Summary
# Introduction to investment and project analysis
This section introduces the fundamental concept of investment and project analysis, defining what an investment entails and the core logic behind financial investment decisions, highlighting its importance for companies.
### 1.1 The concept of investing and project analysis
An investment or the initiation of a new project involves an expenditure or effort made today with the expectation of achieving a profitable return in the future. This return can be financial, such as increased profits, or non-financial, like acquiring a degree.
Financial investment analysis applies this same logic to investors who allocate funds to purchase assets like buildings, machinery, shares, or bonds. The primary objective is for these assets to generate future profits or dividends.
The decision of whether or not to invest is one of the most critical choices a company makes. Investment projects are often considered as separate proposals for decision-making.
### 1.2 The investment decision process
The investment decision typically involves two main steps:
1. **Cost-effectiveness of the investment project:** This assesses the profitability of the investment, often measured by the return on investment (ROI). The analysis is based on future cash inflows and outflows.
2. **Acceptable projects:** Once projects are deemed financially viable, they are ranked according to certain strategic priorities. This includes considering whether the project aligns with the company's overall master plan.
While companies generally invest regularly, there is always a minimum required return that projects must meet.
### 1.3 Basic principles for investment analysis
Effective investment analysis relies on several fundamental principles:
* **Take the relevant cash flows:** Only consider cash flows that are directly impacted by the project. This means retaining only the extra changes in cash (increases or decreases) compared to the company's current cash flows. These are known as marginal cash flows.
> **Tip:** For example, if a project requires hiring an additional half-time employee, only the cash flow associated with that half-time salary should be considered as an incremental cash flow.
* **Work on a cash basis:** All cash outflows (e.g., investment costs, wages) and all cash inflows (e.g., sales revenue) must be accounted for. Non-cash expenses like depreciation should not be directly included in this analysis for objectivity.
> **Example:** When purchasing new machinery, the acquisition cost is a cash outflow. Depreciation, while an accounting concept, is not a direct cash outflow and should be handled separately or considered through its tax implications, not as a direct expenditure in the initial cash flow analysis.
* **Determine the relevant period:** Every investment has a specific useful life. For instance, machinery might have a 5-year life expectancy, while an interior shop renovation might have a 2-year lifespan. It is crucial to identify all relevant cash inflows and outflows that occur within this determined period and compare them to calculate the ROI.
### 1.4 Methods for investment analysis
Three common methods are used to analyze the profitability of an investment project:
1. **The net present value (NPV) method:** This is considered the most financially sound and widely used method in practice.
2. **The payback method (PB method or period):** This method focuses on how quickly the initial investment is recouped.
3. **The internal rate of return (IRR) method:** This method calculates the discount rate at which the NPV of a project becomes zero.
While these methods are essential, non-financial factors also play a role in investment decisions, including:
* Conformity with the strategic plan.
* Degree of urgency or necessity (e.g., replacing essential equipment).
* Availability of financial resources.
* Complementarity with other existing or planned projects.
* Integration within the company's Corporate Social Responsibility (CSR) initiatives.
* The degree of risk associated with the project.
### 1.5 The time value of money and present value
A core concept in investment analysis is the **time value of money**, which posits that one euro today is worth more than one euro received in the future. This is due to factors like potential earning capacity, inflation, and risk.
**Present value (PV)** is the current worth of a future sum of money, discounted at a specific interest or discount rate.
> **Example:** If a sale in three years is expected to generate 10,000 euros and the discount rate is 6%, the present value of that future income will be less than 10,000 euros. This is because receiving the money later means foregoing the opportunity to earn interest on it during the intervening years.
The present value represents the maximum amount a company would be willing to pay for a future cash inflow after accounting for the time value of money, interest, and inflation at a specified rate.
The formula for calculating the present value of a single future cash flow is:
$$PV = \frac{C}{(1 + i)^n}$$
Where:
* $C$ is the sum of money to be received in the future (e.g., future cash inflow).
* $i$ is the annual interest or discount rate.
* $n$ is the duration in years until the cash flow is received.
### 1.6 The net present value (NPV)
The net present value (NPV) is the discounted value of all cash inflows and outflows associated with an investment project. It takes into account the time value of money by discounting all future cash flows back to their present value.
The general formula for NPV is:
$$NPV = \sum_{n=0}^{N} \frac{C_n}{(1 + i)^n}$$
Where:
* $C_n$ is the net cash flow during period $n$.
* $i$ is the discount rate.
* $N$ is the total number of periods.
* The summation starts from $n=0$ to account for the initial investment which occurs at time zero.
The discount rate ($i$) is a crucial component and typically represents:
* A reference rate for investments of similar risk (e.g., government bond yields).
* The average expected inflation for the project's duration.
* The company's Weighted Average Cost of Capital (WACC), which includes a risk premium.
The discount rate significantly impacts the final NPV result.
> **Example:** Consider company Basril deciding whether to buy machinery for 150,000 euros. This machinery is expected to generate varying inflows over five years.
>
> | Year | Outflow (Cash -) | Inflow (Cash +) | PV of Inflow (at 2% discount rate) |
> |------|-----------------|-----------------|------------------------------------|
> | 0 | 150,000 | | |
> | 1 | | 37,450 | 36,715.69 |
> | 2 | | 34,678 | 33,331.41 |
> | 3 | | 42,500 | 40,048.70 |
> | 4 | | 38,677 | 35,731.57 |
> | 5 | | 27,450 | 24,862.31 |
> | **Total** | **150,000** | **180,755** | **170,689.68** |
>
> The sum of the present values of the inflows (170,689.68 euros) is greater than the present value of the outflows (150,000 euros).
