Question

In: Finance

you are the cfo of xyz co. that prints textbooks using an outdated system. the owner...

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 that prints textbooks using an outdated system.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?

Solutions

Expert Solution

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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