I will attach solutions to some of the Questions but with different values. All you need is to redo them using new values. Pretty simple work

 

Question 1

 

Now that they have accumulated a deposit of $40,000 Ed and his partner Susie wish to use the deposit and take out a housing loan to purchase a home. The house costs $725,000. The loan is to be repaid in equal monthly instalments over a term of 25 years.  The interest rate quoted by the bank is an annual effective rate of 5.5%.  Ed has misplaced the paperwork showing the annual nominal rate (j₁₂). Interest is added monthly.

i.            How much is the monthly repayment?

ii.            How much interest will be paid in the fifth year?

iii.            How much do Ed and Susie owe the bank immediately before making the 160^th repayment?

iv.            Provide Ed and Susie with a repayment schedule using excel.

 

(Answers should be accurate to the nearest dollar)

 

Question 2

 

Karine and Arlo are trying to establish a University Fund for their daughter Amelia, who turns 3 today.  They plan for Amelia to withdraw $10,000 on her 18^th birthday and $11,000, $12,000 and $15,000 on her subsequent birthdays (19^th, 20^th and 21^st).  They wish to fund these withdrawals with a 10-year annuity, and they intend to make their first deposit one year from today, and expect to earn an average return of 6.5%pa.

i.            How much will Karine and Arlo have to contribute each year to achieve their goal?

ii.            Create a schedule showing the cash inflows (including interest) and outflows of this fund.  How much will be in the fund on Amelia’s 16^th birthday?

 

(Your answers should be accurate to the nearest dollar)

 

Question 3

 

Stanley has just been advised of a bequest of a lump sum of 111,500 from his Aunt’s will, but it is not due to be available for him for sixteen years (at t = 16 he will receive 111500). Stanley wants to receive some cash earlier than this. He is investigating the purchase of a deferred annuity with the first annual cash flow of the annuity is to be paid at the beginning of year 2 (fifteen cash flows).  Assume that the annuity and the lump sum are of equivalent risk and that j₁₂ = 6.24% pa is the appropriate interest rate (opportunity cost of funds for Stanley). How much is the annual cash flow associated with the annuity?

 

(Accurate to the nearest dollar)

 

Question 4

 

In exchange for a lump sum payment now, Polysuper offers an annual pension over twenty years beginning with a payment of $62,000 at the end of the first year. There are twenty payments in total and the payments will increase at an annual rate of 3%pa. The appropriate opportunity cost of funds is j₂ = 9%pa what is the amount of the lump sum needed today to purchase the pension?

 

(Accurate to the nearest dollar)

 

Question 5

 

a)A ninety day bank bill with 90 days to maturity has a price of $98505. What is the effective annual yield implied by this price and maturity? What is the annual nominal yield? Face value is $100,000. Make sure your answers are clearly labelled.

 

b)     The All Ordinaries price index opened the year at 5578 and had reached 6013 by the end of the year. What was the rate of return on the index?

 

c)Using the approach covered in your textbook calculate the geometric average annual rate of return over four years given the following annual rates, year 1 = 4.84%, year 2 = 5.99%, year 3 = 6.15%, year 4 = 5.83%.

 

d)     Polycorp dividends per share have increased from $6.25 to $13.90 over a six year period. Calculate the annual compounded growth rate in dividends over that period.

 

 (Rates as a percentage accurate to one basis point)

 

Question 6

 

Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $2,000,000.  The bonds were issued six years and nine months ago and still have three years and three months to maturity.  They pay a coupon rate of interest of 6.5% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.12% 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)

 

Question 7

 

Polycorp has a dividend of $6.00 due in a year’s time and is expected to pay a dividend $6.60 at the end of the second year.  Its dividend is expected to grow at 6.5% pa for the following three year. Dividends are then expected to grow at 3% pa for another two years, after which they are expected to grow at 2%pa forever. Shareholders required return on equity is 10.35% pa.  What is the current price (cum-dividend) of Polycorp shares? D₀ is $5.65.

 

(In dollars and cents accurate to the nearest cent)

 

Question 8

 

The required rate of return on the shares in the companies identified below is 12% pa. Calculate the current share price in each case.

 

(a)  The current earnings per share of Alpha Ltd are $3.40. The company does not reinvest any of its earnings. Earnings are expected to remain constant.

(b)  Beta Ltd’s current dividend is $2.35 and dividends are expected to grow at 3% pa indefinitely.

(c)   Gamma Ltd is not expecting to pay dividends for four years, at the end of year five a dividend of $2.39 is planned and dividends are expected to grow at 3.5% pa forever after that.