>
> The Net Present Value (NPV) is calculated as:
> $NPV = 170,689.68 \text{ EUR} - 150,000 \text{ EUR} = 20,689.68 \text{ EUR}$
>
> Since the NPV is positive (20,689.68 euros), this indicates that the project is expected to be profitable after considering the time value of money and a 2% discount rate.
### 1.7 NPV and ROI
Return on Investment (ROI) provides a percentage measure of the profitability relative to the initial investment. It offers a more relative picture of the return compared to the absolute NPV amount.
The ROI can be calculated as:
$$ROI = \frac{NPV}{\text{Initial Investment}} \times 100\%$$
An annualized ROI can be derived by dividing the total ROI by the number of years of the project's life.
> **Example:** Comparing two projects:
> * **Project A:** Investment = 150,000 dollars, NPV = 20,689.68 dollars, Period = 5 years.
> * Total ROI = $(20,689.68 / 150,000) \times 100\% = 13.79\%$
> * Annualized ROI = $13.79\% / 5 = 2.76\%$
> * **Project B:** Investment = 290,000 dollars, NPV = 37,845 dollars, Period = 5 years.
> * Total ROI = $(37,845 / 290,000) \times 100\% = 13.05\%$
> * Annualized ROI = $13.05\% / 5 = 2.61\%$
>
> In this scenario, Project A has a higher ROI (2.76% vs 2.61%). However, Project B generates a significantly larger absolute NPV (37,845 dollars vs 20,689.68 dollars). The choice between focusing on ROI or NPV can depend on the company's strategic objectives and available capital.
### 1.8 Minimum return requirement
Every company aims for a minimum required rate of return on its investments. This benchmark is influenced by:
* The profitability of equity (ROE) for the company.
* The Weighted Average Cost of Capital (WACC).
* Inflation and necessary risk compensation.
A project is generally considered acceptable only if its expected return meets or exceeds this minimum requirement.
### 1.9 Advantages and disadvantages of the NPV method
**Advantages:**
* **Accurate timing:** The NPV method correctly accounts for the timing of cash inflows and outflows, recognizing the time value of money.
* **Objectivity in cost estimation:** Estimating project costs is often more straightforward and objective (e.g., using quotes or tenders).
**Disadvantages:**
* **Difficulty in estimating income:** The size of future income streams can be much harder to estimate accurately.
* **Sensitivity to discount rate:** The discount rate chosen can have a major impact on the final NPV, and selecting the appropriate rate can be challenging.
### 1.10 Application: Invest Co (Exercise Example)
Invest Company is considering launching a new product, a multifunctional storage box.
**Project Details:**
* **Annual Sales:** 15,000 boxes.
* **Selling Price:** 19.00 dollars per box.
* **Production Cost:** 11.50 dollars per box (including raw materials and wages).
* **New Machinery Cost:** 30,000 dollars.
* **Machinery Depreciation:** Linear over 5 years.
* **Financing:** Investment credit with a 5-year term, fixed yearly capital installments, interest rate ($i$) = 5%.
* **New Worker Cost:** 20,000 dollars per year (0.5 FTE).
* **Discount Rate:** 5%.
* **Overhead:** 3,450 dollars per year.
* **Management's Minimum Return Requirement:** 7%.
**Analysis Required:**
1. Calculate the present value (PV) of all relevant cash flows for the next five years.
2. Calculate the profitability and the NPV of this project.
3. Determine if the project should proceed based on the minimum return requirement.
---
# Principles and methods of investment analysis
This topic outlines the fundamental principles for evaluating investment profitability and introduces three key methods: Net Present Value (NPV), Payback Period, and Internal Rate of Return (IRR).
### 2.1 Basic principles for investment analysis
When analyzing investment projects, several core principles guide the assessment to ensure accurate profitability estimations.
#### 2.1.1 Focus on relevant cash flows
The primary principle is to consider only those cash flows that are directly impacted by the investment decision. This means retaining only the incremental changes in cash, whether an increase or decrease, that occur as a result of undertaking the project.
> **Tip:** Think of these as the "extra" cash flows that wouldn't exist if the project were not pursued.
**Example:** If a project requires hiring half a full-time equivalent (FTE) employee, only the cash outflow for that additional labor should be considered, not the entire salary of a full-time position.
#### 2.1.2 Work on a cash basis
Investment analysis should be conducted strictly on a cash basis. This involves accounting for all actual cash inflows (e.g., sales revenue) and cash outflows (e.g., purchase of machinery, wages paid). Non-cash expenses, such as depreciation, should be excluded from this direct cash flow analysis to ensure a more objective assessment of the project's financial performance.
#### 2.1.3 Determine the relevant project period
Every investment has a finite useful life. It is crucial to identify and define this relevant period for the analysis. This period represents the duration over which the investment is expected to generate cash flows.
**Example:** A new machine might have a life expectancy of five years, while an interior shop renovation might have a relevant period of two years. An inventory of all relevant cash inflows and outflows within this specified period is then compiled for comparison.
### 2.2 Methods for profitability analysis
Three primary methods are commonly used to assess the profitability of an investment project:
* Net Present Value (NPV)
* Payback Period (PB Method)
* Internal Rate of Return (IRR)
#### 2.2.1 The method of the net present value (NPV)
The Net Present Value (NPV) method is widely considered the most financially sound and frequently used technique for investment analysis. It accounts for the time value of money, acknowledging that a euro today is worth more than a euro in the future.
