Model Answer
0 min readIntroduction
In the realm of finance, the ‘present value of money’ is a fundamental concept recognizing that a sum of money is worth more now than the same sum will be at a future date due to its earning potential. This principle, known as the time value of money, is crucial for making sound investment decisions. Capital investment decisions, involving significant financial outlays with expected future returns, heavily rely on evaluating projects based on their present values. Ignoring this concept can lead to suboptimal investment choices and reduced profitability for organizations.
Understanding Present Value
The present value (PV) is the current worth of a future sum of money or stream of cash flows, given a specified rate of return. It’s calculated by discounting future cash flows back to their present equivalent using a discount rate that reflects the opportunity cost of capital and the risk associated with the investment. The formula for calculating present value is:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value
- r = Discount Rate
- n = Number of periods
Rationale Behind Present Value
The core rationale stems from the fact that money can earn interest or returns over time. Therefore, receiving a sum of money today allows for investment and potential growth, making it more valuable than receiving the same amount in the future. Inflation also erodes the purchasing power of money over time, further reinforcing the importance of present value calculations. Risk is another factor; future cash flows are uncertain, and a discount rate incorporates a risk premium to account for this uncertainty.
Application in Capital Investment Decisions
1. Net Present Value (NPV)
NPV is a capital budgeting method that calculates the difference between the present value of cash inflows and the present value of cash outflows over a period of time. A positive NPV indicates that the project is expected to be profitable and adds value to the firm.
Formula: NPV = Σ [CFt / (1 + r)^t] – Initial Investment
Where:
- CFt = Cash flow in period t
- r = Discount rate
- t = Time period
2. Internal Rate of Return (IRR)
IRR is the discount rate that makes the NPV of all cash flows from a particular project equal to zero. It represents the project’s expected rate of return. If the IRR is greater than the cost of capital, the project is considered acceptable.
3. Payback Period (Discounted)
While the simple payback period doesn’t explicitly use present value, the discounted payback period considers the time value of money when calculating the time it takes for an investment to recover its initial cost. This provides a more realistic assessment of the project’s liquidity and risk.
4. Profitability Index (PI)
The Profitability Index (PI) is a ratio of the present value of future cash flows to the initial investment. A PI greater than 1 indicates that the project is expected to generate more value than its cost.
Formula: PI = PV of Future Cash Flows / Initial Investment
Example
Consider a project requiring an initial investment of ₹1,00,000 and expected to generate cash flows of ₹30,000 per year for 5 years. Assuming a discount rate of 10%, the NPV can be calculated to determine if the project is worthwhile. A positive NPV would suggest acceptance, while a negative NPV would indicate rejection.
| Year | Cash Flow (₹) | Discount Factor (10%) | Present Value (₹) |
|---|---|---|---|
| 0 | -1,00,000 | 1.000 | -1,00,000 |
| 1 | 30,000 | 0.909 | 27,270 |
| 2 | 30,000 | 0.826 | 24,780 |
| 3 | 30,000 | 0.751 | 22,530 |
| 4 | 30,000 | 0.683 | 20,490 |
| 5 | 30,000 | 0.621 | 18,630 |
| Total | 13,700 |
Conclusion
The concept of the present value of money is indispensable for rational capital investment decisions. By discounting future cash flows, businesses can accurately assess the profitability and viability of projects, maximizing returns and minimizing risks. Ignoring the time value of money can lead to flawed investment choices and ultimately, reduced shareholder value. Sophisticated financial modeling and sensitivity analysis, incorporating varying discount rates, are crucial for robust decision-making in today’s dynamic economic environment.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.