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BAO3403 Investment and Portfolio Management

Instructions: This is a group assessment. You need to form a group with four (o4) members and enrol to group in VU-Collaborate.

The assignment: You are required to answer all the small problems  given below. You can do all your calculation in a MS-Excel workbook (for each question you need to use separate sheet in the workbook and name the sheet by question number) and present your answers in a MS-word document (you can cut and paste your answers from the workbook). Your worksheet calculation should have the excel cell formulas with detailed calculations. Alternatively, you can do your calculation in MS-word document using equations and present your answers with detail workings. You are required to show the base formulas if any you used for your calculations in the word document (example: the way you applied the dividend growth model in equity valuation) to receive full marks. When required, you need to provide justification for your answers.

Submission of your assignment: You need to submit both word copy and the excel copy via the assignment drop-box before the due date. The group number, names and ID numbers of the group members are required to sight on the first page of the assignment

Assessing your assignment: Please note, this assignment is required your commitment to master the basic conceptual application in investment and portfolio management. By, studying lecture notes and relevant book chapters you can find the needed help to solve the given problem in the assignment. Your answers will not be examined before the assignment is formally submitted. This assignment or part of it will not be accepted via email before or after the due date.

Similarity: The maximum similarity score accepted is 40% and the penalty for late submissions without an application for special consideration is 20% of the marks achieved per day. Penalty for emailing the assignment is 20%. Excel files submitted will not be marked. If you encounter any issue when uploading the assignment, send me a screen shot that clearly shows the issue.

Due date: 12 Midnight, 10^th Nov 2022.

Question 1:

You are an investment adviser. One of your clients approaches you for your advice on investing in equity shares of Theta Company. You have collected the following data:

Earnings per share last year $9.25

Payout ratio 30%

Return on equity 20%

Cost of equity capital 15%

The company plans to increase the payout ratio to 40% from year 5.

Required:

i. Estimate the price of an equity share of this company using an appropriate dividend discount model and advise your client whether they should buy a share of the company.

ii. Your client is keen to know whether there are any growth opportunities from their investment. Explain to your client the meaning of this concept using appropriate calculations.

iii. If there are positive or negative growth opportunities, explain the reason for such opportunities.

14+2+1 =17 marks

Question 2:

You are a senior financial analyst of a firm based in Sydney. You have been assigned with the task of training interns who recently joined your firm on how to use the free cash flow model to estimate the value of a company. You have collected data on the following data

Year	2022	2023	2024	2025	2026
Long-term Debt ($M)	56,000	55,000	57,000	56,000	60,000
Interest rate on long-term debt (%)	3.50%	3.50%	3.50%	4.00%	5.00%
EBIT		42,000	40,000	45,000	51,000
Working capital ($M)	10,000	9,000	12,000	10,000	18,000
Depreciation ($M)		37,000	38,000	38,000	40,000
Cap spending ($M)		35,150	37,000	38,000	40,000
Cost of equity		13%	14%	15%	13%
WACC		11%	12%	10%	12%
Number of equity shares (million)	50,000
Terminal growth rate	7%
Tax rate	30%

Using the information, you have collected above, perform calculations to explain to interns as to how the following are calculated:

i. Free cash flow to firm

ii. Free cash to equity

iii. Value of the firm according to the free cash flow to firm method

iv. Value of the firm according to the free cash flow to equity method

v. Estimated price of an equity shares according to the  free cash flow to firm method and the free cash flow to equity method

Note: For parts i and ii prepare a table showing how free cash flow to firm and free cash flow to equity are calculated. Follow the example in the lecture notes for session

5+5+6+6+4 =26 marks

Question 3

Part A

You are the portfolio manager of a large company that invests in many securities including corporate bonds. You have been assigned the task of bond portfolio management. You are provided with the following data in relation to bonds:

Maturity period 12 years

Coupon rate 10%

Par value $1,000

Coupons on bonds are paid annually

Yield to maturity of bonds 7.5%

Required:

i) Fill in the blanks in the following table

ii) Based on the calculations in part i, calculate modified duration and convexity of the bond.

iii) Using the modified duration, calculate the change in bond price in dollars when yield to maturity increases/decreases by two percent

iv) Using the convexity, calculate the change in bond price in dollars when yield to maturity increases/decreases by two percent

Year (t)	Cash flow (CFt)		Wt	t×Wt	t+t2
1
2
3
4
5
6
7
Notes: y = yield to maturity, Wt= weight for year t

4+3+1+2 = 10 marks

Part B

The following data relate to a corporate bond which pays coupons semi-annually:

Settlement date 01 March 2010

Maturity date 31 December 2040

Coupon rate 12%

Yield to maturity 10%

Face value $1,000

Percentage of face value paid back to the investor on maturity 100%

Using MS-Excel, calculate

i. The flat price of the bond.

ii. Accrued interest.

iii. Invoice price of the bond

Note: Show the assumptions, if any, you made in your calculations.