##### 2.2.1.1 Time value of money
The core concept is that money available now can be invested and earn a return, making it more valuable than the same amount received in the future.
##### 2.2.1.2 Present value (PV)
The Present Value (PV) is the current worth of a future sum of money, discounted at a specific interest or discount rate. It represents the maximum amount a company would be willing to pay today for a future cash inflow, considering the time value of money.
The formula for calculating the present value of a single future cash flow is:
$$ PV = \frac{C}{(1 + i)^n} $$
Where:
* $PV$ is the Present Value.
* $C$ is the future cash flow amount.
* $i$ is the annual interest or discount rate.
* $n$ is the number of years until the cash flow is received.
**Example:** A return of 10,000 euros in three years, with a 6% discount rate, has a present value of:
$$ PV = \frac{10,000}{(1 + 0.06)^3} \approx 8,396.2 \text{ euros} $$
##### 2.2.1.3 Calculating the Net Present Value (NPV)
The NPV is the sum of the present values of all cash outflows and inflows associated with an investment project.
The general formula for NPV is:
$$ NPV = \sum_{t=0}^{N} \frac{CF_t}{(1+i)^t} $$
Where:
* $CF_t$ is the net cash flow at time $t$.
* $i$ is the discount rate.
* $t$ is the time period.
* $N$ is the total number of periods.
For projects with initial outflows and subsequent inflows, it can also be represented as:
$$ NPV = \left( \sum_{t=1}^{N} \frac{\text{Cash Inflows}_t}{(1 + i)^t} \right) - \left( \sum_{t=1}^{N} \frac{\text{Cash Outflows}_t}{(1 + i)^t} \right) - \text{Initial Investment} $$
**Choosing the discount rate:** The discount rate (i) should reflect the investment's opportunity cost. This can be based on a reference rate (e.g., government bond yields), expected inflation over the project's life, and a risk premium. The Weighted Average Cost of Capital (WACC) is often used as it incorporates the company's cost of financing and risk.
> **Tip:** The discount rate has a significant impact on the NPV. A higher discount rate will result in a lower NPV, and vice versa.
**Example (Company Basril):**
Company Basril is considering buying machinery for 150,000 euros today. The expected cash inflows over the next five years are: Year 1: 37,450 euros, Year 2: 34,678 euros, Year 3: 42,500 euros, Year 4: 38,677 euros, Year 5: 27,450 euros. The discount rate is 2%.
First, calculate the PV of each inflow:
* Year 1 PV: $37,450 / (1.02)^1 \approx 36,715.69$ euros
* Year 2 PV: $34,678 / (1.02)^2 \approx 33,331.41$ euros
* Year 3 PV: $42,500 / (1.02)^3 \approx 40,048.70$ euros
* Year 4 PV: $38,677 / (1.02)^4 \approx 35,731.57$ euros
* Year 5 PV: $27,450 / (1.02)^5 \approx 24,862.31$ euros
Sum of PV of inflows $\approx 170,689.68$ euros.
NPV = Sum of PV of inflows - Initial Investment
NPV = $170,689.68 - 150,000 = 20,689.68$ euros.
Since the NPV is positive, this indicates the project is expected to generate more value than its cost, considering the time value of money.
##### 2.2.1.4 NPV and Return on Investment (ROI)
While NPV provides an absolute measure of profitability, ROI offers a relative measure.
$$ ROI = \frac{NPV}{\text{PV of Investment}} $$
For Company Basril's machinery project:
ROI = $20,689.68 \text{ euros} / 150,000 \text{ euros} \approx 13.79\%$ over five years.
The annual ROI is approximately $13.79\% / 5 = 2.76\%$ per year.
If compared to investing 150,000 euros in a government bond with a net annual return of 2.81%, the government bond would be preferred as its return is slightly higher than the project's annual ROI.
##### 2.2.1.5 Minimum return requirement
Companies typically set a minimum required ROI (a hurdle rate) for investments. This minimum is influenced by factors like the profitability of equity (ROE), WACC, inflation, and risk compensation.
##### 2.2.1.6 Advantages and disadvantages of the NPV method
**Advantages:**
* Considers the timing of cash flows.
* Easy and objective estimation of costs.
**Disadvantages:**
* The estimation of future income can be challenging.
* The choice of discount rate significantly impacts the result.
#### 2.2.2 The payback method (PB method or period)
The Payback Period method determines the time it takes for an investment's cumulative cash inflows to equal the initial investment cost. It's a measure of liquidity and risk, as shorter payback periods are generally preferred.
**Example:** If an investment costs 10,000 euros and generates annual cash inflows of 2,000 euros, the payback period is 5 years ($10,000 / 2,000$).
> **Tip:** The payback method does not consider cash flows beyond the payback period or the time value of money.
#### 2.2.3 The method of the "internal rate of return" (IRR)
The Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of an investment project equals zero. In essence, it's the effective rate of return that the investment is expected to yield.
$$ \sum_{t=0}^{N} \frac{CF_t}{(1+IRR)^t} = 0 $$
A project is generally considered acceptable if its IRR is greater than the company's required rate of return (hurdle rate).
> **Tip:** Calculating IRR often requires iterative methods or financial calculators/software, as there is no direct algebraic solution for complex cash flow streams.
### 2.3 Application: Invest Co
Invest Company is considering launching a new product: a multifunctional storage box.
**Project Details:**
* Annual sales: 15,000 boxes
* Selling price: 19.00 euros per box
* Production cost per box: 11.50 euros
* New machinery cost: 30,000 euros, depreciated linearly over 5 years.
