Managerial Accounting Questions- Needed in the next 8hrs
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EFN406: MANAGERIAL FINANCE 2014, 3
Assignment: Part A, Financial Mathematics and Security Valuation
General Information
a) Marks: 10 – ten questions each worth one mark. You must have the correct answer and a correct explanation/working to gain the marks allocated to each part. Include cash flow maps or tables wherever possible. Avoid rounding error. Providing a formula and the answer is not enough. Some questions have more than one part, where this is the case you must get all parts correct to gain your one mark. No part marks.
b) Weight: 10%.
c) Format: Calculation and brief working or short answer. (Excel/ Word)
d) Word Limit: A few pages (500 words as a very rough guide; mostly calculations)
e) Due: see Blackboard
f) The assignment must be typed in word or excel and must be your own work (scanned documents are not acceptable)
g) Make sure to highlight or underline your final answer/s in some way. (e.g. Answer = $5089)
h) Upload a soft copy of your Word and/or Excel files to Blackboard under Assessment by the due date and time (must be Microsoft compatible). Failure to upload will result in a mark of zero. Keep a copy of your assignment. If you have problems uploading your file/s then send them by email (before due date and time) to [email protected]
i) Assignments submitted after the due date (late assignments) cannot be uploaded to Blackboard. Instead, they need to be emailed directly to John Polichronis ([email protected]).
j) Late submissions will receive a mark of zero. Please be aware that the suggested solution will be released within one day of the submission date, so any assignment submitted after the due date and time approval will attract a score of zero.
k) Extensions will only be granted in very, very exceptional circumstances and will normally take the form of a different assignment.
l) A hard copy is not required. Under no circumstances should you use assignment minder.
m) Try to be as accurate as possible. Cross-check your answers using excel. Unless otherwise told you should use the following approach:
a. PV and FV accurate to the nearest dollar
b. Prices accurate to two decimal places
c. Rates accurate to one basis point
n) To avoid mixing up assignments, name your assignment using the following format:
· unit code, your last name, your first name, your student number, and the assignment number
· for example: EFN406 last name first name n1234567 Assignment Part A.docx
o) Finally, this cover sheet will form the first page of the document you submit. By submitting this document you are agreeing to the declarations that appear on the next page:
Student to complete and attach to the assignment: |
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Part A |
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Assignment Part A |
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DECLARATION: By submitting this assignment I declare that: 1. This work is entirely my own, and no part of it has been copied from any other person’s work, words or ideas, except as specifically acknowledged through the use of inverted commas and in-text references; 1. No part of this assignment has been written for me by any other person except where such collaboration has been authorised by the Unit Coordinator concerned; I understand my assignment may be scanned as part of the assessment process, and that plagiarism detection software may be utlilised; 1. This assignment has not been submitted for any other unit at QUT or any other institution, unless authorised by the relevant Unit Coordinator; 1. I have read and abided by all of the requirements set down for this assignment.
