Describe the relationship between risk and return

Question 1

In choosing where to invest, return and risk for an investment must be compared. It is not sufficient to choose an investment based only on return without taking risk into consideration. We have studied two methods or measures that compare return and risk. State these two methods, the formula for each and the criteria used in evaluating alternative investment of each method.  

Question 1 Solution

There are two method which are discussed, 1- Arbitrage Pricing Theory & 2-Capital Asset Pricing Model

Arbitrage Pricing Theory

It is a broad principle of  pricing of asset. It postulates predicted return on a financial asset may be modeled as a linear function of various variables or theoretical market indices,

Formula

R i  = R f + β I 1 * R P 1 + β I 2 * R P 2 + … + β k n * R P n,

RP =    Industry risk premium

β =       Asset portfolio Sensitivity

R f=     Risk-free rate of return

Criteria used

The Criteria is predicated on three fundamental assumptions:

• Systematic conditions account for asset returns.
• By diversification, investors may create a portfolio of assets that eliminates real danger.
• There is little room for arbitrage with well-diversified portfolios. If arbitrage possibilities occur, they will be used to the fullest extent possible by investor

CAPM Model

It is a statistical model that illustrates the association among structural risk and the anticipated return on investment, most specifically stocks. CAPM is commonly used in finance for the purpose of pricing speculative securities and calculating projected returns on investment considering their probability and cost of capital.

Formula is

​R i​       = R f​ + β i​ ( R m​−R f​)

where:

Β i​       =          Investment beta

(R m​−R f​)  =   Market Premium based on risk

R m =              Market return

R i       ​=         Investment Returns (Expected)

R f       ​=          Rate of risk free interest

Criteria used

The CAPM model’s fundamental assumptions are as follows.

• Markets are ideal—there are no trading costs, fines, inflation, or limits on short selling.
• Both investors are risk averse.
• Markets operate at a high level of efficiency. Both investors have fair access to all details available.
• Any investor has the ability to borrow and lend an infinite sum at a risk-free pace.
• The beta coefficient is the best way to quantify risk.
• Both reserves are fully liquid and divisible indefinitely.
• The sum of usable assets is fixed for a specified time span.
• Markets are in balance. Each and every investor is a price taker, not a price generator.
• The standard distribution mechanism governs the return of all usable money.

Time value of money and calculate PV, FV & annuities

Question 2 Part a

Solve the following two problems. Use Excel, financial calculator, or PV and FV Tables. Show your work with the formulas and figures inserted in them

(a). Hamad is saving to establish a small business. He deposits a fixed amount of money every month in a bank account that pays a nominal interest rate of 12 %. If this account pays interest every month, then how much he should save at the end of every month to have AED 50,000 in his account after 5 years.         

Question 2 Solution Part a

Solution

FV of annuity Formula = annuity X { (1 + i)^n -1) /i}

Annuity is required to be calculated.

Data

FV                   = AED 50,000

i                       = mean interest every month i.e 12% compounded annually

n                      = Number of year i.e 5 year

Supporting calculation

Adjustment of i=        12% monthly converted to yearly i.e.  interest rate /12 =  1%

Adjustment of n=       5 years of period  X 12 payments = 60

Main Calculation

FV of annuity Formula                       = annuity * { (1 + interest rate)^n -1) / interest rate }

AED 50,000                                        =annuity * { (1 + 1%)^60 -1) /1%}

AED 50,000                                        = annuity * 81.675

Current annuity                                   = 50,000/81.675

Current annuity                                   = 612.22

This amount is monthly savings which i required by Hamad to do on monthly basis to have 50,000 AED after the 5 years time.

Question 2 Part b

(b) What is the present value of an investment that pays AED 100,00 every year for four years if the interest rate is 8 % compounded quarterly

Question 2 Solution Part b

PV of annuity = annuity *  { (1 + interest rate) ^n -1)  /  (1 + i) ^no of years  * interest rate) }

PV Annuity is required to be calculated.

