Question

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?

Answer 1

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.