Below I have attached the question and its answer, please help me by listing the formulae used in each step of the calculation, thanks. You do not need to answer the thesis question, the answer is already given.

PV Plc is considering investing 50,000 in a new machine with an expected life of five years and no residual value. It is expected that 20,000 units will be sold each year at a selling price of 3.00 per unit. Variable production costs are expected to be 1.65 per unit, while incremental fixed costs, mainly the salary of a maintenance engineer, are expected to be 10,000 per year. The company currently uses a discount rate of 12% for projects of a similar risk.

Required

(a) Explain why risk and uncertainty should be considered in the investment appraisal process.

20 Marks

(b) Calculate and comment on the Net Present Value (NPV) of the project.

20 Marks

(c) Evaluate the sensitivity of the projects NPV to a change in the following project variables:

Initial cost

Discount rate

Sales volume

Sales price

40 Marks

(d) Upon further investigation it is found that there is a significant risk that the expected sales volume of 20,000 units might not be achieved. The sales manager suggests that sales volumes could depend on expected economic states that could be assigned the following probabilities:

Economic state	Poor	Normal	Good
Probability	0.3	0.6	0.1
Sales volume (units)	17,500	20,000	22,500

Calculate and comment on the expected NPV of the project.

ANSWER:

(b)

Year	Invest	Contrib	Fixed	Net	Dis Fact	Total
0	(50,000)			(50,000)	1.000	(50,000)
1-5		27,000	(10,000)	17,000	3.605	61,285
						11,285

NPV of sales revenue = 20,000 x 3 x 3.605 = 216,300

NPV of variable costs = 20,000 x 1.65 x 3.605 = 118,965

NPV of contribution = 97,335

(c) Sensitivity analysis:

Initial cost sensitivity = (11,285/50,000) x 100 = 22.57%

Discount rate estimate IRR:

@12% NPV = 11,285 @25% NPV = (4,287)

>>> IRR = 12% + (11,285/15,572)(13%) = 21.4%

>>> Sensitivity = (9.4/12) x 100 = 78.33%

Sales volume

For NPV =0, contribution has to decrease by 11,285. This represents a decrease in sales of (11,285/97,335) x 100 = 11.6%

Sales price

Sensitivity to sales price = (11,285/216,300) x 100 = 5.2%

Variable	Sensitivity
Initial cost	22.57% (3)
Discount rate	78.33% (4)
Sales volume	11.6% (2)
Sales price	5.2% (1)

Sales price is the most sensitive variable, therefore market research should be performed to ensure estimates of selling price are accurate.

(d) Expected sales = (17,500x0.3) +(20,000x0.6) + (22,500x0.1)

= 19,500 units

NPV Expected = 8,852

NPV Best = 23,452

NPV Worst = (882)

The managers will need to satisfy themselves about the accuracy of the latest information, but the fact remains that there is 30% chance of a negative NPV and this may be considered too high a risk. It can be argues that assigning probabilities to expected economic outcomes provides information for better decisions but the probability estimates themselves can carry a high degree of uncertainty and subjectivity.