Chapter 7: Investment Decisions

 Chapter 7: Investment Decisions

 

Question: Explain the concept of investment decisions and discuss the various methods used for evaluating investment projects.

Answer:

Investment decisions refer to the process of deciding where, when, and how to allocate financial resources to investment opportunities to generate returns. These decisions are crucial for a company’s growth and long-term success. The goal of investment decisions is to choose projects or assets that will maximize the firm’s value and wealth for its shareholders.

The process involves evaluating potential projects or investments based on their expected return, risk, and impact on the company's overall financial position.

Methods for Evaluating Investment Projects

There are several techniques used to evaluate investment projects. These methods help determine whether an investment is financially viable, considering both its potential return and associated risks.

1. Net Present Value (NPV) Method

  • Definition: The NPV method involves calculating the present value of expected future cash inflows and outflows associated with an investment. It then subtracts the initial investment to determine the net value added by the project.
  • Formula: NPV=∑Rt(1+r)t−C0\text{NPV} = \sum \frac{R_t}{(1 + r)^t} - C_0 Where:
    • RtR_t = Cash inflows in time period tt
    • rr = Discount rate (cost of capital)
    • C0C_0 = Initial investment
  • Explanation: A positive NPV indicates that the investment is expected to generate value greater than its cost, making it a desirable project. A negative NPV suggests that the project would reduce the company's value.
  • Advantages:
    • Takes the time value of money into account.
    • Provides a clear indication of whether an investment will create or destroy value.
  • Disadvantages:
    • Requires accurate estimation of cash flows and discount rates.

2. Internal Rate of Return (IRR) Method

  • Definition: IRR is the discount rate at which the NPV of an investment project becomes zero. It represents the expected rate of return on the project. The decision rule is to accept projects where the IRR exceeds the required rate of return or cost of capital.
  • Formula: NPV=∑Rt(1+IRR)t−C0=0\text{NPV} = \sum \frac{R_t}{(1 + \text{IRR})^t} - C_0 = 0
  • Explanation: If the IRR is higher than the company’s cost of capital, the project is deemed acceptable. If IRR is lower, the project should be rejected.
  • Advantages:
    • Provides an easy-to-understand rate of return.
    • Does not require the selection of a specific discount rate.
  • Disadvantages:
    • May give multiple IRRs in certain cases with non-conventional cash flows (e.g., alternating positive and negative cash flows).

3. Payback Period Method

  • Definition: The payback period is the time it takes for an investment to recover its initial cost from its cash inflows. The shorter the payback period, the more attractive the investment.
  • Formula: Payback Period=Initial InvestmentAnnual Cash Inflows\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflows}}
  • Explanation: The payback period focuses on liquidity, highlighting how quickly the initial investment can be recouped. A shorter payback period is preferred as it indicates lower risk and quicker recovery of invested capital.
  • Advantages:
    • Simple to calculate and understand.
    • Useful for assessing the risk of an investment.
  • Disadvantages:
    • Ignores the time value of money.
    • Does not account for cash flows beyond the payback period, potentially overlooking long-term profitability.

4. Accounting Rate of Return (ARR) Method

  • Definition: ARR measures the return on an investment based on accounting profits rather than cash flows. It is calculated by dividing the average annual accounting profit by the initial investment.
  • Formula: ARR=Average Annual ProfitInitial Investment×100\text{ARR} = \frac{\text{Average Annual Profit}}{\text{Initial Investment}} \times 100
  • Explanation: A higher ARR indicates a more profitable investment. The decision rule is to accept projects with an ARR higher than the required rate of return.
  • Advantages:
    • Easy to understand and use.
    • Useful when cash flow data is not available.
  • Disadvantages:
    • Ignores the time value of money.
    • Based on accounting profits, which may not reflect true profitability.

5. Profitability Index (PI) Method

  • Definition: The profitability index is the ratio of the present value of future cash flows to the initial investment. It is used to evaluate projects when resources are limited and helps rank projects by profitability.
  • Formula: PI=Present Value of Cash InflowsInitial Investment\text{PI} = \frac{\text{Present Value of Cash Inflows}}{\text{Initial Investment}}
  • Explanation: A PI greater than 1 indicates a profitable investment, while a PI less than 1 suggests a non-profitable investment.
  • Advantages:
    • Useful when there are capital constraints.
    • Helps in ranking multiple projects.
  • Disadvantages:
    • Less useful when comparing projects of different sizes.



