The existence of risks due to uncertainty must be managed in any project undertaken

Question 1

  1. In the project execution context, a risk is an unforeseen event that, if it occurs, will impact the achievement of the project’s objective. The existence of risks due to uncertainty must be managed in any project undertaken. Construction projects are majorly complex projects that are highly technical, involve a large amount of money, and can take a span of several years to complete. These projects face a lot of risks such as weather and unexpected conditions on jobs, cost estimation errors, personnel problems, financial problems, faulty materials, and operational problems. The construction industry mainly uses a lump-sum contract in order to reduce the cost of design as well as administration costs. In a lump-sum contract, a contractor submits the total price instead of bidding for individual items. In this case, the owner assigns all risks to the contractor who manage the risk by asking higher markup in order to take control of unforeseen contingencies. Depending on the risk assessment study and labor expertise of the contractor, the overhead cost will differ from builder to builder. In order to reduce costs, which results in increased profit, the contractor charges a higher price and does not delay the job.
  2. The expected profit of any given job is the sum of each job’s expected profit.

E(X)

Where pi – the probability of getting ith profit

Xi – is the ith profit

Hence;

 

Percentage profit/loss Percentage of jobs(probability) Expected Returns
25% profit 0 0%
20% profit 5 1%
15% profit 15 2.25%
10% profit 25 2.5%
5% profit 30 1.5%
Break-even 10 0%
10% loss 10 -1%
15% loss 5 -0.75%
  E(X) 5.5%

 

Percentage profit/loss Percentage of jobs (probability) Expected Returns
25% profit 4 1%
20% profit 6 1.2%
15% profit 20 3%
10% profit 30 3%
5% profit 30 1.5%
Break-even 5 0%
10% loss 5 -0.5%
15% loss 0 0%
  E(X) 9.2%

 

The previously expected profit was 5.5 percent. The recruitment of new experienced business development staff boosted the expected profit to 9.2 percent. The contribution margin to the overall expected profit is 3.7 percent. If the annual contract volume of the firm is $200, the firm will pay $7.4 million (3.7%*$200) to the new staff to remain at the previously expected profit.

 

 

Question 2

  1. Moral reasons – employees should be taken care of in such a way that employees should not be let to fall sick or get injured in the workplace. This is meant to reduce the cost to the society caused by workplace accidents. In order to do so, a safe workplace is provided by the contractor by ensuring safe working methods, involving them in risk management procedures, and the development of working procedures.
  2. Financial reasons – in this case, the business can measure the cost versus the consequences as investment responsibilities that include introducing training sessions, bringing new better equipment or machines, using simple information as well as giving simple instruction and supervision that ensure a safe and efficient working place. This is because any accident that occurs in the workplace have financial consequence such a small accident resulting in loss of time which affect the firm’s productivity as well as its earnings.
  • Legal reasons – in setting the company’s health and safety objectives, statute law, Acts, and Regulations that parliament has provided are used in order to ensure compliance with the legislation needs. This will help in avoiding criminal or civil prosecution that could reduce the time of work or even termination of the contract that results in losses or reduced profits.

 

 

State of the economy Probability End of year 1 (€ million) Expected return Yr 1 End of year 2 (€ million) Expected return Yr 2
Recession 0.2 1.0 0.2 1.5 0.3
Growth 0.3 3.0 0.9 3.5 1.05
Expanding 0.5 5.0 2.5 5.5 2.75
      3.6   4.1

From the table above, the expected return of each year at each state is given by;

E(X)

Where pi – the probability of getting ith return

Xi – is the ith return

The risk-adjusted discount rate is given to be 10 percent. Hence, the expected return at each state is given as follows;

The initial capital outlay is €4.0

E(R) = Year 1 = 3.6 and year 2 = 4.1

NPV =  +  +  = 2.659

Variance =

E’(R) = -2.31

0.2(1-3.6)2 + 0.3(3 – 3.6)2 + 0.5(5-3.6)2 + 0.2(1.5 – 4.1)2+0.3(3.5-4.1)2 + 0.5(5.5 – 4.1)2 = 4.88

Standard deviation =

=

= 2.21

  • Transform zero into z-score

Mean = 2.659

Z = = -1.203

P (z < -1.203) = 0.5 – 0.1056

= 0.3944

= 39.44%

  1. It means that the probability that NPV is less than zero is 39.44 percent.

Question 3

  1. Allais Paradox arises by comparing the choices of two participants in two different experiments, whereby each has two gambles to make a choice, A and B.

In the hypothetical and small monetary value, when people are presented to make a choice between 1A and 1B, people choose 1A. On the other hand, if they are presented to make a choice between 2A and 2B, they will choose 2B. However, the same person who has chosen 1A or 2B would choose both 1A and 2B, which contradicts the expected utility theory, which states that a person should choose either 1A and 2A or 1B and 2B.

  1. If the contractor undertake 150k, Expected mean = 0.2*150 + 0.5*100+0*0.3 = 80

If the contractor undertake the work for 100k, then t6he average mean of expectation is

0.3*100+0.6*80+0.1*0 = 78

Therefore if the contractor wants to maximize profits, then they have to undertake the 150k.

