AC.F101_mock_exam_section_A_2021.dvi 2021 MOCK EXAMINATIONS PART I ACCOUNTING AND FINANCE AC.F101 Quantitative Methods for Accounting & Finance 3 hours plus 30 minutes upload time Answer all of the...

AC.F101_mock_exam_section_A_2021.dvi
2021 MOCK EXAMINATIONS
PART I
ACCOUNTING AND FINANCE
AC.F101 Quantitative Methods for Accounting & Finance
3 hours plus 30 minutes upload time
Answer all of the questions.
There are 150 marks in total for the examination paper:
60 marks for Section A, 60 marks for Section B and 30 marks for Section C.
The number of marks is given in
ackets at the end of each question or part question.
Section A
60 marks
1. (a) Sketch, on the same pair of axes, the graphs of:
• y = ex;
• y = e−x; and
• y = ex + e−x.
[4]
(b) The function
f(x) = ex + e−x
is defined for all real values of x. State the range of f . [1]
2. A geometric progression has third term 2 and sixth term 16.
(a) Find the first term and common ratio of the progression. [3]
(b) Find the sum of the first 10 terms of the progression. [2]
3. Calculate the value of
∫
10
0
x5 − 10x4 + 4x+ 3330 dx.
[3]
4. My assets are invested in three portfolios P1, P2 and P3. These portfolios are made up of
shares in three companies S1, S2 and S3:
• P1 is split 25% : 55% : 20% between S1, S2 and S3 respectively;
• P2 is split 40% : 5% : 55% between S1, S2 and S3 respectively; and
• P3 is split 30% : 55% : 15% between S1, S2 and S3 respectively.
I am considering three alternative possibilities for how I should divide up my assets between
P1, P2 and P3. These alternatives are known as A1, A2 and A3:
• A1 splits my assets 90% : 5% : 5% between P1, P2 and P3 respectively;
• A2 splits my assets 10% : 80% : 10% between P1, P2 and P3 respectively; and
• A3 splits my assets 15% : 15% : 70% between P1, P2 and P3 respectively.
If the expected returns on S1, S2 and S3 are u, v and w respectively, and the co
esponding
expected returns on A1, A2 and A3 are r, s and t respectively, find a 3× 3 matrix M so that:


s
t

 = M


u
v
w

 .
[5]
Page 2
5. Consider the function
h(x) = ln (1− x)
where x is close to zero.
(a) Find the derivative h′(x), the second derivative h′′(x) and the third derivative h′′′(x). [6]
(b) Hence write down the first three non-zero terms of the Maclaurin series of h(x). [4]
You may not assume the Maclaurin series for ln (1 + x) in this question.
6. Calculate the value of
∫
2
0
(1 + x)(1 + ex) dx.
[7]
7. Let
f(x, y) = x3y − xey
e a function of two variables x and y.
(a) Show that the stationary points of z = f(x, y) occur when:
3x2y − ey = 0;
x3 − xey = 0.
[5]
(b) Show, from the second equation, that stationary points must occur when either x = 0 o
x2 = ey. [1]
(c) Now show, from the first equation, that there are in fact no stationary points when x = 0. [2]
(d) Finally show that there are two stationary points, and find their x and y co-ordinates. [5]
8. The unknown constants x, y and z satisfy:
4x+ 3y − 2z = 21
9x− 10y − 8z = −68
−4x+ 2y + 3z = 13
(a) Find the values of x, y and z which satisfy these three equations. You may use any
method, but show all your working. [10]
(b) Interpret your result geometrically. [2]
Typeset using LATEX 2ε
Page 3

2021 (MOCK) EXAMINATION
Part I      (FIRST YEAR)
ACCOUNTING AND FINANCE
Ac.F101 Quantitative Methods in Accounting and Finance
6
Please turn ove
SECTION B
SECTION B CONSISTS OF QUESTIONS 3, 4, and 5.
ANSWER any two.
TOTAL 60 MARKS
QUESTION 3
ANSWER ALL PARTS OF THIS QUESTION
A. A college admissions officer developed the following estimated regression equation relating the final college performance GPA to the students SAT mathematics score and secondary education level GPA.
= XXXXXXXXXX0235x1 + 0.00486x2
where X1 = secondary education level GPA
X2 = SAT mathematics score
Y = final college performance GPA
Computer output follows:
    Predictor
     Coef
    SE Coef
     T
     
    Constant
    -1.4053
    0.4848
    -2.90
     
    X1
     XXXXXXXXXX
     XXXXXXXXXX
     ______
     
    X2
    ________
     XXXXXXXXXX
    ______
     
    S = 0.1298
    R-Sq =
     _______%
    R-Sq(adj) =
    _______%
    Analysis of Variance
     