* Machinery financed by a 5-year investment credit at 5% annual installments.
* New worker cost (0.5 FTE): 20,000 euros per year.
* Discount rate: 5%
* Overhead for the project: 3,450 euros per year.
* Management's minimum required return: 7%
**Exercise:**
1. Calculate the PV of all relevant cash flows for the next five years.
2. Calculate the profitability and the NPV of this project for the next five years.
3. Will Invest Company proceed with this project, given the 7% minimum return requirement?
**Analysis Steps (Illustrative):**
1. **Calculate Annual Revenue:** $15,000 \text{ boxes} \times 19.00 \text{ euros/box} = 285,000$ euros.
2. **Calculate Annual Variable Costs:** $15,000 \text{ boxes} \times 11.50 \text{ euros/box} = 172,500$ euros.
3. **Calculate Annual Depreciation:** $30,000 \text{ euros} / 5 \text{ years} = 6,000$ euros.
4. **Calculate Annual Operating Cash Flow (before financing):**
Revenue - Variable Costs - Worker Cost - Overhead - Depreciation = Cash Flow.
$285,000 - 172,500 - 20,000 - 3,450 - 6,000 = 83,050$ euros per year.
5. **Consider Financing Costs:** The cost of financing the machinery needs to be accounted for separately, often by considering the actual cash outflows for loan repayments.
6. **Calculate PV of Cash Flows:** Discount each year's net cash flow (including initial investment and any financing cash flows) back to the present using the 5% discount rate.
7. **Calculate NPV:** Sum of the PV of all cash flows.
8. **Evaluate against Minimum Return:** Compare the calculated NPV and/or IRR to the 7% hurdle rate. If NPV is positive and IRR exceeds 7%, the project is likely acceptable.
---
# Time value of money and net present value calculation
This section explains the fundamental concept of the time value of money and its application in calculating the net present value of investment projects.
### 3.1 The time value of money
The core principle of the time value of money (TVM) is that money available today is worth more than the same amount of money in the future. This is primarily due to the potential earning capacity of money, where funds received today can be invested and generate returns, as well as factors like inflation which erodes purchasing power over time.
#### 3.1.1 Present value
The present value (PV) is the current worth of a future sum of money, discounted at a specific rate. It represents the maximum amount a company would be willing to pay today for a future cash inflow.
The formula for calculating the present value of a single future cash flow is:
$$ PV = \frac{C}{(1 + i)^n} $$
Where:
* $C$ is the future cash flow amount.
* $i$ is the annual discount rate (expressed as a decimal).
* $n$ is the number of years until the cash flow is received.
**Example:**
If an investment is expected to generate a return of 10,000 dollars in three years, and the discount rate is 6 percent, the present value is calculated as:
$PV = \frac{10,000}{(1 + 0.06)^3} = 8,396.20 \text{ dollars}$
This means that 10,000 dollars received in three years is equivalent to 8,396.20 dollars today, given a 6 percent discount rate.
### 3.2 Net present value (NPV)
The net present value (NPV) is a key metric for evaluating investment projects. It represents the discounted value of all cash flows (inflows and outflows) associated with an investment project over its lifetime.
The NPV is calculated by summing the present values of all expected cash inflows and subtracting the present values of all expected cash outflows.
The general formula for NPV is:
$$ NPV = \sum_{t=0}^{n} \frac{C_t}{(1 + i)^t} $$
Where:
* $C_t$ is the net cash flow during period $t$.
* $i$ is the discount rate.
* $n$ is the total number of periods.
* For $t=0$, $C_0$ is the initial investment (a negative cash flow).
Alternatively, it can be expressed as:
$$ NPV = (\text{Sum of PV of cash inflows}) - (\text{Sum of PV of cash outflows}) $$
#### 3.2.1 Discount rate considerations
The choice of the discount rate is critical as it significantly impacts the NPV. Common considerations for the discount rate include:
* **Reference rate:** This could be the rate of return on a risk-free investment, such as government bonds.
* **Inflation:** Expected inflation rates for the project's duration should be incorporated.
* **WACC (Weighted Average Cost of Capital):** This represents the average rate of return a company expects to pay to its security holders to finance its assets. It often includes a risk premium.
**Example:**
Consider a machinery purchase of 150,000 dollars, with expected cash inflows over five years. The total undiscounted inflows are 180,755 dollars. If the discount rate is 2 percent:
| Year | Outflow (cash -) | Inflow (cash +) | PV of Inflow |
| :--- | :--------------- | :-------------- | :----------- |
| 0 | 150,000 | | |
| 1 | | 37,450 | 36,715.69 |
| 2 | | 34,678 | 33,331.41 |
| 3 | | 42,500 | 40,048.70 |
| 4 | | 38,677 | 35,731.57 |
| 5 | | 27,450 | 24,862.31 |
| **Total** | **150,000** | **180,755** | **170,689.68** |
The sum of the present values of the inflows is 170,689.68 dollars. The present value of the outflow (initial investment) is 150,000 dollars.
$NPV = 170,689.68 \text{ dollars} - 150,000 \text{ dollars} = 20,689.68 \text{ dollars}$
A positive NPV indicates that the project is expected to generate more value than its cost, considering the time value of money.
#### 3.2.2 NPV and Return on Investment (ROI)
While NPV provides an absolute monetary value of expected profit, the Return on Investment (ROI) expresses this profitability as a percentage relative to the initial investment.
