Question

ABC Ltd is evaluating to invest in two projects. Project X may yield a return of £1.5m with a probability of 20%, or a return of £5m with a probability of 60%. Project Y, instead, may earn a negative return of £3m with a probability of 70% or a positive return of £7m with a probability of 30%. 

How much is the expected return for project X and Y? [8 marks] 2) What is the standard deviation? [6 marks] 3) Compare and briefly discuss the expected return and risk of the projects.

Answer 1

1.How much is the expected return for project X and Y?

Expected return = $\sum$ (Return_i$\times Probability$_i)

For project X: (20% $\times$ 1.5m) + (60% $\times$ 5m)

= 300,000 + 3m

Expected return for project X is €3.3million

For project Y: (70% $\times$ -3m) + (30% $\times$ 7m)

= -2.1m + 2.1m

Expected return for project Y is €0

2) What is the standard deviation

$\sigma$ = $\sqrt\frac{\sum(x-\mu)^{2}}{n-1}$

Project X $\sigma$ = $\sqrt{(1.5m-3.3m)^{2}\times0.2 + (5m-3.3m)^{2}\times0.6}$

Project X $\sigma$ = 1,543,372.93

Project Y $\sigma$ = $\sqrt{(-3m-0)^{2}\times0.7 + (7m-0)^{2}\times0.3}$

Project Y $\sigma$ = 4,582,575.70

3) Compare and briefly discuss the expected return and risk of the projects.

Project X has an expected return of €3.3m while project Y has an expected return of €0 on investment. Going by expected return, Project X poses has a higher expected return for ABC ltd. than project Y.

Project X has a standard deviation of 1,543,372.93 whereas project Y has a standard deviation of 4,582,575.70. Project Y thus has a higher standard deviation than project X. This means that project Y has a much higher market volatility than project X and thus a a higher risk to invest. Project X does not stray as far from its expected value, relative to Y, and thus not a great risk. However, project Y has a higher deviation from its expected return in the positive direction and may have a greater payout potential for ABC ltd.