From the table above, we can find that;

For experiment 1:

1U (120K) < 0.9U (150K) + 0.1U (0K)

Experiment Two

1U (80K) > 0.75U (100K) +0.25U (0K)

Experiment 3

1U (100K) < 0.85U (150K) + 0.25U (0K)

For the first and the third experiment, the client will get more by putting the money in the lottery. Hence, the contractor should price at 80k because the client will get less than if they invest in a lottery.

Question 5

Risk-return characteristics Product
Alpha Beta Gamma Delta Epsilon
Expected return on product 20% 10% 5% 15% 3%
Proportion       of investment 0.05 0.45 0.1 0.25 0.15

 

Expected return of the portfolio = E(X)

Where pi – the probability of getting ith return

Xi – is the ith expected return

E(X) = 0.05(20%) + 0.45(10%) + 0.1(5%) + 0.25(15%) + 0.15(3%)

= 10.2%

Expected return of the portfolio = 10.2%*150k

= 15.3k

  1. First, the difference between the English bid and the sealed bid is the consensus of knowledge about the value of the property. In an English auction, the bidder knows about the other bid while in the sealed auction, the bidders do not know about other bidders. Hence, there is pressure and urgency that make people act emotionally in an English bid, which is absent in a sealed bid.
  2. External hedging involves third parties such as banks in order to manage the risk exposure in a foreign exchange market. The methods under this risk management technique include futures, forwards, money markets, currency swaps, and options. On the other hand, leading and lagging involve the adjustment of payment time that is being made in foreign currencies. Leading involves making payment prior to the due date while lagging is making payment after the due date.
  3. The real interest rate is the interest rate adjusted for inflation. It is the difference between the nominal interest rate and the rate of inflation.

Real interest rate in UK = nominal interest rate (15%) – inflation rate (5%) = 10%

Real interest rate in US = nominal interest rate (5.05%) – inflation rate (2%) = 3.05%

  1. Interest rate in US = 3.05%

Interest rate in UK                                          = 10%

Spot rate (S0) US dollars per unit of UK euro = $1.50/£

Change in foreign currency exchange rate  = 0.0674

  • Future spot rate (St) = S0(1+0.0674) = $1.601
  1. For a no-arbitrage condition to achieved in the market, the one-year forward exchange rate between the two currencies (USD and Pound) should be £1=$1.601. Interest Rate Parity is a condition of no-arbitrage where there is a state of equilibrium in the market, and investor is indifferent on interest rates in the two countries. If the spot rate after the three month period differs from $1.601, then an investor will make losses.

Question 6

  1. In accordance with the economic theory, the managers of a firm should maximize the expected earnings without taking into consideration the variability of their profits. Scultz (1984), change this concept by offering a viable economic reason for firm managers’ concern. He said that managers should be concern about the variability of the financial performance of a company. From that time, there are several kinds of literature that have developed that justifies active risk management that involves managerial self-interest, cost of financial distress, capital market imperfections, and tax effects. In the manager’s self-interest, the managers are faced with limited ability to make investment diversification because of limited wealth and high concentration of human capital returns in the business they manage. This creates risk aversion and prefers stability. The second and third mainly focuses on the impact of declined profitability on the firm’s future fortunes. It is known that financial distress is costly, and therefore obtaining external financing also is costly because the firm’s viability is costly. On the tax effects, if the company has reduced volatility in taxable income reported, the expected tax burden is reduced.

Most of the firms affected by declining profits due to inefficient portfolios include large construction companies, property management firms, financial institutions, confectionary manufacturers, automobile manufacturers. For a construction company, it is faced with unforeseen circumstances such as bad weather conditions, poor quality materials, and workplace risks such as injury to workers. On the property management firms, the risk includes physical damage to the property. In order to mitigate risk, therefore, the project managers should ensure the property as well as conducting a regular inspection on the property in question. Financial institutions, on the other hand, are faced with a lot of risks that include liquidity risks, credit risks, interest rate risks, operational risks such as fraud and mistakes by staff, foreign exchange risks, and technology risks. Therefore, these institutions should diversify their portfolio in order to manage risks. These include allocating their investments among various financial instruments as well as other industries.

  1. The correlation between the two sets of data is different. DC(1) and DC(2) show a strong positive correlation meaning that there is a strong linear relationship between them, while DC(3) and DC(4) show a weak negative correlation between them. These are shown in the table below.
  DC (1) DC( 2)
DC(1) 1
DC(2) 0.98514 1

 

 

  DC (3) DC (4)
DC(3) 1
DC(4) -0.29047 1

 

  1. Portfolio risk
Risk-return characteristics Double-C Treble-B
Expected return on security 20% 15%
Amount Invested $600,000 $400,000
Standard-deviation of security 9% 7%

 

Portfolio risk is the standard deviation of a portfolio. It is calculated using the formula:

σp =  1σ2 1 + w2 2σ2 2 + 2w1w2σ12.

Where weight are;

For Double C =  = 0.6

Treble B =  = 0.4

If correlation is -1:

δn = Square root of 0.62(92)+0.42(72)+2*(-1)*0.6*0.4*9*7 = 2.6%

 

If correlation is 0:

δn = Square root of 0.62(92)+0.42(72)+2*(0)*0.6*0.4*9*7 = 6.08%

 

If correlation factor is 1

δn = Square root of 0.62(92)+0.42(72)+2*(1)*0.6*0.4*9*7 = 8.2%

 

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