1. If the above declaration is found to be false, you may receive reduced or zero marks for this assignment, and you will be dealt with under QUT’s Student Rule No. 29 - Academic Dishonesty, and the associated procedures for Academic Dishonesty which are available at: http://www.qut.edu.au/admin/mopp/Appendix/append01cst.html#Rule29 and http://www.qut.edu.au/admin/mopp/C/C_09_07.html |
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Criteria |
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6 |
5 |
4 |
Fail |
Problem solving - Questions |
Selects techniques that meet all context requirements |
Selects techniques matched to the key issues |
Uses a range of techniques for the context |
Uses a basic level response |
Little relationship established to context |
Technical skills - Questions |
Consistently performs complex techniques correctly |
Carries out a range of complex techniques at a sound level of accuracy |
Shows awareness of and able to carry out most necessary techniques |
Able to perform basic skills at a satisfactory or mechanical level |
Fails to consistently perform even basic skills correctly |
Understanding and use of concepts - Questions |
Outstanding range and depth of multiple links to suggested models and concepts |
Significant use and synthesis of most suggested models and concepts |
Sound use and synthesis of major suggested models and concepts |
Some use and synthesis of basic models and concepts |
Lack of application of models and concepts |
Analysis - Questions |
Can analyse a range of data and situations correctly using appropriate techniques |
Can analyse a range of data soundly using appropriate techniques |
Can analyse data and situations using appropriate techniques |
Can analyse a limited range of data using a range of techniques with minor error |
Unable to coherently analyse data |
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Grade |
Overall Performance |
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7 |
Overall your work demonstrates originality based on proficiency in all the assessment task requirements. It also reflects consistent excellence in the application of relevant concepts, analysis, and technical skills. All calculations correct. Mark of 9.5 to 10. |
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6 |
Overall your work demonstrates a comprehensive awareness and understanding of the set material. It also reflects proficiency in application of relevant concepts, analysis and technical skills. 8.5 to 9 |
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5 |
Overall your work demonstrates the ability to use and apply fundamental concepts and skills. It goes beyond mere replication of content knowledge. It reflects satisfactory and sometimes proficient application of relevant concepts, analysis and technical skills. 7.5 to 8 |
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4 |
Overall your work satisfies the basic learning requirements of the assessment item. It reflects satisfactory application of concepts, analysis and technical skills. 5 to 7.5 |
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Fail |
Overall your work does not satisfy the basic learning requirements of this assessment task. Less than 5. |
Outline
You should solve the following ten questions showing your full workings in brief form. Each question is worth one mark. You must have the correct answer and show your working or correct explanation to get one mark (very brief or one line answers are not acceptable). An incorrect answer or an answer without the working will be given zero. No part marks. For questions where two or more answers are requested you must get all parts correct to get the one mark. Include cash flow maps or tables wherever possible. Avoid rounding error.
Read the questions carefully
Question 1
Now that they have accumulated a deposit of 95,000 John and Betty take out a housing loan to purchase a home. The house costs $655,000. It is to be repaid in equal monthly instalments over a term of 20 years. The interest rate quoted by the bank is an effective annual rate of 8.5% pa. Jack has misplaced the paperwork showing the annual nominal rate (j12) with monthly compounding.
i. How much is the monthly repayment?
ii. How much do John and Betty owe the bank immediately before making the 120th repayment?
iii. After making the 160th repayment John and Betty receive an amount of $50,000, which they use to reduce their loan. They wish to keep the same term of the loan and reduce their repayments. How much is the new repayment, if the interest rate remains the same?
(Answers to must be accurate to the nearest dollar)
(Answers to must be accurate to the nearest dollar)
At the beginning:
Loan = (655,000-95000) = 560,000. This is the PV of the loan.
Term is 20 years, repayments monthly, so n = 20*12 = 240
The effective annual rate is given as 8.5%. We need the monthly rate. Cannot just divide by 12, rather we must reverse the compounding. Thus (1+.085)1/12-1 = .006821 or .6821%
Interest rate is j12 = 8.19% pa nominal interest charged monthly. This is not needed.
Part (i)
Let R represent the repayment amount.
Use the PV of annuity formula rearranged to find repayment amount.
R = PV/PVIFA(i,n)
R = 560000/[(1 – (1+.006821)-240)/.006821] R = 4,749
Part (ii)
The amount owed at any time is the PV of the remaining payments.
Immediately before the 120th payment means that number 120 is due but has not been paid yet, so the relevant of payments is = 240 -120 + 1 = 121, but as an annuity due.
PV = R + R x PVIFA(.006045,120)
PV = 4749 + 4749 x [1-(1.006821)-120]/.006821 = 393,022
Part (iii)
After making the 160th payment there are 80 payments left. The amount owed is PV of the remaining 80 payments.
n = 80
i = .006821
The amount owing is 4749*(1-(1.006821)-80)/.006821 = 292,050
Repay 50,000 leaving 242,050
Now calculate the new repayment needed to pay off the loan balance, if the term and the rate remain the same.
