Question

Risky Cash Flows

The Bartram-Pulley Company (BPC) must decide between two mutually exclusive investment projects. Each project costs $7,250 and has an expected life of 3 years. Annual net cash flows from each project begin 1 year after the initial investment is made and have the following probability distributions:

Project A		Project B
Probability	Cash Flows	Probability	Cash Flows
0.2	$7,000	0.2	$        0
0.6	6,750	0.6	6,750
0.2	8,000	0.2	20,000

BPC has decided to evaluate the riskier project at a 13% rate and the less risky project at a 8% rate.

1. What is the expected value of the annual cash flows from each project? Do not round intermediate calculations. Round your answers to the nearest dollar.

   	Project A	Project B
   Net cash flow	$	$

   What is the coefficient of variation (CV)? (Hint: σ_B=$6,522 and CV_B=$0.81.) Do not round intermediate calculations. Round σ values to the nearest cent and CV values to two decimal places.

   	σ	CV
   Project A	$
   Project B	$

2. What is the risk-adjusted NPV of each project? Do not round intermediate calculations. Round your answers to the nearest cent.

   Project A		$
   Project B		$

3. If it were known that Project B is negatively correlated with other cash flows of the firm whereas Project A is positively correlated, how would this affect the decision?

   This would tend to reinforce the decision to -Select-acceptrejectItem 9 Project B.

   If Project B's cash flows were negatively correlated with gross domestic product (GDP), would that influence your assessment of its risk?

   -Select-YesNoItem 10

Answer 1

Part a)

The expected value of the annual cash flows from each project is calculated as below:

Probability (1)	Project A Cash Flows (2)	Project B Cash Flows (3)	Expected Value Project A (1*2)	Expected Value Project B (1*3)
0.2	7,000	0	1,400	0
0.6	6,750	6,750	4,050	4,050
0.2	8,000	20,000	1,600	4,000
			$7,050	$8,050

Net Cash Flow (Project A) = $7,050

Net Cash Flow (Project B) = $8,050

_____

The standard deviation and covariance of Project A is arrived as follows:

Standard Deviation = [Probability 1*(Cash Flow 1 - Net Cash Flow)^2 + Probability 2*(Cash Flow 2 - Net Cash Flow)^2 + Probability 3*(Cash Flow 3 - Net Cash Flow)^2]^1/2

Substituting values in the above formula, we get,

Standard Deviation of Project A = [.2*(7,000 - 7,050)^2 + .6*(6,750 - 7,050)^2 + .2*(8,000 - 7,050)^2]^(1/2) = $485

Coefficient of Variation (Project A) = Standard Deviation of Project A/Expected Value of Project A = 484.77/7,050 = $0.07

Standard Deviation of Project B = [.2*(0 - 8,050)^2 + .6*(6,750 - 8,050)^2 + .2*(20,000 - 8,050)^2]^(1/2) = $6522

Coefficient of Variation (Project B) = Standard Deviation of Project B/Expected Value of Project B = 6,521.88/8,050 = $0.81

____

Tabular Representation:

	σ	CV
Project A	$485	$0.07
Project B	$6522	$0.81

_____

Part b)

The risk-adjusted NPV is calculated as below:

Standard deviation and coefficient of variation are both the measures of risk. A project with higher standard devation/coefficient of variation would be more risky. Therefore, project B would be treated as riskier project and project A would be considered as less risky project.

Risk-Adjusted NPV = -Initial Investment + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3

Risk-Adjusted NPV (Project A) [Less Risky Project] = -7,250 + 7,050/(1+8%)^1 + 7,050/(1+8%)^2 + 7,050/(1+8%)^3 = $10918.53 or $10,919

Risk-Adjusted NPV (Project A) [Riskier Project] = -7,250 + 8,050/(1+13%)^1 + 8,050/(1+13%)^2 + 8,050/(1+13%)^3 = $11,757.28 or $11,757

____

Tabular Representation:

	NPV
Project A	$10,919
Project B	$11,757

_____

Part c)

If it were known that Project B is negatively correlated with other cash flows of the firm whereas Project A is positively correlated, how would this affect the decision?

This would tend to reinforce the decision to select Project B. It is because Project B would become less risky as it will have lesser effect on the company's overall portfolio.

_____

Part d)

If Project B's cash flows were negatively correlated with gross domestic product (GDP), would that influence your assessment of its risk?

Yes. It is because Project B will provide more profits when the economy is down and therefore, it would be considered less risky as compared to Project A during such times. In such a case, the company would again benefit from accepting project B.