In: Finance
you are the cfo of xyz co. that prints textbooks using an outdated system. the owner provides you with the following information about a new project "alpha" that will last for 7 years. the project requires a new machine that costs 100,000 today. the project will not generate any cash flow at time 1. in years 2 and 3 annual cash flows is 25,000. in years 4 and 5 annual cash flow is 30000 in year 6 it is -10,000 and in year 7 it is 60,000. the required rate of return is 6%.
what is the payback period?
what is the discounted payback period?
what is the NPV of the project?
a). Calculating the Payback Period for the Project:-
Year | Cash Flows of Project ($) | Cummulative Cash Flows of Project ($) |
0 | (100,000.00) | (100,000.00) |
1 | - | (100,000.00) |
2 | 25,000.00 | (75,000.00) |
3 | 25,000.00 | (50,000.00) |
4 | 30,000.00 | (20,000.00) |
5 | 30,000.00 | 10,000.00 |
6 | (10,000.00) | - |
7 | 60,000.00 | 60,000.00 |
60,000.00 |
- Payback Period = Years before the Payback period occurs + (Cummulative cash flow in the year before recovery/Cash flow in the year before recovery)
= 4 years + [(20,000/30,000)*12 months]
= 4 years & 8 months
b). Calculating the Discounted Payback Period:-
Year | Cash Flows of Project ($) | PV Factor @6.00% | Present Value of Project ($) | Cummulative Discounted Cash Flows of Project ($) |
0 | (100,000.00) | 1.0000 | (100,000.00) | (100,000.00) |
1 | - | 0.9434 | - | (100,000.00) |
2 | 25,000.00 | 0.8900 | 22,249.91 | (77,750.09) |
3 | 25,000.00 | 0.8396 | 20,990.48 | (56,759.61) |
4 | 30,000.00 | 0.7921 | 23,762.81 | (32,996.80) |
5 | 30,000.00 | 0.7473 | 22,417.75 | (10,579.05) |
6 | (10,000.00) | 0.7050 | (7,049.61) | (17,628.66) |
7 | 60,000.00 | 0.6651 | 39,903.43 | 22,274.77 |
60,000.00 | 22,274.77 |
- Discounted Payback Period = Years before the Discounted Payback period occurs + (Cummulative cash flow in the year before recovery/Discounted Cash flow in the year before recovery)
= 6 years + [(17,628.66/39,903.43)*12 months]
= 6 years & 5 months
c). Calculating the NPV of the Project:-
Year | Cash Flows of Project ($) | PV Factor @6.00% | Present Value of Project ($) |
0 | (100,000.00) | 1.0000 | (100,000.00) |
1 | - | 0.9434 | - |
2 | 25,000.00 | 0.8900 | 22,249.91 |
3 | 25,000.00 | 0.8396 | 20,990.48 |
4 | 30,000.00 | 0.7921 | 23,762.81 |
5 | 30,000.00 | 0.7473 | 22,417.75 |
6 | (10,000.00) | 0.7050 | (7,049.61) |
7 | 60,000.00 | 0.6651 | 39,903.43 |
60,000.00 | 22,274.77 |
So, NPV of the Project is $22,274.77
If you need any clarification, you can ask in comments.
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