R = PV/PVIFA(i,n)
R = 242,050/[(1 – (1+.006821)-80)/.006821] R = 3,936
Full marks for all three, half marks for 2 out of three
See also the Repayment Schedule in the Excel Solution (Can use a repayment schedule, provided an explanation is given).
Question 2
Today is Stanley’s 55th birthday. He plans to retire on his 65th birthday. He wants to put aside the same sum of money every birthday (starting next birthday) up to and including his 65th. He then wants to be able to withdraw $8000 every birthday (starting with his 65th) up to and including his 85th birthday. He believes that an interest rate of 7% pa is a reasonable estimate of the opportunity cost of funds. How much does he need to put away each birthday?
(Your answers should be accurate to the nearest dollar)
55 |
56 |
…………. |
65 |
66 |
67 |
68 |
69 |
……….. |
85 |
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X |
………….. |
X; 8000 |
8000 |
8000 |
8000 |
8000 |
8000 |
8000 |
i = .07
Let X equal the unknown amount.
n = number of payments of 8000 = 21
If we find the PV of an annuity of 21 payments of 8000 (annuity due), this will give us the amount we need to accumulate by age 65.
V65 = 8000 + 8000 x PVIFA(20,.07) = 92,752
So this then represents the FV of an annuity of X, 10 cash flows and rate of 7%.
X = 92752/FVIFA(10, .07) = $6,713
1 mark for the correct answer
Question 3
A perpetuity with the first annual cash flow paid at the beginning of year 5 is equivalent to receiving $109,000 in 18 years’ time. Assume that the perpetuity and the lump sum are of equivalent risk and that j12 = 14.32% pa is the appropriate interest rate.
How much is the annual cash flow associated with the perpetuity?
(Accurate to the nearest dollar)
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109000 |
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CF |
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CF |
Let the cash flow be denoted by CF. Cash flows in the perpetuity are annual so you need to convert the nominal rate to an annual effective rate first (annual cash flows need an annual rate).
i = (1+j12/12)12 -1 = 15.2983%
Compare the two different options at the same point in time eg both at t = 3 or both at t = 0.
Here we are using t = 3
The Perpetuity
PV3 = CF4/i = CF/.152983
Lump Sum
PV3 = 109000/(1.152983)15 = 12,885
These are equivalent so CF/.152983 = 12885
Rearranging we get CF = 12885*.152983 = 1971
We could also use t = 0, but the (1.152983)-3 cancels out from both sides leaving CF/.152983 = 12885
Question 4
In exchange for a lump sum payment now, Polysuper offers an annual pension over thirty years beginning with a payment of $30,000 at the end of the first year. There are thirty payments in total and the payments will increase at an annual rate of 4 % pa. The appropriate opportunity cost of funds is j2 = 9% pa what is the amount of lump sum needed to purchase the pension?
(Accurate to the nearest dollar)
This is a growing annuity.
PV0 is the unknown (the lump sum needed to purchase the annuity.
CF1 = 30,000 (given)
The cash flows will grow at g = 4%pa
The annuity is over 30 years, so n = 30
Opportunity cost of funds = j2 = 9%pa.
We need to convert this to the Annual Effective Rate, r = (1+ .09/2)2 – 1 = 9.20%.
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27 |
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30000 |
31200 |
32448 |
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83174 |
86501 |
89961 |
93560 |
PV can be solved by calculating the CF for each year and then discounting to zero (see spreadsheet).
Or
You can use the PV of a growing annuity formula (google or derive it yourself).