(d)  Delta limited plans to pay dividends of 1.55, 2.75, and 3.50 at the end of years 3, 4, 5 respectively followed by a dividend of 4.20 pa in perpetuity after that.

 

 (Accurate to the nearest cent)

 

Question 9

You wish to insure your Ferrari.  Mooncorp Insurance has quoted you an annual premium to insure your car of $12915. You are offered a 10% 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 $1160, rather than the lump sum, with no payment in the first month (ie the first payment is at the end of the second month followed by ten further monthly payments). What is the effective annual opportunity cost of paying monthly?

 

You must provide one complete manual trial calculation of the IRR to demonstrate that you understand the process. Also provide an explanation of this opportunity cost. Failure to follow this instruction will attract a mark of zero.

 

(Accurate to one basis point)

 

Question 10

0	1	2	3	4	5	6	7	8	9	//	12	∞
-2000			-2000			-2000			-2000	//	-2000

(a)   What is the present value of a series of payments of $2000 every three years in perpetuity with the first payment made immediately, if the annual rate is 8% per annum?

 

 

 

 

(b)  Polycorp debentures are selling for $111 (FV = 100) and mature in eight years. The coupon rate is 11%pa. What is the effective annual yield on the debentures?

 

(c)   Polycorp debentures are selling for $103 (FV = 100) and mature in eight years. The coupon rate is 5%pa, with coupons paid quarterly. What is the effective annual yield on the debentures?

 

 

(Answer (a) to the nearest dollar; (b) and (c) as a percentage to the nearest basis point)

 

 

EFN406: MANAGERIAL FINANCE 2014, 2

 

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:
Student Name:	Arzyaman Boroowa	Student Number:	N7347189
Assignment Number:	Part A	Title:	Assignment Part A
Tutor’s Name:	Jason Hay
Due Date:	22/08/2014	Day and Time of Class:	Tuesday – 8 AM to 10 AM.
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

 

 

Criteria	7	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
Grade	Overall Performance
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.
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
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
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
Fail	Overall your work does not satisfy the basic learning requirements of this assessment task. Less than 5.

 

 

 

 

 

Question 1

 

Now that they have accumulated a deposit of 85,000 Jack and Jill 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 7.5%pa. Jack has misplaced the paperwork showing the annual nominal rate (j12) with monthly compounding.

 

1. How much is the monthly repayment?

1. How much do Jack and Jill owe the bank immediately before making the 120th repayment?

1. After making the 160th repayment Jack and Jill 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)

 

Solution

 

Given,

· Deposits in hand: $85,000

· Cost of House: $655,000

· Loan Required (PV): $655,000-$ 85,000 = $570,000

· Time Period = 20 years (but since it’s compounded monthly we will be taking the loan period as 240)

· Effective Annual Interest Rate = 7.5%

Equivalent Monthly Interest Rate ( i) =

 

= 0.006044919

 

 

 

(i) We can find the monthly repayments ‘C’ using in Ordinary Annuity Formula.

 

 

C = $4506.49109

 

Answer: $ 4506

 

 

(ii) To find the amount that is owed before the 120th payment, we find the present value at 120th period using annuity due formula

 

 

 

 

 

 

 

 

(iii) Since the 160th payment is made, we will find the present value at 160th period using ordinary annuity.

 

 

 

 

 

If Jack and Jill makes a payment of $50,000 at the moment.

 

Amount Owing= =$235,182.3265

 

To calculate the new repayment per month we use the same cash flow formula as in Part, (i) and time period left (n) will be equal to 79 remaining period ( as the 160th payment is made.

 

 

 

 

 

 

 

 

 

 

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)

 

Solution:

 

To find the required amount that Stanley needs to set aside every year we will first find the Present Value at 64th year (using ordinary annuity formula) and add a $8,000 for the 65th year.

 

Given,

 

Withdrawal every year (C) = $ 8,000

Interest Rate (i) = 0.07

Time Period (n) = 20

 

 

 

 

 

 

 

 

Now we will discount the by 10 years to , that is the present value.

 

 

We will now find the yearly “put aside’ i.e C at

 

 

 

 

 

 

 

 

 

 

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)

 

Solution

 

 

 

 

We know that the Future Value is $109000 in 18 years time.

 

Given

 

 

Finding the equivalent annual effective interest rate

 

 

 

 

 

 

Using the annual effective interest rate and Future Value, we can discount it to find the present value of the sum

 

 

 

 

 

 

 

At this point, if we discount the present value of perpetuity at Time 4, the value should be equal to

 

Equating:

 

 

 

 

 

 

 

 

 

Answer: $ 1,971

 

 

 

 

 

 

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 3%pa. The appropriate opportunity cost of funds is j2 = 8%pa what is the amount of lump sum needed to purchase the pension?