Data

Annuity           = AED 100,000

i                       = 8% compounded quarterly

n                      = Number of year i.e 4 year

Supporting calculation

Adjustment of i=        8% compounded quarterly converted to yearly i.e.  i/4 = 8% /4  = 2%

Adjustment of n=       4 years X 4 quarters = 16

Main Calculation

PV of annuity Formula = annuity * { (1 + interest rate)^n -1) / (1 + interest rate)^n X interest rate) }

= 100,000 X { (1 + 0.02)^16 -1) / (1 + 0.02)^16 X 0.02) }

= 100,000 X 13.5775

= 1,357,750 AED PV of investments that pays AED 100,00 every year for four years.

Calculate the value of Securities

Question 3 Part a

Solve the following two problems. Use Excel, financial calculator, or PV and FV Tables. Show your work with the formulas and figures inserted in them.                

(a) What must be the present value of an AED 10,000 bond with a 9 % coupon rate, semiannual coupons that has 8 years to maturity if the discount rate is 10 %. 

Question 3 Part a Solution

Data

PV       = AED 10,000

i           = 9% Semi Annually

n          = Number of year i.e 8 year

Supporting calculation

Coupon Payment                    =(9% Semi Annually / 2  ) X 10,000 = 450 AED

The discount rate  to maturity = 10 % / 2 payment in years = 5%

Adjustment of n                                  = 8 years X 2 payment in years = 16

Price of Bonds = Payment of Coupon x [ [ (1 – 1 / (1 + Interest rate)^years ] / Interest rate] + Face value / (1 + Interest rate)^years

Bonds Price = 450  *  [ [ (1 – 1 / (1 + 0.05) ^ ¹⁶ ] / 0.05 ] + 10,000 / 1.05 ^ ¹⁶

= 450  * 10.84 + 4,581.12

= 4,876.99 + 4,581.12

= 9,458.12

Question 3 Part b

A public shareholding announced that it is not going to pay dividends for the next 9 years. However, it also announced that it will pay AED 5 as a dividend to common stockholders in year 10 and the dividends will grow by 2 % every year starting year 11. What price would you pay at present if the required rate of return is 7 %.                          

Question 3 Part B Solution

Return Rate     = 7%

Dividend         = 5 AED

Growth Rate   (g)                    =2%

Share prince   year 10 = Dividend at 10 years /(Return rate – growth rate)

= 5 /(0.07-0.02) = 5/0.05 = 100

Share price today        = Share price in year 10 beginning / (1+r)^10-1

                                    = 100/(1+0.07)^9

                                    = 54.393 AED

The price reason to pay at 7% rate of return is 54.393 AED

Calculate the cost of capital.

Question 4 

Tammuz Enterprises, a public shareholding company, wants to calculate its weighted average cost of capital WACC. It has raised AED 1,000 million in capital (funds) distributed as follows: AED million 50 as preferred stock, AED 400 million as common stock and AED 550 million from debt (bonds). The firm has a marginal tax rate of 30 % and it borrows at a coupon rate of 12 % it pays to its bondholders. The price of its preferred stock is AED 80 and the dividend it pays to these stockholders is AED 6.

The current flotation cost it would incur if it issued new preferred stock, is 2 %. Furthermore, the firm’s stock beta coefficient is 0.95 and the risk-free return rate is 6 % while the required market return rate is 13 %. Using the above information, First, calculate the component cost of each source of capital and then calculate the WACC for the firm. Show you work step by step. 

Question 4 Solution

After Tax cost of bond ( Kd ) = Rate of Interest * ( 1 – rate of tax )

Capital Budgeting

Question 5

A company wants to decide which project to undertake out of two projects A and B.  For this purpose, it wants to evaluate each project that have the same initial investment (cost) but different cash flows for the next three years. The following table gives information on these two projects. The discount rate to be used is 8 %, which is the WACC for the company.  Use two methods of capital budgeting: The Net Present Value (NPV) Method and the Internal Rate of Return (IRR) Method, to evaluate and compare the two projects. Based on the outcome of calculations, choose the best project A or B and explain your decision for each method.  Show all your work for each method step by step.                            