     
     
     
    Source
    DF
     SS
     MS
     F
    Regression
    2
    1.76209
     _____
     _____
    Residual E
or
     _____
    _______
    _____
     
    Total
    9
    1.88
     
     
i. Calculate the missing outputs and compute F and test using α = 0.05 to see whether a significant relationship is present.
(8 marks)
ii. Did the estimated regression equation provide a good fit to the data? Explain.
(5 marks)
iii. Use the t test and α = 0.05 to test H0: β1 = 0 and H0: β2 = 0.
(5 marks)
iv. Interpret the coefficients in this estimated regression equation.
(2 marks)
B. Using the following data:
    Y Variable
    X Variable
    25
    2
    25
    3
    20
    5
    30
    1
    16
    8
i. Estimate the regression model
XXXXXXXXXXmarks)
ii. Predict the value of Y when X = 10
                                 (2 marks)
QUESTION 4
ANSWER ALL PARTS OF THIS QUESTION
A. Suppose an analyst is interested in testing the hypotheses that wages (measured in 1000s of GBP) are positively related to work experience (measured in number of years of employment) and education (measured in number of years of college education), and that men earn higher wages than women do.
i. How would you test the analyst’s hypotheses using linear regressions?
(12 marks)
ii. Further, suppose the analyst is also interested in testing the hypothesis that the returns to education are higher for men than women, explain how you would change the regression equation used previously.
(8 marks)
(Note: In both cases, ensure to write out any regression equation you would employ, and ensure to explain how you would use the regression coefficients to test the analyst’s hypotheses.)
    
B. A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new TV commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating ‘after’ would be less than or equal to the mean rating ‘before’. Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use = 0.05 and the following data to test the hypothesis and comment on the value of the commercial.
(10 marks)
    
    Purchase rating
    
    Purchase rating
    Individual
    Afte
    Before
    Individual
    Afte
    Before
    1.
    6
    5
    5
    3
    5
    1.
    6
    4
    6
    9
    8
    1.
    7
    7
    7
    7
    5
    1.
    4
    3
    8
    6
    6
QUESTION 5
ANSWER ALL PARTS OF THIS QUESTION
A. The table below summarises the joint probability distribution for the percentage monthly return for two ordinary shares 1 and 2. In the case of share 1, the % return X has historically been -1, 0 or 1. Co
espondingly, for share 2, the % return Y has been -2, 0 or 2.
Percent monthly return probabilities for shares 1 and 2:
             
     
     
    Share 2
     
     
    %Monthly Return
    -2
    0
    2
     
    -1
    0.1
    0.1
    0.0
    Share 1
    0
    0.1
    0.2
    0.0
     
    1
    0.0
    0.1
    0.4
        
i. Determine E(Y), E(X), Var(X) and Var(Y)                 (8 marks)
ii. Determine the co
elation coefficient between X and Y.         (8 marks)
iii. What do you deduce from b.?                         (4 marks)
B. Consider an equal-weighted portfolio of 70 risky securities. Assume that each security is expected to return 10%, there standard deviations are all equal to 20%, and that each pairwise covariance is 3.96%. What is the standard deviation of this portfolio?
XXXXXXXXXXmarks)
9
END OF PAPER
Ù
y

1

2019 EXAMINATIONS

PART I

ACCOUNTING AND FINANCE

AcF 100 INTRODUCTION TO ACCOUNTING AND FINANCE

3 hours + 15 minutes reading time

Answer ONE question each from both Sections A and B. Answer TWO
questions from Section C and then ONE question from Section D. All questions
in Sections A and B are worth 33 marks each. Sections C and D are worth 17
marks each.

ANSWER EACH SECTION IN A SEPARATE ANSWER BOOKLET








2
SECTION A – FINANCIAL ACCOUNTING
ANSWER ONE QUESTION FROM THIS SECTION (EITHER QUESTION 1 OR
QUESTION 2) AND SHOW ALL YOUR WORKINGS

Q.1

As the accountant for Drox plc, you have produced the following statement of profit or
loss for the year ended 31 March 2019 and the statements of financial position as at
31 March 2019 and 31 March 2018.

Drox plc
Statement of profit or loss for the year ended 31 March 2019

£m
Sales revenues 311
Cost of sales (152)
Gross profit 159
Administrative expenses (30)
Distribution expenses (39)
Other operating income 6
Operating profit 96
Interest payable (6)
Profit before tax 90

Statement of financial position as at 31 March
XXXXXXXXXX
£m £m
Non-cu
ent assets
Buildings (at net book value XXXXXXXXXX
Plant and machinery (at net book value XXXXXXXXXX
XXXXXXXXXX
Cu
ent assets