 

(Accurate to the nearest dollar)

 

Solution

 

Since the given question has we will first convert it into the effective rate compounded annually.

 

Effective annual rate (i)

== 0.0816 ( r )

Given,

 

C (First Cash inflow) = $30,000

g (growth rate of the annual cash inflow) = 0.03

n (time interval of the cash inflow) = 30 years.

 

Using the formula of a present value of a growing annuity we will calculate the lump sum needed to purchase the pension now:

 

 

 

 

 

 

 

 

 

Question 5

 

1. A ninety day bank bill with 90 days to maturity has a price of $99227.95. 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.

1. 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?

1. 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 nor arithmetic)

 

(Rates as a percentage accurate to one basis point and prices accurate to two decimal places)

 

 

Solution:

 

( i )

 

We know

 

 

We also know

 

 

 

 

 

Equation 2

 

 

Replacing Equation 2 in Equation 1 we get

 

 

 

 

 

We have

 

Present Value = $ 99,277.95

Future Value = $ 100,000.

 

Putting values in equation 3 we get,

 

 

 

 

 

 

 

 

 

 

(ii)

 

Now

 

Effective Annual Interest = 4.21 % p.a

 

 

 

Using Equation 3 we get

 

 

 

 

 

 

 

.

 

(iii)

 

Given

 

 

 

 

 

Geometric Average Rate of Return ( r )

 

 

 

 

 

 

 

Answer: 6.88% p.a

 

 

 

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 6.5% 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)

 

 

Solution

 

( 7.3 )

 

We assume that the coupon payments are made at the end of every six months.

 

Coupon Rate = 6.5% per annum = 0.065 per annum = 0.0325 semi annually

 

Coupon Interest = 0.0325 X 1,500,000 = $ 48,750

 

Market Yield = 4.02% per annum = 0.0402 per annum= 0.0201 semi-annually.

 

First, we assume that we are at 7 years 6 months, where the Present Value will be

 

 

 

 

 

 

Now we will discount this Present Value at 7 years 6 months to 7 year 3 months.

 

 

 

 

 

 

,

 

 

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 4% 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)

 

Solution

 

 

 

 

 

Ke=10.85%= 0.1085

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To calculate cum dividend price from ex dividend price, we just add back the dividend.

 

 

 

 

 

 

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)

 

Solution

 

 

Firstly, we will need to find the effective annual interest rate (i) from the given .

 

 

 

 

 

Now we know the formula for perpetuity

 

 

 

Using this formula, we can find the Ex Divided Price of the Share at the end of year 8, which is also the price at the beginning of year 9.

 

 

 

 

 

Now Adding Dividend back to find the cum dividend price.

 

Cum Dividend Price at the beginning of 9th year =

 

 

 

 

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)

 

Solution

 

 

Given,

 

Discount = 15 % = 0.15

 

Present Value = 3100 – (15% of 3100) = $ 2,635

 

Monthly payment = $280

 

n=11 months

 

Now, if we find the using ordinary annuity formula and discount it to Time zero, it should be equal to the Present Value of $ 2,635

 

By the above mentioned statement, we get:

 

 

 

 

 

 

Now we will use trial and error method to find which value of ‘I’ will give use an answer of $ 2,635

 

Using i=5%

 

 

This value is too small, so we will reduce the value of ‘I’.

 

Using i=3%

 

 

This value too small again, but the margin is small. We will now try it by reducing I by 0.5

 

Using i=2.50%

 

 

Although the value is still small then the required value, we are very close to the target value of 2635, we will now decrease the ‘I’ by a small margin

 

Using i=2.25%

 

 

 

 

This time, the value is too large but by a very small margin, so we will try and increase the value of I by a small margin

 

Using i=2.30%

 

 

 

The value is just a little smaller, so we will try and reduce i by 0.01%

 

Using i=2.29%

 

 

 

Hence, we got the Present Value of $ 2635, using i = 2.29%

 

Converting i into effective annual rate:

 

 

 

 

 

 

 

 

 

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)

 

Solutions

a) Given,

Opening Value= $ 12,130,000

Closing Value = $ 12,720,000

Dividend for the year = $ 255,000

 

 

 

 

 

 

 

 

 

b) Given,

Opening Value= 5226

Closing Value = 5695

 

 

 

 

 

 

 

 

 

c)

 

Given,

Opening Value= $ 23.45

Closing Value = $ 27.42

Dividend for the year = $ 1.13

 

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