Initial Investment and Cash Flows of

Projects A and B in AED

Question 5 Solution

Criticize Financing Decisions in business environment

Question 6 Part a

COVID 19 has adversely affected many economic activities in most countries in 2020. Although many economies recovered in the past few months, there is still a great risk facing many firms. There are problems facing investors wanting to start a new business. The following are questions on the relevant information needed to start a new business venture in the UAE.                                                                   

• Identify five economic areas that have demonstrated good performance in the UAE during 2020 despite the effects of COVID 19. Starting a business in these sectors will be more likely successful

Question 6 part a Solution

Following are the sectors which were well performed during 2020 despite of COVID-19: –

• Programs relating to digital technology/online platforms
• Telecommunications and internet service providers, i.e. subscriptions to internet networks and wifi, as well as computers and their accessories
• Electronic media, e.g., a television channel or
• Online payment portals, i.e. e-commerce websites
• Food, i.e. to alter the flavor
• E-commerce and home delivery, i.e. pharmaceutical and pharmaceutical logistics.
• Healthcare i. personal hygiene devices and instructional materials
• Education, including distance learning and professional growth.

Question 6 Part b

Suppose you have initially selected a specific area to start a new line of business from one of the five areas above. There is some relevant information available about similar businesses that are currently operating in the market. What information do you look for to evaluate the feasibility of the new business judging from the material you have learned in this course?   

Question6 part b Solution

• Identify the rivals.

To begin, you’ll need to determine who your true competitors are in order to compare data accurately. What is effective in a similar company to yours might not be effective with your brand. But how are you going to do this? Consider two types of “competitors”: overt and indirect. Direct rivals are companies that sell a comparable products to yours and run in the same regional region as you. In the other hand, an indirect rival could provide goods that are not identical but may fulfill a similar consumer demand or resolve a similar issue. On paper, it seems to be very straightforward.

• Research the offerings that your rivals sell.

The product or service is at the core of every market, which is why this is a good place to start. You’ll want to evaluate a competitor’s whole product range as well as the consistency of the goods or services they have. Additionally, you can consider their prices and any consumer incentives they might be providing. Several points to remember include the following:

Is the supplier low-cost or high-cost?

Are they mostly focused on bulk transactions or on one-off purchases?

What %age of the industry do they control?

What are their ideal consumers’ features and needs?

Do they have a separate promotional strategy for internet orders than in-store sales?

• Do a competitive analysis of a competitor’s market strategies and outcomes.

 Conducting a sales review on the rivals’ products may be challenging. You’ll want to find out the responses to the following questions:

How is the distribution mechanism structured?

How are they selling?

Should they have several locations, and if so, how would this benefit them?

Are they growing in size? Scaling back?

Do they provide reselling services to partners?

Why are their customers not purchasing?

For severing their ties with the business?

What is their annual revenue? What is the average number of sales?

Is it customary for them to give discounts for their goods or services?

To what extent is a salesperson engaged in the process? .

• Examine the rivals’ marketing strategies.

Analyzing a competitor’s website is the quickest and most accurate way to determine their marketing activities. Following were the question

Is there a podcast available?

Is static multimedia material such as info graphics and cartoons being used?

What are PowerPoint presentations?

Should they have a Frequently Asked Questions section?

Are there any highlighted articles?

Are you aware of news releases?

Is there a media package available?

• Keep an eye on your competitors’ content strategies.

Consider the following when reviewing your competitor’s content:

Is their material accurate?

as there any grammatical or pronunciation errors?

Is the text arranged in a way that makes it readable? (Are bullet points, bold headings, and numbered lists being used?)

Is their material free and open to the public, or do readers have to opt-in?

Who is responsible for writing their content? (Do you have an in-house team? A single individual? Numerous contributors?)

Do their papers have a visible byline or bio?

• Conduct an analysis of the competitor content interaction.

Following are the information that must be kept in mind before start of business

Some subjects elicit a stronger response than others.

The messages are either pessimistic or constructive, or a combination of the two.

Individuals tweet more often on some subjects than others.

Readers are more receptive to Facebook alerts on specific material.

Don’t fail to take care of what the rival categorizes their content using tags and whether each piece of content has social network follow and retweet buttons. Both of these would include constructive participation.