SUMS:

Question: Calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) for the following investment project, and determine whether the project should be accepted:

  • Initial Investment: ₹2,00,000
  • Cash Flows:
    • Year 1: ₹80,000
    • Year 2: ₹90,000
    • Year 3: ₹1,00,000
    • Year 4: ₹1,10,000
  • Discount Rate: 10%

Answer:

We will calculate Net Present Value (NPV) and Internal Rate of Return (IRR) for this investment project step by step.

1. Net Present Value (NPV)

Formula:

NPV=∑Cash Flow in each year(1+r)t−Initial Investment\text{NPV} = \sum \frac{\text{Cash Flow in each year}}{(1 + r)^t} - \text{Initial Investment}

Where:

  • Cash Flow in each year = ₹80,000, ₹90,000, ₹1,00,000, ₹1,10,000
  • Discount Rate (r) = 10% (or 0.10)
  • Initial Investment = ₹2,00,000

Step-by-Step Calculation:

We will calculate the present value (PV) for each cash flow and then subtract the initial investment to get the NPV.

  • PV for Year 1:

PV1=80,000(1+0.10)1=80,0001.10=72,727.27\text{PV}_1 = \frac{80,000}{(1 + 0.10)^1} = \frac{80,000}{1.10} = 72,727.27

  • PV for Year 2:

PV2=90,000(1+0.10)2=90,0001.21=74,380.17\text{PV}_2 = \frac{90,000}{(1 + 0.10)^2} = \frac{90,000}{1.21} = 74,380.17

  • PV for Year 3:

PV3=1,00,000(1+0.10)3=1,00,0001.331=75,131.48\text{PV}_3 = \frac{1,00,000}{(1 + 0.10)^3} = \frac{1,00,000}{1.331} = 75,131.48

  • PV for Year 4:

PV4=1,10,000(1+0.10)4=1,10,0001.4641=75,210.71\text{PV}_4 = \frac{1,10,000}{(1 + 0.10)^4} = \frac{1,10,000}{1.4641} = 75,210.71

Now, add all the present values and subtract the initial investment:

NPV=(72,727.27+74,380.17+75,131.48+75,210.71)−2,00,000\text{NPV} = (72,727.27 + 74,380.17 + 75,131.48 + 75,210.71) - 2,00,000 NPV=2,97,449.63−2,00,000=97,449.63\text{NPV} = 2,97,449.63 - 2,00,000 = 97,449.63

So, the Net Present Value (NPV) is ₹97,449.63.

Since NPV > 0, the project should be accepted.

2. Internal Rate of Return (IRR)

The IRR is the discount rate at which the NPV of the project equals zero. It is the rate that makes the present value of cash inflows equal to the initial investment. We can use trial and error or financial calculator methods to estimate the IRR.

Step-by-Step Calculation (Using Approximate Trial Method):

Start by testing two different discount rates:

At 10% Discount Rate:

We already calculated the NPV at a 10% rate, and we know it’s ₹97,449.63, which is positive.

At 20% Discount Rate:

Let’s test the IRR at a 20% discount rate.

  • PV for Year 1:

PV1=80,000(1+0.20)1=80,0001.20=66,666.67\text{PV}_1 = \frac{80,000}{(1 + 0.20)^1} = \frac{80,000}{1.20} = 66,666.67

  • PV for Year 2:

PV2=90,000(1+0.20)2=90,0001.44=62,500.00\text{PV}_2 = \frac{90,000}{(1 + 0.20)^2} = \frac{90,000}{1.44} = 62,500.00

  • PV for Year 3:

PV3=1,00,000(1+0.20)3=1,00,0001.728=57,874.02\text{PV}_3 = \frac{1,00,000}{(1 + 0.20)^3} = \frac{1,00,000}{1.728} = 57,874.02

  • PV for Year 4:

PV4=1,10,000(1+0.20)4=1,10,0002.0736=53,054.34\text{PV}_4 = \frac{1,10,000}{(1 + 0.20)^4} = \frac{1,10,000}{2.0736} = 53,054.34

Now, add all the present values and subtract the initial investment:

\text{NPV at 20%} = (66,666.67 + 62,500.00 + 57,874.02 + 53,054.34) - 2,00,000 \text{NPV at 20%} = 2,40,094.03 - 2,00,000 = 40,094.03

Since the NPV is still positive at 20%, we know the IRR is somewhere between 10% and 20%.

You can continue testing other rates between 10% and 20% (e.g., 15%) to refine your estimate. However, based on the trial, we can conclude the IRR is approximately 17-18%.

Conclusion:

  • NPV = ₹97,449.63 (positive, so the project should be accepted)
  • IRR = Approximately 17-18% (greater than the discount rate of 10%, confirming the project is acceptable)

Since the NPV is positive and the IRR is greater than the required rate of return, the project is financially viable and should be accepted.

 

 

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