Question

In: Statistics and Probability

A company has to choose between two new machines, the Alpha and the Beta. Both machines...

A company has to choose between two new machines, the Alpha and the Beta. Both machines would cost $30 000 and have an expected lifetime of 4 years. Estimates of the

annual cash inflows which each machine would generate are given below

Machine

Year

0

1

2

3

4

Alpha

Cash flow

-$30,000

$14,000

$15,000

$15,000

$14,000

Beta

Cash flow

-$30,000

$8,000

$13,000

$15,000

$21,500

The company staff decides that 12% is an appropriate discount rate.

  1. Find the net present value (NPV) of both projects.
  2. Which project would you invest in? What does your answer depend on?

Solutions

Expert Solution

a)

NPV is calculated as follows

PV = cash flow / (1 + r)ⁿ

Setting this in Excel

Rate 0.12
Machine Alpha Beta
Year Cash flow Present Value Cash flow Presenet Value
0 ($30,000) ($30,000) ($30,000) ($30,000)
1 $14,000 $12,500.00 $8,000 $7,142.86
2 $15,000 $11,957.91 $13,000 $10,363.52
3 $15,000 $10,676.70 $15,000 $10,676.70
4 $14,000 $8,897.25 $21,500 $13,663.64
Net Present Value $14,032 $11,847

Excel sheet is

and the formula applied is

So, the NPV of alpha = $14,031.86

and NPV of Beta = $11,846.72

b)

I would invest in Project alpha as the NPV of alpha is greater than that of Beta


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