Time Value of Money

[amh]

Net Present Value of Money (NPV)

NPV is the difference between the present value of future cash inflows against the present value of cash outflows (often the initial investment) utlizing identifed interest rate.

The Idea

Money today is worth more than the same amount in the future because of interest, inflation, and opportunity cost. NPV accounts for this by discounting future cash flows to their value today.

What it tells you ;

Positive NPV → investment is profitable. (Accept the project)
NPV = 0 - Break Even
Negative NPV → investment will not profitable (Reject the project)

[amh]

Net Present Value (NPV) measures if an investment's future cash flows are worth more than its upfront cost today, after adjusting for the time value of money (e.g., inflation or interest rates). A positive NPV means it's profitable; negative means avoid it. Here's a simple mechanical engineering case: evaluating a new CNC machine purchase.

## Case Example: CNC Machine Upgrade
Your company considers buying a CNC machine for RM 100,000. It saves RM 30,000/year in labor for 5 years. Discount rate: 8% (common for engineering projects, reflecting borrowing costs). No salvage value.

- **Year 0 (initial cost):** -RM 100,000
- **Year 1 cash flow:** +RM 30,000 → Present value = 30,000 / (1+0.08)^1 = RM 27,778
- **Year 2:** +RM 30,000 → PV = 30,000 / (1+0.08)^2 = RM 25,720
- **Year 3:** +RM 30,000 → PV = RM 23,815
- **Year 4:** +RM 30,000 → PV = RM 22,051
- **Year 5:** +RM 30,000 → PV = RM 20,418

**Total PV of inflows:** RM 119,782
**NPV = RM 119,782 - RM 100,000 = +RM 19,782** (Profitable—proceed!)

## Quick Calculation Table

| Year | Cash Flow (RM) | Discount Factor (8%) | Present Value (RM) |
|------|----------------|----------------------|--------------------|
| 0 | -100,000 | 1.000 | -100,000 |
| 1 | 30,000 | 0.926 | 27,778 |
| 2 | 30,000 | 0.857 | 25,720 |
| 3 | 30,000 | 0.794 | 23,815 |
| 4 | 30,000 | 0.735 | 22,051 |
| 5 | 30,000 | 0.681 | 20,418 |
| **Total** | | | **+19,782 NPV**