the meaning, calculation and interpretation of net present value (NPV)

10.3 Investment Appraisal – Net Present Value (NPV)

What is NPV?

💰 Net Present Value is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. Think of it as the “real” profit you’ll get from an investment when you take into account the time value of money. If the NPV is positive, the project is expected to add value; if it’s negative, it will reduce value.

Why does time matter?

📈 Money today is worth more than the same amount in the future because you could invest it and earn interest. Imagine you have a treasure chest that grows a little bit each year. The earlier you get the treasure, the more it can grow. NPV helps you compare projects that give cash flows at different times.

How to calculate NPV?

The basic formula is:

\$\$

NPV = \sum{t=0}^{n} \frac{Ct}{(1+r)^t}

\$\$

• \$C_t\$ = cash flow at time \$t\$ (negative for outflows, positive for inflows)
• \$r\$ = discount rate (expressed as a decimal, e.g., 10% = 0.10)
• \$t\$ = period (0, 1, 2, …, \$n\$)

Example: A Simple Project

Suppose a company wants to buy a machine that costs £10,000 today (time 0). The machine will generate £3,000 each year for 5 years. The discount rate is 10%.

1. List the cash flows:

   • t = 0: –£10,000
   • t = 1: +£3,000
   • t = 2: +£3,000
   • t = 3: +£3,000
   • t = 4: +£3,000
   • t = 5: +£3,000

2. Discount each cash flow to present value:

   • PV₀ = –£10,000 / (1+0.10)⁰ = –£10,000
   • PV₁ = £3,000 / (1+0.10)¹ ≈ £2,727.27
   • PV₂ = £3,000 / (1+0.10)² ≈ £2,479.34
   • PV₃ = £3,000 / (1+0.10)³ ≈ £2,253.07
   • PV₄ = £3,000 / (1+0.10)⁴ ≈ £2,047.42
   • PV??

     = £3,000 / (1+0.10)⁵ ≈ £1,861.35

3. Sum all present values:

   \$\$

   NPV = -10,000 + 2,727.27 + 2,479.34 + 2,253.07 + 2,047.42 + 1,861.35 \approx £1,368.45

   \$\$

4. Interpretation: Since NPV ≈ £1,368.45 > 0, the project is expected to add value and should be accepted.

Interpreting NPV

• NPV > 0 – The project is expected to create value. ??

  Accept the project.

• NPV = 0 – The project breaks even. The decision may depend on other factors.
• NPV < 0 – The project will destroy value. ❌ Reject the project.