In: Statistics and Probability
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.
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