Present Worth Analysis

Present Worth Analysis Net Present Worth of initial and future cash flows can be used to select among alternative projects It is important to understand what Net Present Worth means, especially when the cash flows include both revenue and expenses

Present Worth Equivalence says that we can shift any sum to an equivalent sum at some other point in time the equivalent sum at the present time (right now) is called present worth (PW). PW is the comparable equivalent value at the present time of a future sum or set of sums. PW or NPV can be thought of as the difference between a future set of cash inflows and cash outflows shifted to the present. This is typical of any investment. You make a cash outlay expecting future cash payments PW is also called net present value (NPV), although that term is more often used when referring to the total present worth of a series of sums

Present Worth Analysis Present worth analysis is when we compare the net present value of multiple mutually exclusive options. Present worth analysis considers only future incomes and expenditures. Costs incurred in the past are called sunk costs and are irrelevant when comparing future cash flows Financing and investment activities are considered separate activities and then their NPVs combined. The goal is to maximize the PW of investment benefits, minimize the PW of financing costs, and maximize the NPV of a combination of financing and investment activities

Steps taken. Estimate the interest rate that the firm wishes to earn on its investments Determine the service life of the project Ascertain the cash overflows over each service period Find out the cash overflows over each service period Calculate the net cash flows (inflow-outflow)

Decision process For a single investment period PW > 0.select the project Positive PW means the equivalent inflows is greater than the worth of outflows. Hence the project is profitable PW < 0 reject the project A negative PW means that worth of outflows is less than the worth of inflows. Hence the project will incur losses PW = 0 indifferent to investment

Decision process For mutually exclusive alternatives, PW can be calculated by 2 prominent methods P = initial investment R(n) = net revenue at end of nth year C(n) = net cost of operation and maintenance at the end of n year i = interest compounded annually S = salvage value at end of nth year Revenue based PW PW(i) = - P + R(P/A, i, n) + S(P/F, i, n) Cost based PW PW(i) = P + C(P/A, i, n) - S(P/F, i, n)

Purpose To compare mutually exclusive alternatives based on present worth, under the assumption that each alternative is expected to provide the same service. Generally, the cash flows to be considered are: first cost, annual costs, non-recurring costs, revenues, and salvage value. The cash flow series can be finite or infinite. Terminology Salvage Value the amount of money you can expect to receive by selling an asset when you have used up the full life of the asset. MARR (Minimum Attractive Rate of Return) I expect or need a minimum return in order to be willing to invest my money.

Example Problem - 1 Project A costs Rs10,000 and will last for 10 years. Annual, end of the year revenues will be Rs3,000, and expenses will be Rs1,000. There is no salvage value. Project B costs Rs10,000 and will also last for 10 years. Annual revenues will be Rs3,000 with annual expenses of Rs1,500. Salvage value is Rs5,000. Conduct an economic analysis to select the preferred project using a MARR of 10% per year, compounded annually

Example Problem 1 (contd) Project A costs Rs10,000 and will last for 10 years. Annual, end of the year revenues will be Rs3,000, and expenses will be Rs1,000. There is no salvage value. Given Lifetime = 10 YRS MARR = 10%/YR, compounded annually 1 st Cost = Rs10,000/- Annual Revenues = Rs3,000/YR Annual Costs = Rs 1,000/YR Salvage Value= Re 0 Net Annual = Annual Revenues Annual Costs = Rs3000/YR Rs1000/YR = Rs2000/YR NPW A = A (P/A, i, n) 1 ST COST = Rs2,000(P A,10%,10) Rs10,000/- = Rs 2,000(6.1446) Rs 10,000 = Rs 2,289/-

Example Problem 1 (contd) Project B costs Rs10,000 and will also last for 10 years. Annual revenues will be Rs3,000 with annual expenses of Rs 1,500. Salvage value is Rs 5,000. Given Lifetime = 10 YRS MARR = 10%/YR, compounded annually 1 st Cost = Rs 10,000/- Annual Revenues = Rs 3,000/YR Annual costs = Rs 1,500/YR Salvage Value = Rs 5,000/- Net Annual = Annual Revenues Annual Costs = Rs 3,000/YR Rs 1,500/YR = Rs 1,500/YR NPW B = A(P A, i, n) + Salvage (P F, i, n) 1 ST Cost = Rs 1,500(P A,10%,10) + Rs 5,000(P F,10%,10) Rs 10,000 = Rs 1,500(6.1446) + Rs 5,000(0.3855) Rs 10,000 = Rs 1,144 PREFER A

What does this mean? NPW A = Rs 2,289/- NPW B = Rs 1,144/- We prefer project A over project B. Does NOT mean a Rs 2,289/- profit! Concept: We favor Project A by Rs2,289 over taking Rs 10,000 and putting it in an account earning 10%. In other words With expenses and revenues known, select the largest NPW > 0 Select Project A

Further You would be willing to pay as much as Rs 10,000 + Rs2,289 = Rs12,289 for the project. At that price and at i = 10%, you are indifferent between: Investing Rs12,289 for 10 years at i = 10%. Obtaining Rs2,000 at the end of each of the next 10 years (and reinvesting each receipt at 10%) Illustrating F 10 = (10,000 + 2,289) (F/P, 10%, 10) = (10,000 + 2,289) (2.594) = Rs 31,875/- F 10 = 2000 (F/A, 10%, 10) = 2000 (15.937) = Rs 31,875/-

Thus The project only costs Rs 10 000, but at i = 10% it is equivalent to investing Rs 10 000 + Rs 2 289 for 10 years. Since PW > 0, you are actually earning more than 10% on investment Present Worth Analysis When applied correctly, NPW can be used to select among various alternative projects. The larger the NPW the better. Requires establishing MARR. MARR is used as the (i) in the equations.

Future Worth Analysis It is the comparison of future worth of various alternatives with maximum net revenue or minimum net cost Revenue dominated FW(i) = -P(1+i)ⁿ + R1(1+i)ⁿ ¹ +. + Rn + S FW(i) = -P(F/P, i, n) + R(F/A, i, n) + S Cost dominated FW(i) = P(1+i)ⁿ + C1(1+i)ⁿ ¹ +.+ Cn + S FW(i) = -P(F/P, i, n) + C(F/A, i, n) - S

Future worth analysis..decision Process For project evaluation.. If FW > 0 => project is accepted If FW < 0 => project is rejected If FW = 0 => one will be indifferent to the investment Steps for computing FW of Cash flow Determine the interest rate Estimate the service life of the project Calculate the cash inflow for each period over the service life Ascertain the cash outflow over each service period Find out the net cash flow (inflow-outflow)

Equivalent Annual Worth All receipts and disbursements are converted into an equivalent uniform annual amount. It is important method of comparing worthiness of various engineering alternatives because this method also takes into account annual profits and losses. Calculating Equivalent Annual Worth (EAW) 1. Compute the net present worth 2. Multiply present worth by capital recovery factor EAW = PW(i) X (A/P, i, n) EAW = PW(i) i(1+i)ⁿ (1+i)ⁿ - 1

Steps for computing EAW.. Estimate the cash flows (inflow and outflow) over each service period Calculate service life of the project Determine the internet rate Compare with before tax cash flows Do not include intangible considerations for EAW comparisons Decision process. EAW > 0 => accept investment proposal EAW < 0 => reject investment process EAW = 0 => indifferent to the investment