Payback & NPV Examples

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N04 HL P1 Q5

Payback Calculation
Year
Machine A $
Machine B $
1
45,000
25,000
Part of 2
20,000 (0.57 of 35,000)
35,000
Part of 3
-
25,000 (0.45 of 55,000)
Investment
65,000
85,000

1 + 0.57 = 1.57 (Machine A has payback period of 1.57 years) 2 + 0.45 = 2.45 (Machine B has payback period of 2.45 years)

Accounting Rate of Return Calculation

Machine A $
Machine B $
Net Return
155,000
205,000
Total Return-Investment
155,000 – 65,000 = 90,000
205,000 – 85,000 = 120,000
Average Return
90,000 / 5 years = 18,000
120,000 / 5 years = 24,000
ARR =
(Average / Investment)
(18,000 / 65,000) x 100 = 28%
(24,000 / 85,000) x 100 = 28%

Net Present Value Calculation
Year
Discount Factor
Machine A $
Machine B $

Cash Flow
Present Value
Cash Flow
Present Value
0
1
(65,000)
(65,000)
(85,000)
(85,000)
1
0.909
45,000
40,905
25,000
22,725
2
0.826
35,000
28,910
35,000
28,910
3
0.751
25,000
18,775
55,000
41,305
4
0.683
25,000
17,075
55,000
37,565
5
0.621
25,000
15,525
55,000
21,735
Total
-
121,190
-
152,240
Net Present Value

56,190

67,240

Machine A has a faster payback period. If Riveau Yachts does not want to take risks such as cash flow problems, it should choose Machine A. Payback period is also more accurate as it is more predictable. However, the net present value calculations shows that Machine B has a higher net present value of returns. Net Present Value is a better method or appraising investments because it takes time value of money into consideration. Thus, choose Machine B.

Assessing financial advantages and disadvantages to investing in each of the machines.

Machine A
Machine A has a faster payback period and therefore, gives Riveau Yachts the advantage of having less risk if they were to have any cash flow problems in the future. Since Riveau Yachts is a business that makes boats, where said technology progresses fast, having a shorter payback period can also mean that they have a higher chance to break even on the investment before Machine A has to be replaced with a newer machine. Machine A has the same calculated ARR as Machine B but requires less investment. It is therefore easier to raise finance for Machine A as investors will see it as a project of less risk. Machine A has a lower NPV than that of Machine B, meaning that Machine A is less profitable. Also evident from the NPV, Machine A’s net present value begins to decrease after year 3, indicating a possibility of high maintenance cost of Machine A or a possibility that it is not future proof, causing it’s popularity to be expected to be significantly lower after its first 2 years. Machine B

The NPV forecasted for Machine B is higher than that of Machine A with a steady increase in net present value throughout the years, in contrast with Machine A’s decrease. This may mean that Machine B is more up to date and therefore can maintain its popularity and usefulness even in the future. This can create the advantage of Riveau Yachts not having to make a start a new project shortly after the investment of Machine B. This therefore means that Riveau Yachts may save money on investments by investing in Machine B despite the higher cost of Machine B. The payback period of Machine B is longer than that of Machine A. This means that if Riveau Yachts are to face cash flow problems in the future, it may not be able to counter the problem due to lack of funds. The higher payback and higher initial investment required for Machine B also means that it will be harder to find finance from investors as it is a more lengthy and risky project. The ARR of Machine B is the same as Machine A. However, Machine B costs more and therefore makes it a second choice, as it is a bigger risk to the business. (Though risk is not always a bad thing. Do not use the risk of a project to determine whether or not it is worthwhile, as risks always have to be made. Bigger risks also usually...
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