PV0 = = $443,315
Or PV of growing perpetuity first cash flow at t = 1 minus the PV of a growing perpetuity first cash flow at t = 31
[30000/(.0920 -.04)] – [30000*(1.04)30/(.0920-.04]*(1.0920)30 = $443,315
Question 5
a) A ninety day bank bill with 90 days to maturity has a price of $99,327.95. What is the effective annual yield implied by this price and maturity? (Be careful I am not asking for the annual nominal yield, which by convention is normally quoted in financial markets.) Face value is $100,000.
b) What would be the price of this bank bill if you decide to sell it with 80 days left to maturity and the appropriate interest rate was 4.21% pa effective?
c) Calculate the geometric average rate of return over three years given the following annual rates, year 1 = 5.55%, year 2 = 6.75%, year 3 = 8.37%. (geometric not arithmetic)
(Rates as a percentage accurate to one basis point and prices accurate to two decimal places)
(a)
99327.95 = 100000/(1+i*90/365)
(1+i*90/365) = 100000/99327.95
i*90/365 = 1.006766 -1 = .006766
This is the 90 day rate
EAR = (1+ .006766)(365/90) – 1 = 2.77247% or .0277.
We could solve for “i” in the process above and then use (1+i*90/365)365/90 -1 to get the same answer.
We can also go directly to the answer by (100,000/99,327.95)365/90 – 1.
Watch the rounding here. Forgive rounding error but not conceptual errors.
Multiplying .006766 by 365 and dividing by 90 gives the nominal rate. This is not what is asked for by the question so it is incorrect.
(b)
n = 80
year = 365
FV = 100000
EAR = 4.21% or .0421
PV = 100000/(1.0421)80/365 = 99100.23
(c)
Year 1 .0555
Year 2 .675
Year 3 .837
(1 + 0r3) = [(1.055)*(1.0675)*(1.0837)]1/3
0r3 = [(1.055)*(1.0675)*(1.0837)]1/3 - 1
0r3 = .0688 or 6.88%
Question 6
Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $1,500,000. The bonds were issued seven years and three months ago and still have two years and nine months to maturity. They pay a coupon rate of interest of 7% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.02% pa. The convention in Zanadu financial markets is that the market yield and coupon rate are quoted as annual nominal rates. What is the current market value of the bonds?
(In dollars accurate to three decimal places)
The relevant time period is a half year (because semi-annual cash flows):
n = 2.75 years = 5.5 half-years
i = .0402/2 = .0201
Coupon = (.07/2)*1,500,000 = 52,500
FV = 1,500,000
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9m |
15m |
21m |
27m |
33m |
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0.5 |
1.5 |
2.5 |
3.5 |
4.5 |
5.5 |
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52500 |
52500 |
52500 |
52500 |
52500 |
1552500 |
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51980 |
50956 |
49952 |
48968 |
48003 |
1391543 |
Price = 52,500 /(1+.0201).5 + 52,500 /(1+.0201)1.5 + 52,500 /(1+.0201)2.5 +52,500 /(1+.0201)3.5 +52,500 /(1+.0201)4.5 +1,552,500/(1+.0201)5.5 = $1,641,401.239
You cannot use PVIFA(.201, 5.5) as “n” in the PVIFA must be an integer (there are 6 cash flows not 5.5).
[52,500*PVIFA(.0201,6) + 1,500,000/1.02016]*1.0201.5 will work.
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1 |
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52500 |
52500 |
52500 |
52500 |
52500 |
1552500 |
As will [52,500 + 52,500*PVIFA(.0201,5) + 1500000/(1.0201)5]/(1.0201).5
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52500 |
52500 |
52500 |
52500 |
52500 |
1552500 |
Can you see why?
Must use 1.0201.5 not 1.01005 to be perfectly correct.
Question 7
Polycorp has a dividend of $5.00 due in a year’s time and is expected to pay a dividend $5.50 at the end of the second year. Its dividend is expected to grow at 8% pa for the following year. Dividends are then expected to grow at 5% pa for another two years, after which they are expected to grow at 3.5%pa forever. Shareholders required return on equity is 10.85% pa. What is the current price (cum-dividend) of Polycorp shares? Polycorp has just paid a dividend of $4.75.