$ROI = \frac{NPV}{\text{PV of Investment}} \times 100\%$
In the previous example:
$ROI = \frac{20,689.68 \text{ dollars}}{150,000 \text{ dollars}} \times 100\% = 13.79\%$
The ROI per year would be:
$ROI/\text{yr} = \frac{13.79\%}{5 \text{ years}} = 2.76\%$
> **Tip:** While NPV is generally considered the most financially sound method for investment appraisal, companies may still use ROI for comparing projects of different scales or when a percentage return is more intuitive for management. However, a project with a higher NPV might be preferred even if its ROI is slightly lower, especially if capital is not a constraint.
#### 3.2.3 Minimum required return
Companies establish a minimum required return, often based on factors like the profitability of equity, WACC, inflation, and the required risk compensation. A project should only be considered if its NPV is positive and its expected return meets or exceeds this minimum threshold.
> **Tip:** The discount rate used in NPV calculations should reflect the riskiness of the project. Higher-risk projects typically require a higher discount rate, which will lower their NPV.
#### 3.2.4 Advantages and disadvantages of NPV
**Advantages:**
* Accurately accounts for the timing of cash flows.
* Provides a clear, absolute measure of expected profitability.
* Considered the theoretically superior method for investment appraisal.
**Disadvantages:**
* The estimation of future income can be challenging and subjective.
* The choice of the discount rate can significantly influence the NPV outcome.
* Does not inherently consider factors beyond financial returns, such as strategic alignment or CSR initiatives, unless implicitly incorporated into the discount rate or cash flow estimates.
### 3.3 Application example: Invest Co
Invest Company is considering launching a new product, a multifunctional storage box.
**Project Details:**
* Annual sales: 15,000 boxes
* Selling price: 19.00 dollars per box
* Production cost: 11.50 dollars per box
* New machinery cost: 30,000 dollars (to be depreciated linearly over 5 years)
* Machinery financed by an investment credit: 5-year term, fixed yearly capital installments, interest rate $i = 5\%$.
* New worker cost (0.5 FTE): 20,000 dollars per year.
* Annual overhead: 3,450 dollars per year.
* Discount rate: 5 percent.
* Management requires a minimum return of 7 percent.
**1. Calculate the PV of all relevant cash flows for the next five years.**
This involves identifying all cash inflows and outflows for each of the five years, calculating their present values using the 5% discount rate, and then summing them up. This would require a detailed year-by-year breakdown of revenue, production costs, depreciation (though depreciation itself is non-cash, it impacts taxes which are cash flows, but for simplicity in this overview, we will focus on direct cash impacts as presented in the source), labor costs, overhead, machinery financing payments (principal and interest), and considering the initial machinery investment.
**2. Calculate the profitability and the NPV of this project for the next five years.**
After calculating the PV of all cash flows, the NPV would be determined by summing these PVs. Profitability can be expressed through the NPV itself and potentially an ROI calculation if the PV of the initial investment is clearly defined.
**3. Will you go on with this project?**
This decision would be made by comparing the project's NPV with the management's required minimum return of 7 percent. If the project's NPV is positive and its implied rate of return (which can be inferred from the NPV calculation using the 7% hurdle rate) meets or exceeds 7 percent, the project would be recommended.
---
# Return on Investment (ROI) and comparative analysis
This topic explores the Return on Investment (ROI) as a key profitability metric, contrasting it with Net Present Value (NPV) and examining how it informs investment decisions, including the concept of a minimum required ROI.
### 4.1 The concept of investment and profitability analysis
An investment involves an expenditure or effort today with the expectation of future returns. Financial investment analysis focuses on whether assets purchased by investors will generate profits or dividends. A crucial decision for any company is whether to invest in a new project. This decision-making process typically involves two steps:
1. **Assessing Cost-Effectiveness:** Determining the profitability of an investment project.
2. **Ranking Acceptable Projects:** Prioritizing projects based on strategic fit and other factors.
While companies regularly invest, a minimum required rate of return is essential.
### 4.2 Basic principles for investment analysis
Estimating future cash inflows and outflows is fundamental to investment analysis. Key principles include:
* **Consider Relevant Cash Flows:** Focus on the incremental cash flows, which are the changes in cash flows that occur specifically because of the project. This excludes cash flows that would occur regardless of the project.
> **Tip:** Only retain the cash flows that are directly impacted by the investment decision.
* **Work on a Cash Basis:** Include all actual cash outflows (e.g., investment costs, wages) and cash inflows (e.g., sales revenue). Depreciation is not a cash outflow and should be excluded for a more objective analysis.
* **Determine the Relevant Period:** Identify the useful life of the investment (e.g., the lifespan of machinery or a shop interior). All relevant cash inflows and outflows within this period must be inventoried and compared.
### 4.3 Methods for investment analysis
Three primary methods are used to analyze the profitability of a project:
* The Net Present Value (NPV) method.
* The Payback (PB) method.
* The Internal Rate of Return (IRR) method.
The NPV method is considered the most financially sound and widely used in practice. However, non-financial factors also play a significant role in investment decisions, including alignment with strategic plans, urgency, available financial resources, complementarity with other projects, corporate social responsibility integration, and the degree of risk involved.
#### 4.3.1 Time value of money and present value
The concept of the time value of money is critical: one euro today is worth more than one euro in the future due to its earning potential.
* **Present Value (PV):** The current value of a future sum of money, discounted at a specific interest or discount rate.
> **Example:** A return of 10,000 euros expected in three years, with a 6% annual interest rate, is worth less than 10,000 euros today. The PV accounts for the opportunity cost of not having the money available now.
The formula for calculating the present value of a single future cash flow is:
$$PV = \frac{C}{(1 + i)^n}$$
Where:
* $C$ = The future sum of money.
