he retires so that he can receive his desired retirement annuity?

Question 5

A deferred annuity with the first payment occurring four years from now has twenty semi-annual payments of $1,000 each. The appropriate discount rate for calculating the present value of these cash flows is J₂ = 10% p.a. Report the present value of the annuity (a) one year before the first payment and (b) today

Question 6

Using the annuity cash flows from Question 5 as a series of deposits made into a savings account and the interest rate from Question 5 as the return on savings, what is the balance of the account at the last deposit (includes the last deposit)?

Question 7

Calculate the price of a $100 thirty-year bond with annual coupons of 8% p.a. when yields are quoted nominally at 6% p.a., 8% p.a. and 10% p.a. For each price, indicate whether the bond is selling at a discount, at par or at a premium. Remember, prices are rounded to 3 decimal places.

Question 8

Handel Ltd will pay dividends of $0.10, $0.20 and $0.30 per share in three years’ time, four years’ time and five years’ time, respectively. One analyst assumes that future dividends will grow by 3% p.a. while another thinks that 5% p.a. is a more appropriate constant dividend growth assumption. Using a 12% p.a. required rate of return, price the share under both growth assumptions and report the difference in prices.

SOLUTION

Amount	Interest Rate
10000	10.00%
5000	5.00%
2000	0.40%
400	0.20%
0	0.00%
-400	0.20%
-2000	0.40%

Amount	Interest Rate
10000	10.00%
5000	5.00%
2000	0.40%
400	0.20%
0	0.00%
-400	0.20%
-2000	0.40%