**Unit Code & Title :** ACFI7027 Quantitative Methods For Finance**Objectives :-** The assignment tests understanding of the full range of topics covered in the module. As with the mid-term assessment, you need to be able to explain the calculations you are performing.**Required :** There are four tasks to complete. No references are needed.**ACFI7027 Quantitative Methods For Finance Assessment 2 – UK.**

**Learning outcomes assessed :-**

1.Understand introductory mathematical approaches relevant to finance and to apply these to simple investment and financing decisions, including calculus, logarithms and geometric progression.

2.Understand the main ways of using descriptive statistics to summarise financial information and the fundamental principles of statistical inference and hypothesis testing and their relevance to financial enquiry

3.Interpret simple econometric studies and communicate the relevance of their results for financial decision-making

4.Critically evaluate mathematical and statistical results, drawing conclusions from them and presenting quantitative data in the appropriate manner

5.Perform computer-aided data analysis using Excel

**Task 1 :**– Your task is to investigate possible determinants of house prices in a city. Data has been collected for 28 recent transaction with eight potential independent variables and one dependent variable – selling price. The variables are:

1. An index of house prices in the immediate locality of the house (LOCAL)

2. The number of bathrooms (BATH)

3. The area of the site in hundreds of square meters (AREA_SITE)

4. The size of the living space in hundreds of square meters (AREA_LIVE)

5. The number of garages (GARAGE)

7. The number of rooms (ROOMS)

8. The number of bedrooms (BEDROOMS)

9.The age in years (AGE)

10. The selling price in .£000 (PRICE)

**The data is in the Excel file House Prices, available from Moodle.**

1.Check for multi collinearity and explain what this is and why it is a problem

2.Using your multicollinearity check, or otherwise, eliminate five of the eight independent variables and create a regression model with PRICE as the dependent variable and three of the other variables as the independent

variables. Present the output from this model and explain why you have chosen to retain your three variables

3.State the null and alternate hypotheses when testing the significance of the one of your independent variables.

4.State with reasons, whether your model is useful for predicting house prices

5.The assumptions that underpin the Ordinary Least Squares (OLS) regression method include:

i. Errors are normally distributed

ii. Homoscedasticity of errors

iii. Errors are not serially correlated

For each of these assumptions, explain how you would check or test whether the assumption is violated and the impact on the conclusion if the assumption is violated.

**Task 2 :-**

1.Explain the concept of stationarity and why it is important in time series analysis.

2.Explain how the Dickey-Fuller (DF) test determines whether a data series is stationary or not.

3.Explain how the Augmented Dickey-Fuller (ADF) test improves on the original DF test

**Task 3Broad gate Financing plc has issued a corporate bond with the following characteristics :**

Work with a nominal bond value of £100.

**ACFI7027 Quantitative Methods For Finance Assessment 2 – UK.**

1.If the annual return demanded by investors for this bond is 2%, use the formula for the sum of a geometric progression to calculate the value on 6 July 2021 of the series of payments made to the holder of a bond with a

nominal value of £100.

2.What is the date of the first coupon payment whose present value on 6 July 2021 is less than £4.00?

3.Explain how the formula for the sum of a geometric progression is relevant when valuing this stream of cash flows.

**Task 4 :-**

A firm sells two products. Find the quantity of each product, Q1 and Q2, that will be sold in a year to maximise profit.

The market for the products is not perfectly competitive so the firm faces a downward-sloping demand curve for both products. They are estimated to be:

P1 = 100 – 0.1 x Q1

P2 = 250 – 0.5 x Q2

Where P1 and P2 are the selling prices for the two products in £

Fixed costs for the firm are £20,000 per year

Variable costs for the two products are £10 per unit for product 1 and £50 per unit for product 2.

Because of synergies in the production process, the annual production costs obtained by adding the fixed and variable costs are reduced by £0.1 x Q1 x Q2

**Required:**

1.Obtain a formula for the total annual revenue from producing and selling quantities Q1 and Q2.

2.Obtain a formula for the total annual cost of producing quantities Q1 and Q2.

3.Hence find a formula for the annual profit of the firm

4.Find the profit maximising quantities Q1 and Q2, and hence the profit maximising prices, P 1 and P 2 and the maximum profit.

**Assessment criteria :-**

1.Techniques correctly applied to the data

2. Explanations are appropriate for the target reader and demonstrate understanding of the techniques

3. Work well-presented

**ACFI7027 Quantitative Methods For Finance Assessment 2 – UK.**

**Presenting coursework for assessment :**

1.There is no overall maximum length for this assignment but observe the maximum words given for the various tasks above.

Assignments must be word-processed in 11 point Arial and 1.5 line spaced Margins must be as follows: Top, Bottom: 2.5 cm, Left, Right: 3 cm

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