Three public investments alternatives are available: A1, A2 and A3

A.

NPW of proposal A1 = PW of benefits - PW of cost - PW of initial investment

NPW of proposal A1 = 400-100-100 = $200

NPW of proposal A2 = 700-300-200 = $200

NPW of proposal A3 = 500-200-150 = $150

NPW of A1 and A2, are equal at $200. So, both of them can be selected. Though, A1 has same NPW with lower investment. So, A1 can be preferred over A2.

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B.

B/C ratio for proposal A1 = Total benefits / total costs = 400/(100+100)

B/C ratio for proposal A1 = 2

B/C ratio for proposal A2 = 700/(300+200) = 1.4

B/C ratio for proposal A3 = 500/(200+150) = 1.43

proposal A1 will be selected, because it has highest B/C ratio among all the proposals.

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C.

proposal A1 will be selected, because it has profitability index among all the proposals.

Profitability index calculation is the same as that of B/C ratio.

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D.

Incremental B/C ratio will start with proposal with lowest investment and compare with the next higher investment.

So, base proposal is A1 and it is to be compared with A3.

Now,

Incremental B/C ratio (A3 - A1) = (500-400)/((200-100) + (150-100))

Incremental B/C ratio (A3 - A1) = .67

Since value of Incremental B/C ratio (A3 - A1) is less than 1, then A3 is rejected and A1 is selected.

Now, A1 is compared with A2.

Incremental B/C ratio (A2 - A1) = (700-400)/((300-100) + (200-100))

Incremental B/C ratio (A2 - A1) = 1

Since Incremental B/C ratio (A2 - A1) is 1 and not greater than 1, then A1 is selected and A2 is rejected.

So, proposal A1 will be selected.

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E.

Incremental profitability index is the same as that of Incremental B/C ratio. So, proposal A1 will be selected.