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In: Economics

The first cost, life, and annual benefit for a prospective project are uncertain. Optimistic (OP), most...

The first cost, life, and annual benefit for a prospective project are uncertain. Optimistic (OP), most likely (ML), and pessimistic(PS) estimates are given. If the interest rate is 20%, what is the expected NPV?

Parameter Pessimistic Most Likely Optimistic
Fist cost 150000 100000 80000
Annual benefit 25000 45000 50000
Project life 5 7 9

Solutions

Expert Solution

Interest rate = 20%

Pessimistic:

First cost = 150,000

Annual benefit = 25,000

Life = 5 years

Net present value is calculated as: [First Cost - Present value of annual benefit]

Year Annual Benefit Present value of annual benefit
1 25000 20833.33
2 25000 17361.11
3 25000 14467.59
4 25000 12056.33
5 25000 10046.94
74,765.30

Net present value = -150,000 + 74,765.3 = 75,234.70

Most Likely:

First cost = 100,000

Annual benefit = 45,000

Life = 7 years

Net present value is calculated as: [First Cost - Present value of annual benefit]

Year Annual Benefit Present value of annual benefit
1 45000 37500.00
2 45000 31250.00
3 45000 26041.67
4 45000 21701.39
5 45000 18084.49
6 45000 15070.41
7 45000 12558.67
162,206.63

Net present value = -100,000 + 162,206.63 = 62,206.63

Optimistic:

First cost = 80,000

Annual benefit = 50,000

Life = 9 years

Net present value is calculated as: [First Cost - Present value of annual benefit]

Year Annual Benefit Present value of annual benefit
1 50000 41666.67
2 50000 34722.22
3 50000 28935.19
4 50000 24112.65
5 50000 20093.88
6 50000 16744.90
7 50000 13954.08
8 50000 11628.40
9 50000 9690.33
201,548.33

Net present value = -80,000 + 201,548.33 = 121,548.33

Rahul Sunny answered 9 months ago
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