(Accurate to the nearest cent)
D1 = 5.00 be careful here the question provided D1 and D2
D2 = 5.50
g1 = .08 for one year
g2 = .05 for next two
g3 = .035 forever after
ke = .1085
D3 = 5.5*1.08 = 5.94
D4 = 5.5*1.08*1.05 = 6.24
D5 = 5.5*1.08*1.052 = 6.55
D6 = 5.5*1.08*1.052 *1.035 = 6.78
P5 = D6/(k – g) =6.78/(.1085-.035) = 92.22
P0 = D1/(1+ke) + D2/(1+ke)2 + D3/(1+ke)3 + D4/(1+ke)4 + D5/(1+ke)5 + [D6/(k – g)]/ (1+ke)5
P0 = 4.51 + 4.48 + 4.36 + 4.13 + 3.91 + 55.10 = 76.49 ex dividend
To find cum dividend add D0 giving 81.24 cum dividend
I am not concerned about small rounding error; do not deduct any marks for this, but the wrong procedure can produce an answer close to the above. Incorrect procedure receives zero marks.
Question 8
Gamma Ltd is not expecting to pay dividends for three years, at the end of year four, a dividend of $2.65 is planned and dividends are expected to be constant forever after that. The required rate of return for Gamma Ltd equity is j4 = 12.5% pa. What is the expected price (cum-dividend) of Gamma Ltd’s shares at the beginning of year nine? Explain your logic.
(Accurate to the nearest cent)
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2.65 |
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Cash Flows are annual so we need the correct annual rate.
AER = (1+.125/4)4 – 1 = .13098
P8 = D9/k + 2.65 = 2.65/.13098 + 2.65 = $22.88
Very easy mark but must show clearly that they have calculated the Price at beginning of year nine, which is end of year eight. Also you are asked for the cum-dividend price, so you assume D8 is not yet paid and so you add this on.
Question 9
Mooncorp Insurance has quoted you an annual premium to insure your car of $3100. You are offered a 15% discount if you pay the lump sum immediately. They also offer an alternative payment method. You can pay the account in full by making 11 equal end-of-the month payments of $280, rather than the lump sum. The first payment is at the end of the second month. What is the effective annual opportunity cost of paying monthly?
You must provide one complete manual calculation of the IRR to demonstrate that you understand the process. Failure to follow this instruction will attract a mark of zero.
(Accurate to one basis point)
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Price = 3100
Monthly Payments = 280
Early payment Discount = .15 or 15%
IRR = 2.2918%; but this is the rate per month (monthly cash flows)
EAR = (1+.022918)12-1 = 31.25%
The answer may vary depending the degree of accuracy used (31.25 uses excel, I will allow rounding error but not incorrect method).
Question 10
Calculate the return for each of these investments (capital gain/loss plus dividend).
a) My portfolio ends the year with a value of $12.72 million after paying dividends at the end of the year to the value of $255,000. The value of the fund at the beginning of the year was $12.13 million.
b) At the same time the All Ordinaries Index ended the year at 5695 after starting at 5226.
c) A share in BHP was selling for $23.45 at the beginning of the year and selling for $27.42 at the end of the year after paying a dividend of $1.13.
(Your answers should be as a percentage accurate to one basis point)
Return = (closing balance – opening balance + dividends)/opening balance
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1 |
Dividend |
Return |
Basis Points |
(a) |
Portfolio |
12.13 |
12.72 |
0.255 |
6.97% |
697 |
(b) |
Index |
5226 |
5695 |
0 |
8.97% |
897 |
(c) |
BHP |
23.45 |
27.42 |
1.13 |
21.75% |
2,175 |
Very easy question.
Either return as percentage or basis points earns the marks. Must have all three to get the marks
10