Project Evaluation and Selection: Methods and Tools

Project evaluation is the process of assessing whether an investment or project is worth pursuing. Businesses use different methods to compare costs, expected returns, and risks before making a final decision.

The goal of project evaluation is to choose the most profitable project using financial tools. The four most common methods are:

1. Payback Period (PBP)
2. Internal Rate of Return (IRR)
3. Net Present Value (NPV)
4. Profitability Index (PI)

Each method analyzes cash flows differently and has advantages and disadvantages. Let’s explore them one by one using a common example.

Example for All Methods

Given Investment Details:

• Initial Investment (ICO): 100,000
• Annual Cash Flows:
  • Year 1: 34,432
  • Year 2: 39,530
  • Year 3: 39,359
  • Year 4: 32,219
• Tested Discount Rates: 15% and 20%

I extend my sincere gratitude and acknowledgment to Dr. Safyan Majid, from the Institute of Business & Management (IB&M), UET Lahore, for his invaluable assistance and insights in shaping this knowledge. His expertise in Financial Management has greatly enriched the content, making it more relevant to contemporary finance practices. This acknowledgment also highlights his continuous contributions to promoting awareness and fostering meaningful discourse on Corporate Social Responsibility (CSR), benefiting both the student and professional community

For detail pl review the post

• https://solbiztech.com/blog/sbt-blog-1/time-value-of-money-definitions-concepts-and-when-to-use-each-technique-15

1. Payback Period (PBP)

Definition

The Payback Period measures how long it takes to recover the initial investment from future cash flows. It focuses on liquidity rather than profitability.

Formula

PBP = Last Full Year + [Remaining Investment / Next Years Cash Flow]

Step-by-Step Calculation

1. Year 1: 34,432(Cumulative:

34,432)

Year 2: 39,530(Cumulative:

73,962)

Year 3: 39,359(Cumulative:

1. 113,321 → Crossed $100,000!)

Payback Period (PBP) Calculation

PBP = a + (b - c) / d

PBP = 2 + (100,000 - 73,962) / 39,359

PBP = 2 + (26,038 / 39,359)

PBP = 2.66 years

Explanation

• a = 2 → Year
• b = 100,000 → Initial Investment
• c = 73,962 → Cumulative inflow at Year 2
• d = 39,359 → Cash flow at Year 3
• The remaining amount ($26,038) is recovered in Year 3.
• The exact Payback Period (PBP) is 2.66 years.

Let's convert 0.66 years into months and days.

Step 1: Convert 0.66 Years to Months

• Since 1 year = 12 months, we multiply:
• 0.66×12=7.92 months
• 0.66×12=7.92 months
• So, 0.66 years is approximately 7 full months and some extra days.

Step 2: Convert 0.92 Months to Days

• Since 1 month = 30 days (approximate), we multiply:
• 0.92×30=27.6 days
• 0.92×30=27.6 days
• So, 0.92 months is approximately 28 days.

Final Answer:

• 0.66 years ≈ 7 months and 28 days
• Total Payback Period = 2 years, 7 months, and 28 days

Acceptance Criteria

• If PBP ≤ required payback period, accept the project.
• If PBP > required payback period, reject the project.

Advantages and Disadvantages

2. Internal Rate of Return (IRR)

Definition

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) = 0. It tells us the exact return (%) a project generates over time.

Formula

ICO = sum [CF/[(1+r)^t]]

Step-by-Step IRR Calculation Using interpolation:

ICO = (CF1 / (1 + IRR)^1) + (CF2 / (1 + IRR)^2) + ... + (CFn / (1 + IRR)^n) Where:

• ICO = Initial Cash Outflow (Investment)
• CF1, CF2, ..., CFn = Cash Flows for each year
• r = Internal Rate of Return
• n = Number of years

100,000 = (34,432 / (1 + r)^1) + (39,530 / (1 + r)^2) + (39,359 / (1 + r)^3) + (32,219 / (1 + r)^4)

Where: Let's Assume the two r as per below

• ( r_1 = 15% ) (lower discount rate)
• ( r_2 = 20% ) (higher discount rate)

Present Value Calculation at 15% and 20% Discount Rates

Where:

• NPV1 = 100,000 - 104,681.01 => 4,168.01 (NPV at 15%)
• NPV2 = 100,000 - 94,434.10 => -5,565.90 (NPV at 20%)
• Both NPV are not equal to *zero

In other words

• Present Value at 15% > ICO > Present Value at 20%
• 104,168.01 > 100,000 > 94,434.10

Finding IRR Using Interpolation

We apply the linear interpolation method, which estimates the exact IRR:

IRR = r1 + [(NPV1 / (NPV1 - NPV2)) × (r2 - r1)]

Where:

• r1 = 15% (lower discount rate)
• r2 = 20% (higher discount rate)
• NPV1 = 4,168.01 (NPV at 15%)
• NPV2 = -5,565.90 (NPV at 20%)

Step-by-Step Calculation:

IRR = 15 + [(4,168.01 / (4,168.01 - (-5,565.90))) × (20 - 15)]

IRR = 15 + [(4,168.01 / (4,168.01 + 5,565.90)) × 5]

IRR = 15 + [(4,168.01 / 9,733.91) × 5]

IRR = 15 + (0.4285 × 5)

IRR = 15 + 2.14

IRR ≈ 17.14%

Advantages and Disadvantages

3. Net Present Value (NPV)

Definition

The Net Present Value (NPV) is the total present value of cash inflows minus the initial investment. It measures the absolute dollar value the project adds.

Formula

NPV = SUM [CF_t / {(1+r)^t}] - ICO

Step-by-Step NPV Calculation

• At 15% Discount Rate

NPV = [29,955.84 + 29,884.68 + 25,898.22 + 18,429.27] - 100,000

NPV = 104,168.01 - 100,000

NPV = 4,168.01

• At 20% Discount Rate

NPV = [28,681.86 + 27,433.82 + 22,788.86 + 15,529.56] - 100,000

NPV = 94,434.10 - 100,000

NPV = -5,565.90

Advantages and Disadvantages

4. Profitability Index (PI)

Definition

The Profitability Index (PI) shows how much value is created per dollar invested.

Formula

PI = SUM [CF_t / {(1+r)^t}] / ICO

Step-by-Step PI Calculation

• At 15% Discount Rate

PI = 104,168.01 / 100,000 = 1.0417

• At 20% Discount Rate

PI = 94,434.10 / 100,000 = 0.9443

Advantages and Disadvantages

Final Thoughts

Author:
Mohsin Yaseen
On behalf of SolBizTech Team
https://www.linkedin.com/in/rmyasin