5.1 Capital Budgeting - 5.1 Capital Budgeting Explained
Key Concepts
- Net Present Value (NPV)
- Internal Rate of Return (IRR)
- Payback Period
- Profitability Index (PI)
- Discounted Payback Period
Net Present Value (NPV)
Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period. A positive NPV indicates that the project is expected to generate value and is financially viable. NPV is calculated using the formula:
\[ \text{NPV} = \sum \frac{R_t}{(1 + i)^t} - C_0 \]
Where \( R_t \) is the cash flow at time \( t \), \( i \) is the discount rate, and \( C_0 \) is the initial investment.
Example: A company invests $100,000 in a project with expected annual cash flows of $30,000 for 5 years. If the discount rate is 10%, the NPV is calculated as:
\[ \text{NPV} = \frac{30,000}{(1 + 0.10)^1} + \frac{30,000}{(1 + 0.10)^2} + \frac{30,000}{(1 + 0.10)^3} + \frac{30,000}{(1 + 0.10)^4} + \frac{30,000}{(1 + 0.10)^5} - 100,000 \]
\[ \text{NPV} \approx 113,723.55 - 100,000 = 13,723.55 \]
Since the NPV is positive, the project is financially viable.
Internal Rate of Return (IRR)
Internal Rate of Return (IRR) is the discount rate at which the NPV of a project equals zero. IRR is used to evaluate the attractiveness of a project or investment. A higher IRR indicates a more favorable investment. The IRR is calculated by solving the NPV equation for \( i \) when NPV = 0.
Example: Using the same project as above, the IRR is the rate \( i \) that satisfies:
\[ 0 = \frac{30,000}{(1 + i)^1} + \frac{30,000}{(1 + i)^2} + \frac{30,000}{(1 + i)^3} + \frac{30,000}{(1 + i)^4} + \frac{30,000}{(1 + i)^5} - 100,000 \]
Solving for \( i \), we find that the IRR is approximately 15.24%. This means the project generates a return of 15.24%.
Payback Period
The Payback Period is the time it takes for a project to recover its initial investment. It is a simple measure of liquidity and risk. Shorter payback periods are generally preferred as they indicate quicker recovery of the investment.
Example: If a project requires an initial investment of $100,000 and generates cash flows of $25,000 per year, the payback period is calculated as:
\[ \text{Payback Period} = \frac{100,000}{25,000} = 4 \text{ years} \]
The project will recover its initial investment in 4 years.
Profitability Index (PI)
The Profitability Index (PI) is the ratio of the present value of future cash flows to the initial investment. It is used to rank projects and determine their relative profitability. A PI greater than 1 indicates that the project is profitable.
Example: Using the same project as above, if the present value of future cash flows is $113,723.55, the PI is calculated as:
\[ \text{PI} = \frac{113,723.55}{100,000} = 1.137 \]
Since the PI is greater than 1, the project is profitable.
Discounted Payback Period
The Discounted Payback Period is similar to the payback period but considers the time value of money. It is the time it takes for the cumulative discounted cash flows to equal the initial investment. This method provides a more accurate measure of liquidity and risk.
Example: Using the same project as above, if the discounted cash flows are $27,272.73, $24,793.39, $22,539.44, $20,490.40, and $18,627.64, the discounted payback period is calculated as:
\[ \text{Discounted Payback Period} = 4 \text{ years} + \frac{100,000 - (27,272.73 + 24,793.39 + 22,539.44 + 20,490.40)}{18,627.64} \approx 4.18 \text{ years} \]
The project will recover its initial investment in approximately 4.18 years, considering the time value of money.