* $i$ = The annual interest or discount rate.
* $n$ = The duration in years.
#### 4.3.2 The net present value (NPV)
The Net Present Value (NPV) is the discounted value of all cash outflows and inflows associated with an investment project over its life.
The general formula for NPV is:
$$NPV = \sum_{t=0}^{n} \frac{Cash \, inflow_t}{(1 + i)^t} - \sum_{t=0}^{n} \frac{Cash \, outflow_t}{(1 + i)^t}$$
Where:
* $t$ = The time period.
* $n$ = The total number of periods.
* $i$ = The discount rate.
The discount rate typically reflects a reference rate (e.g., government bond yield), expected inflation, and potentially a risk premium, often represented by the Weighted Average Cost of Capital (WACC). The choice of discount rate significantly impacts the final NPV.
> **Example:** Company Basril is considering purchasing machinery for 150,000 euros. The machinery is expected to generate the following cash inflows over five years: Year 1: 37,450 euros; Year 2: 34,678 euros; Year 3: 42,500 euros; Year 4: 38,677 euros; Year 5: 27,450 euros. The discount rate is 2%.
>
> Calculating the present value of each cash inflow and summing them gives a total PV of inflows of 170,689.68 euros.
>
> $$NPV = PV \, of \, Inflows - Initial \, Investment$$
> $$NPV = 170,689.68 \, euros - 150,000 \, euros = 20,689.68 \, euros$$
>
> A positive NPV indicates that the project is expected to generate more value than its cost, considering the time value of money.
#### 4.3.3 Return on Investment (ROI)
Return on Investment (ROI) is a measure of profitability that expresses the return as a percentage of the initial investment. It provides a more direct comparison of returns relative to the capital employed.
A simplified calculation for ROI, often expressed annually for comparison, can be derived from NPV:
$$ROI = \frac{NPV}{PV \, of \, Investment} \times 100\%$$
Or, for annual ROI:
$$ROI_{annual} = \frac{ROI}{n} \times 100\%$$
Where:
* $n$ = The number of years of the investment.
> **Example (Company Basril continued):**
>
> * **Project 1 (Machinery):**
> $ROI = \frac{20,689.68 \, euros}{150,000 \, euros} \times 100\% = 13.79\%$
> $ROI_{annual} = \frac{13.79\%}{5 \, years} = 2.76\%$ per year.
>
> If Company Basril has a second option to invest 150,000 euros in a government bond with a net annual return of 2.81%, the bond would be preferred because its annual ROI is higher.
#### 4.3.4 Comparative analysis using NPV and ROI
NPV and ROI are often used together to evaluate and rank investment projects.
* **NPV:** Provides the absolute increase in wealth expected from a project.
* **ROI:** Provides the percentage return relative to the investment, allowing for easier comparison between projects of different scales.
> **Example:**
> * **Project A:** Investment = 150,000 dollars, NPV = 20,689 dollars, Life = 5 years. Annual ROI = 2.76%.
> * **Project B:** Investment = 290,000 dollars, NPV = 37,845 dollars, Life = 5 years. Annual ROI = 2.61%.
>
> In this scenario, Project A has a higher annual ROI (2.76% vs. 2.61%), suggesting it is more efficient in generating returns relative to its initial cost. However, Project B generates a significantly higher absolute NPV (37,845 dollars vs. 20,689 dollars), indicating it will add more absolute value to the company. The choice between them might depend on the company's capital availability and strategic goals.
### 4.4 Minimum required return
Every company establishes a minimum required rate of return for its investments. This threshold ensures that projects not only generate a profit but also meet a certain standard of profitability.
The minimum required ROI is influenced by:
* **Profitability of Equity (ROE):** The return expected by shareholders.
* **Weighted Average Cost of Capital (WACC):** The average rate of return a company expects to pay to its security holders to finance its assets.
* **Inflation and Risk Compensation:** The required return must also compensate for the erosion of purchasing power due to inflation and the inherent risks of the investment.
If a project's calculated ROI or NPV does not meet this minimum requirement, it would typically be rejected.
### 4.5 Advantages and disadvantages of NPV
**Advantages:**
* Accurately accounts for the timing of cash inflows and outflows through discounting.
* Relatively straightforward to estimate costs.
**Disadvantages:**
* Estimating the size of future income can be challenging.
* The discount rate's selection can have a major impact on the calculated ROI.
> **Tip:** Sensitivity analysis can be performed to understand how changes in the discount rate affect the project's viability.
### 4.6 Application Example: Invest Co
Invest Company is considering a new product: a multifunctional storage box.
* **Sales:** 15,000 boxes annually at 19.00 dollars per box.
* **Production Cost:** 11.50 dollars per box.
* **Machinery Purchase:** 30,000 dollars, depreciated linearly over 5 years.
* **Financing:** Investment credit with a 5-year term, fixed yearly capital installments at 5% interest.
* **Labor Cost:** 20,000 dollars per year (0.5 FTE).
* **Discount Rate:** 5%.
* **Overhead:** 3,450 dollars per year.
* **Management Requirement:** Minimum return of 7%.
**Analysis Steps:**
1. **Calculate the PV of all relevant cash flows for the next five years.** This would involve calculating annual revenues, variable costs, fixed labor costs, overhead, depreciation (for tax calculations, if applicable, though the problem focuses on cash flows), and loan repayments, then discounting them to their present values.
2. **Calculate the profitability and NPV of this project.** Based on the present values calculated in step 1, determine the NPV.
