Sammy's Ski Lodge has enough financial capital to undertake any or all of the following projects: I. Buying a lift machine that will last 3 years and produce $3000 worth of services the first year, $2000 the second year, and $1000 the third year.
II. Developing and building a robot lift operator that will last 5 years and produce $5000 worth of services each year.
III. Building a new restaurant that will last 5 years and produce $30,000 worth of food and drink sales each year.

Required:
a. If Sammy's only alternative to the above projects is putting his money in the bank and earning 5% interest, what is the present discounted value of each project's revenue stream?
b. The PDV of project (I.)'s revenue stream is:
c. The PDV of project (II.)'s revenue stream is:
d. The PDV of project (III.)'s revenue stream is:
e. Project (I) costs $5,800; project (II) costs $20,000; and project (III) costs $100,000. What is the NPV (Net Present Value = PDV of revenues minus PDV of costs) of each project? Which project(s) will Sammy choose to undertake? Why?

Solution :

Project 1

Year  Cash Flow       PVF at rate 5%          PV

1          3000               0.952381              2857.143

2         2000               0.907029            1814.059

3         1000                0.863838            863.8376

Therefore, total PDV = 5535.039

The revenue stream of PDV of project 1 = 5535.039

Project 2

Year  Cash Flow       PVF at rate 5%          PV

1          5000               0.952381              4761.905

2         5000               0.907029             4535.147

3         5000               0.863838              4319.188

4         5000              0.822702               4113.512

5        5000                0.783526             3917.631

Therefore, total PDV = 21647.38

The revenue stream of PDV of project 2 = 21647.38

Project 3

Year  Cash Flow       PVF at rate 5%          PV

1          3000               0.952381              28571.43

2         3000               0.907029             27210.88

3         3000               0.863838              25915.13

4         3000              0.822702               24681.07

5         3000                0.783526             23505.78

Therefore, total PDV = 129884.3

The revenue stream of PDV of project 3 = 129884.3

The NPV

For Project 1  :     PVCI - PVCO

                          = 5535 - 5800

                         = -265

For Project 2  :     PVCI - PVCO

                          = 21647 - 20000

                         = 1647

For Project 3  :     PVCI - PVCO

                          = 129884 - 100000

                         = 29884

Therefore, project 2 and 3 will be chosen.

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