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 6 months ago

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