2+2+1 = 5 marks

Part C

A company must make a payment of $40,000 in 12 years. The market interest rate is 9.5%. The company’s portfolio manager wishes to fund the obligation using five-year zero-coupon bonds and perpetuities paying annual coupons.

i. How can the manager immunize the obligation?

ii. Suppose that two years have passed, and the interest rate remains at 9.5%.  Is the position still fully funded? Is it still immunized? If not, what actions are required?

6 marks

Question 4

The following data relate to two listed companies, X and Y:

	X	Y
Average (expected) return	18%	10%
Standard deviation of returns	22%	18%
Correlation between returns of X and Y	-0.15

i. You want to form a portfolio combining X and Y. Determine the weights for X and Y to minimise the variance of the portfolio

ii. Calculate the return and standard deviation of the minimum variance portfolio

iii. Tabulate and draw the investment opportunity set for the two shares. Use investment proportions for X of 0% to 100% in increments of 10%.

8 marks

Question 5

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $150,000 or $450,000, with probabilities of 0.3 and 0.7, respectively. The alternative riskless investment in T-bills pays 4%.

i. If you require a risk premium of 8%, how much will you be willing to pay for the portfolio?

ii. Suppose the portfolio can be purchased for the amount you found in (i). What will the expected rate of return on the portfolio be?

iii. Now suppose you require a risk premium of 12%. What is the price you will be willing to pay now?

iv. Comparing your answers to (i) and (ii), what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell?

1*4 = 4 marks

Question 6

Suppose 3% risk free rate and a well-diversified portfolio P has a beta of 1.35 and an alpha of 1% when regressed against a systematic factor S. Another well diversified portfolio Q has a beta of 0.95 and an alpha of 1.5%.

i. Using the above information, explain if there is any arbitrage opportunity.

ii. If there is an arbitrage opportunity, what action would you take to capitalise on this opportunity?

2+3=5 marks

Question 7

XYZ stock price and dividend history are as below.

Year	Share price at the beginning of the year	Dividend paid at the end of the year
2014	$110.00	$4.00
2015	$112.00	$5.00
2016	$110.00	$3.00
2017	$113.00	$2.00
2018	$115.00	$6.00

An investor buys three shares of XYZ at the beginning of 2014, buys another two shares at the beginning of 2015, sells two shares at the beginning of 2016, buys two shares at the beginning of 2017, and sells all remaining shares at the beginning of 2018. Using the above information calculate the following for the investor:

i. Arithmetic average return

ii. Geometric average return

iii. Dollar-weighted return

2+1+2= 6 marks

Question 8

Assume that you manage a risky portfolio with an expected rate of return of 25% and a standard deviation of 20%. The T-bill rate is 7%. Your client chooses to invest 70% of a portfolios in your portfolio and the balance in T-bills.

i. What is the expected return and standard deviation of your client's portfolio?

ii. Suppose your portfolio includes the following investments in the given proportions: share X - 30%, share Y – 20%, and the balance is share Z. What are the investment proportions of each stock in your client's overall portfolio, including the position in T-bills?

iii. What is the Sharpe ratio (S) of your risky portfolio and your client's overall portfolio? Interpret the Sharpe ratios.

iv. Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL.

1+2+2+3=8 marks

Question 9

The standard deviation of the market-index portfolio is 15%. Stock A has a beta of 1.6 and a residual standard deviation of 20%.

i. What would make for a larger increase in the stock’s variance: an increase of 0.10 in its beta or an increase of 2% in its residual standard deviation?

ii. An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 80% and to invest 20% in stock A. Which of the changes in (i) will have a greater impact on the portfolio’s standard deviation?

4+1 = 5 marks