Engineering Economics - ME2001 Notes

Engineering Economics - ME2001 Course Overview

  • Instructor: Dr. S. S. Sharma
  • Department: Mechanical Engineering
  • Course Credits: 3
  • Course Structure: 3 hours lecture (3 0 0 3)

Estimation Models

Time Value for Money

  • Concept: A rupee today is worth more than a rupee tomorrow.
  • Example:
      - XYZ's grandfather offers a gift of Rs. 100,000 at the end of the fifth year or Rs. 75,000 today.
      - Decision consideration:
        - Rs. 75,000 is more attractive due to certainty and potential investment returns.
        - Rs. 100,000 in the future will have diminished purchasing power due to inflation.

Payback Period

Scope

  • Purpose: Aids investors and managers in making quick economic decisions regarding investments.
  • Advantage: Projects with shorter payback periods promise quicker cash inflows, making it ideal for cash-poor firms.
Pros
  • Simple and cost-effective technique.
  • Directly relates annual cash flows from proposals to the net investment required.
Cons
  • Ignores long-term profitability post-payback.
  • Does not account for the time value of money.

Definition

  • The payback period refers to the time required to recover the cost of an initial investment.

Methods for Estimation

  • Even cash flow
  • Uneven cash flow

Even Cash Flow

Definition

  • Occurs when net annual cash inflow is constant.

Formula

  • Payback Period: extPaybackPeriod=extInitialInvestmentextAnnualCashInflowext{Payback Period} = \frac{ ext{Initial Investment}}{ ext{Annual Cash Inflow}}

Example Calculation

  • Company X:
      - Initial Cost: 10,50010,500
      - Expected Annual Cash Inflow: 2,5002,500 for 7 years.
  • Calculation:
    extPaybackPeriod=10,5002,500=4.2extyearsext{Payback Period} = \frac{10,500}{2,500} = 4.2 ext{ years}

Case Study: XYZ Beverage Company

  • Decision Analysis for Equipment Purchase
      - Initial Equipment Cost: 37,50037,500.
      - Annual Cash Inflows: 75,00075,000.
      - Annual Cash Outflows:
        - Ingredients: 45,00045,000.
        - Salaries: 13,50013,500.
        - Maintenance: 1,5001,500.
  • Calculation for Net Annual Cash Inflow:
    extNetCashInflow=75,000−(45,000+13,500+1,500)=15,000ext{Net Cash Inflow} = 75,000 - (45,000 + 13,500 + 1,500) = 15,000
  • Payback Calculation:
    extPaybackPeriod=37,50015,000=2.5extyearsext{Payback Period} = \frac{37,500}{15,000} = 2.5 ext{ years}
  • Recommendation: Purchase the equipment since 2.5 years is less than the maximum desired payback period of 4 years.

Uneven Cash Flow

Definition

  • Occurs when cash inflows vary by period.

Payback Calculation Method

  • Cumulative cash inflow calculated to determine payback.
  • Formula for specific cash flow periods:
    extPaybackPeriod=t+extUnrecoveredInvestmentatStartofNextPeriodextCashInflowinFollowingPeriodext{Payback Period} = t + \frac{ ext{Unrecovered Investment at Start of Next Period}}{ ext{Cash Inflow in Following Period}}

Example Investment

  • Initial Investment: 200,000200,000
  • Expected Cash Inflows over 6 years:
      - Year 1: 70,00070,000
      - Year 2: 60,00060,000
      - Year 3: 55,00055,000
      - Year 4: 40,00040,000
      - Year 5: 30,00030,000
      - Year 6: 25,00025,000
  • Cumulative Inflows per Year:
      - Year 1: 70,00070,000
      - Year 2: 130,000130,000
      - Year 3: 185,000185,000
      - Year 4: 225,000225,000
      - Year 5: 255,000255,000
      - Year 6: 280,000280,000
  • Calculation:
      - Unrecovered Investment End of Year 3:
    200,000−185,000=15,000200,000 - 185,000 = 15,000
      - Payback Period Calculation:
    extPaybackPeriod=3+15,00040,000=3+0.375=3.375extyearsext{Payback Period} = 3 + \frac{15,000}{40,000} = 3 + 0.375 = 3.375 ext{ years}
  • Recommendation: Management should evaluate the investment based on a maximum desired payback of 3 years.

Rate of Return (ROR)

Definition

  • ROR represents the annual return on investment; it is the reciprocal of simple payback.

Calculation

  • Example for Company X:
      - Initial investment: 10,50010,500
      - Annual Cash Inflow: 2,5002,500 for 7 years.
  • ROR Calculation:
    ext{ROR} = rac{2,500}{10,500} = 0.2380 ext{ or } 23.80 ext{%}

Future Value (F)

Definition

  • Future value is the estimated value of a current asset at a future date based on a rate of growth.
  • Importance: Used by investors to estimate the future worth of an investment.

Future Value Calculations

  • Future Value of a Lump Sum:
    F=Pimes(1+iimesn)F = P imes (1 + i imes n)
  • Future Value of an Annuity:
    F=Pimes(1+i)nF = P imes (1 + i)^n
      Where to define:
      - PP = Present Amount
      - nn = Number of Years
      - FF = Future Value
      - ii = Interest Rate

Present Value Calculation

Definition

  • Present Value is the worth of a future sum of money in today's terms, adjusted for a specified interest rate over time.
  • Example Calculation:
      - Present Value with a future payment of 1,0001,000 in 5 years at a 10% interest rate.
    P=F(1+i)n=1,000(1+0.1)5=621P = \frac{F}{(1 + i)^n} = \frac{1,000}{(1 + 0.1)^5} = 621

Net Present Value (NPV)

Definition

  • NPV is the difference between the present value of cash inflows and cash outflows over a period of time.

Inputs for NPV Calculation

  • NPV calculation influences investment decisions:
      - If NPV > 0: Accept the project.
      - If NPV < 0: Reject the project.
      - If NPV = 0: Accept or Reject based on other considerations.

NPV Calculation Example

  • Project requires an initial investment of 2,0002,000 and cash flows of:
      - Year 1: 100100
      - Year 2: 100100
      - Year 3: 100100
      - Year 3 (One-time): 2,5002,500
      - Discount rate: 10%.