3. **Determine if the project should proceed.** Compare the project's required return (implicitly derived from its NPV and investment) against the management's minimum required return of 7%. If the project's return meets or exceeds 7%, it would be considered for acceptance.
---
# Application case study: Invest Co
This case study demonstrates the practical application of investment analysis principles to evaluate a new product launch decision for Invest Company.
### 5.1 Overview of investment analysis principles
Investment analysis involves evaluating the potential profitability of projects by examining future cash flows. The core idea is to assess whether an expenditure or effort made today will yield sufficient future returns. Key principles include:
* **Identifying relevant cash flows:** Only incremental cash flows directly attributable to the project should be considered. This means focusing on the changes in cash position that occur *because* of the project.
* **Working on a cash basis:** Analysis should be based on actual cash inflows and outflows, not accounting entries like depreciation.
* **Determining the relevant period:** The analysis should cover the entire useful life of the investment.
### 5.2 Methods for investment analysis
Several methods are used to assess project profitability, with the Net Present Value (NPV) method being considered the most financially sound and widely used. Other methods include the Payback Period and the Internal Rate of Return (IRR).
#### 5.2.1 Net present value (NPV) method
The NPV method accounts for the time value of money, recognizing that money received in the future is worth less than money received today.
##### 5.2.1.1 Time value of money and present value
The **time value of money** principle states that a euro today is worth more than a euro in the future due to potential earning capacity and inflation. The **present value (PV)** of a future sum is its value in today's terms, calculated by discounting future cash flows at a specified interest or discount rate.
The formula for calculating the present value of a single future cash flow is:
$$ PV = \frac{C}{(1 + i)^n} $$
Where:
* $C$ is the future cash flow amount.
* $i$ is the annual interest or discount rate.
* $n$ is the number of years until the cash flow is received.
##### 5.2.1.2 Calculating Net Present Value (NPV)
The NPV is the sum of the present values of all cash inflows minus the sum of the present values of all cash outflows associated with an investment project.
$$ NPV = \sum \frac{\text{Cash receipts}}{(1 + i)^n} - \sum \frac{\text{Cash expenses}}{(1 + i)^n} $$
The **discount rate** ($i$) is crucial and typically comprises a reference rate (e.g., government bond yield), expected inflation, and a risk premium. The Weighted Average Cost of Capital (WACC) is often used as the discount rate.
**Example:**
Company Basril is considering purchasing machinery for 150,000 dollars. The machinery is expected to generate the following cash inflows over five years:
* Year 1: 37,450 dollars
* Year 2: 34,678 dollars
* Year 3: 42,500 dollars
* Year 4: 38,677 dollars
* Year 5: 27,450 dollars
Using a discount rate of 2% per annum:
* PV of Year 1 inflow: $\frac{37,450}{(1 + 0.02)^1} \approx 36,715.69 \text{ dollars}$
* PV of Year 2 inflow: $\frac{34,678}{(1 + 0.02)^2} \approx 33,331.41 \text{ dollars}$
* PV of Year 3 inflow: $\frac{42,500}{(1 + 0.02)^3} \approx 40,048.70 \text{ dollars}$
* PV of Year 4 inflow: $\frac{38,677}{(1 + 0.02)^4} \approx 35,731.57 \text{ dollars}$
* PV of Year 5 inflow: $\frac{27,450}{(1 + 0.02)^5} \approx 24,862.31 \text{ dollars}$
The sum of the present values of the incomes is approximately 170,689.68 dollars.
The NPV is calculated as: $170,689.68 \text{ dollars} - 150,000 \text{ dollars} = 20,689.68 \text{ dollars}$.
Since the NPV is positive, it suggests the project is financially viable.
#### 5.2.2 Return on Investment (ROI)
ROI provides a percentage measure of the profitability of an investment relative to its initial cost.
$$ ROI = \frac{NPV}{\text{PV of investment}} $$
For Project 1 (Basril machinery), the ROI is:
$$ ROI = \frac{20,689.68 \text{ dollars}}{150,000 \text{ dollars}} \approx 0.1379 \text{ or } 13.79\% $$
The average annual ROI is $13.79\% / 5 \text{ years} = 2.76\% \text{ per year}$.
> **Tip:** While NPV provides an absolute measure of value creation, ROI offers a relative measure, which can be useful for comparing projects of different scales. However, when comparing projects, always consider both the absolute NPV and the ROI. A project with a higher NPV may be preferred even if its ROI is slightly lower, especially if capital is not a binding constraint.
##### 5.2.2.1 Minimum return requirement
Companies set a minimum required rate of return, often based on their profitability of equity (ROE), WACC, inflation, and risk compensation. Projects must meet or exceed this minimum threshold to be considered acceptable.
**Example:**
If Invest Company's management requires a minimum return of 7% on new products, a project with an ROI below 7% would be rejected, regardless of its NPV.
### 5.3 Application: Invest Co product launch
Invest Company is considering launching a new multifunctional storage box. The analysis involves calculating cash flows, profitability, and NPV, with a specific management requirement for minimum return.
**Project Details:**
* **Product:** Multifunctional storage box.
* **Annual Sales Volume:** 15,000 boxes.
* **Selling Price:** 19.00 dollars per box.
* **Production Cost per Box:** 11.50 dollars (including raw materials and hourly wages).
* **New Production Machinery Cost:** 30,000 dollars.
* **Machinery Depreciation:** Linear over 5 years.
* **Financing:** Investment credit with a 5-year term (fixed yearly capital instalments, interest rate $i=5\%$).
* **Additional Labour Cost:** 20,000 dollars per year (0.5 FTE).
