Question

If I have multiple alternatives, explain and give examples of the criteria used to determine which alternative is chosen when evaluating using, and please use  Net Present Worth, PW-Cost, or PW-Benefit.

Answer 1

While using the present worth (PW) method of comparison the cash flow of each alternative will be reduced to time zero by assuming an interest rate i. The, depending on the type of decision, the best alternative will be selected by comparing the present worth amounts of the alternatives. The signs of various amounts at different points in time in a cash flow is to be decided based on the type of the decision problem.

Cost Dominated Cash Flow: In this, the costs (outflows) will be assigned with positive sign and the profit, revenue, salvage value (all inflows) will be assigned with negative sign. This method is used when the decision is to select the alternative with minimum cost, and the alternative with the least present worth amount will be selected.

PW(i) = P + C1[1/(1 + i)¹] + C2[1/(1 + i)²] + ………………….. + Cj[1/(1 + i)^j] + Cn[1/(1 + i)ⁿ] – S[1/(1 + i)ⁿ]

In the above,

P = Initial investment

Cj = Net cost of operating and maintenance at the end of the j^th year

S = Salvage value at the end of the n^th year

i = Interest rate compounded annually

Revenue Dominated Cash Flow: In this, the profit, revenue, salvage value (all inflows) will be assigned positive sign, and the costs (outflows) will be assigned negative sign. This method is used when the decision is to select the alternative with the maximum profit (benefit), and the alternative with the maximum present worth will be selected.

PW(i) = – P + R1[1/(1 + i)¹] + R2[1/(1 + i)²] + ………………….. + Rj[1/(1 + i)^j] + Rn[1/(1 + i)ⁿ] + S[1/(1 + i)ⁿ]

In the above,

P = Initial investment

Rj = Net revenue at the end of the j^th year

S = Salvage value at the end of the n^th year

i = Interest rate compounded annually