* **Discount Rate:** 5% per year.
* **Annual Overhead:** 3,450 dollars.
* **Project Duration:** 5 years.
* **Management's Minimum Return Requirement:** 7%.
**Tasks for analysis:**
1. Calculate the Present Value (PV) of all relevant cash flows for the next five years.
2. Calculate the profitability (ROI) and the NPV of this project for the next five years.
3. Determine if the project should proceed based on the management's minimum return requirement.
---
## Common mistakes to avoid
- Review all topics thoroughly before exams
- Pay attention to formulas and key definitions
- Practice with examples provided in each section
- Don't memorize without understanding the underlying concepts
Glossary
| Term | Definition |
|------|------------|
| Expenditure | An outlay of money or resources to acquire something or to provide a service. It represents an outflow of funds from an individual or organization. |
| Profitable | Yielding a financial gain or benefit; producing profit. An investment is considered profitable if its returns exceed its costs. |
| Financial Investment Analysis | The systematic evaluation of the potential profitability and risks associated with an investment proposal to determine whether to commit funds. |
| Funds | Financial resources available for investment, typically money or capital that can be used for purchasing assets or undertaking projects. |
| Assets | Items of economic value owned by an individual or company, from which future benefits are expected. Examples include buildings, machinery, shares, and bonds. |
| Profit | The financial gain made in a transaction; the difference between the amount earned and the amount spent in buying, operating, or producing something. |
| Investment Projects | Separate proposals for potential investment that require a decision-making process to assess their viability and strategic fit. |
| Cost-effectiveness | The degree to which an investment project provides a favorable ratio between the costs incurred and the benefits achieved. |
| Return on Investment (ROI) | A performance measure used to evaluate the efficiency or profitability of an investment. It is typically expressed as a percentage. |
| Future Cash Flows | The projected inflows and outflows of cash associated with an investment project over its economic life. |
| Strategic Priorities | Key objectives and goals that guide an organization's long-term direction and decision-making, influencing project selection. |
| Master Plan | A comprehensive strategic document outlining an organization's long-term vision, goals, and the actions required to achieve them. |
| Marginal Cash Flows | The incremental changes in cash (increases or decreases) that occur as a direct result of undertaking a specific project, compared to the baseline scenario. |
| Cash Basis | An accounting method that records revenues and expenses at the time cash is actually received or paid, rather than when they are earned or incurred. |
| Cash Outflows | Payments of cash made by an organization, such as for investments, wages, or operating expenses. |
| Cash Inflows | Receipts of cash by an organization, such as from sales or returns on investments. |
| Depreciation | An accounting method of allocating the cost of a tangible asset over its useful life. It is not a cash flow and is therefore excluded from cash basis analysis. |
| Relevant Period | The specific duration over which an investment is expected to generate benefits or cash flows, determined by the asset's useful life or project timeframe. |
| Net Present Value (NPV) | A financial metric that calculates the difference between the present value of cash inflows and the present value of cash outflows over a period of time, used to analyze the profitability of a projected investment. |
| Payback Method (PB Method or Period) | A capital budgeting technique that determines how long it takes for an investment to generate cash flows sufficient to recover its initial cost. |
| Internal Rate of Return (IRR) | The discount rate at which the Net Present Value (NPV) of all the cash flows from a particular project or investment equals zero. |
| Strategic Plan | A document outlining an organization's long-term objectives and the strategies to achieve them. |
| Urgency | The degree to which an investment or action is time-sensitive and requires immediate attention, often due to replacement needs or critical operational requirements. |
| Financial Resources | The capital available to an organization to fund its operations, investments, and other financial commitments. |
| Complementarity | The extent to which a project enhances or is enhanced by other existing or potential projects within an organization. |
| Corporate Social Responsibility (CSR) | A business approach that contributes to sustainable development by delivering economic, social, and environmental benefits for all stakeholders. |
| Risk | The possibility that an investment’s actual return will be different from its expected return, including the possibility of losing some or all of the original investment. |
| Time Value of Money | The concept that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. |
| Present Value (PV) | The current worth of a future sum of money or stream of cash flows, given a specified rate of return or discount rate. |
| Discount Rate | The interest rate used to determine the present value of future cash flows. It typically reflects the time value of money and the risk associated with the investment. |
| Interest Rate | The percentage of a sum of money charged by a lender for its use, or paid by a borrower. |
| Inflation | A sustained increase in the general price level of goods and services in an economy over a period of time, leading to a fall in the purchasing power of money. |
| WACC (Weighted Average Cost of Capital) | The average rate of return a company expects to pay to its security holders to finance its assets. It is a blend of the cost of debt and the cost of equity, weighted by their proportions in the capital structure. |
| Prime Cost | The original cost or purchase price of an asset, often used as the basis for calculating depreciation or other financial metrics. |
| Actualization Rate | A term synonymous with discount rate, used to bring future cash flows back to their present value. |
| Government Bond | A debt security issued by a national government to raise capital, typically considered a relatively safe investment. |
| ROE (Return on Equity) | A measure of a company's profitability that calculates how much profit a company generates with the money shareholders have invested. |
| Overhead | Indirect costs or expenses not directly attributable to a specific project or product, but necessary for the overall operation of a business. |
| Linear Depreciation | A method of depreciation where an asset's cost is spread equally over its useful life. The annual depreciation expense remains constant. |
| Investment Credit | A loan or line of credit specifically provided to finance investments, such as the purchase of machinery or other capital assets. |
| Capital Instalments | Payments made towards the repayment of a loan principal over time. |