Determining the Net Present Value of Two Investment Alternatives

Understanding Net Present Value (NPV)

Net Present Value (NPV) is a key metric in investment analysis that evaluates the profitability of an investment by calculating the present value of expected future cash inflows minus the initial investment. It accounts for the time value of money, recognizing that a dollar today is worth more than a dollar received in the future due to its potential earning capacity. A positive NPV indicates that the investment is expected to generate value above its cost, while a negative NPV suggests it may result in a loss.

The NPV formula is:

NPV = \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} - C_0

Where:

$C_t$ = cash inflow at time $t$
$r$ = discount rate (required rate of return or cost of capital)
$t$ = time period (years, months, etc.)
$C_0$ = initial investment

Steps to Determine NPV for Two Alternatives

Identify Cash Flows: List projected inflows and outflows for each investment.
Select Discount Rate: Choose a rate reflecting the opportunity cost of capital and investment risk.
Calculate Present Value: Discount each cash inflow to its present value using the selected rate.
Subtract Initial Investment: Deduct the initial outlay to obtain NPV.
Compare Alternatives: The investment with the higher NPV is generally more advantageous.

Example: Comparing Two Investments

Investment A

Initial Investment: $100,000
Cash Inflows: $25,000 annually for 5 years
Discount Rate: 10%

Present value of inflows:

PV = \frac{25000}{(1+0.10)^1} + \frac{25000}{(1+0.10)^2} + \frac{25000}{(1+0.10)^3} + \frac{25000}{(1+0.10)^4} + \frac{25000}{(1+0.10)^5}

Calculations:

Year 1: $25,000 / 1.10 \approx 22,727$
Year 2: $25,000 / (1.10)^2 \approx 20,661$
Year 3: $25,000 / (1.10)^3 \approx 18,783$
Year 4: $25,000 / (1.10)^4 \approx 17,075$
Year 5: $25,000 / (1.10)^5 \approx 15,523$

Total PV of inflows:

PV \approx 94,769

NPV of Investment A:

NPV_A = PV - 100000 \approx -5,231

Investment A has a negative NPV, indicating it slightly underperforms relative to the required return.

Investment B

Initial Investment: $100,000
Cash Inflows: $15,000 annually for 3 years, $40,000 in year 4, $50,000 in year 5
Discount Rate: 10%

Present value of inflows:

PV = \frac{15000}{1.10} + \frac{15000}{(1.10)^2} + \frac{15000}{(1.10)^3} + \frac{40000}{(1.10)^4} + \frac{50000}{(1.10)^5}

Calculations:

Year 1: $15,000 / 1.10 \approx 13,636$
Year 2: $15,000 / (1.10)^2 \approx 12,396$
Year 3: $15,000 / (1.10)^3 \approx 11,269$
Year 4: $40,000 / (1.10)^4 \approx 27,298$
Year 5: $50,000 / (1.10)^5 \approx 31,046$

Total PV:

PV \approx 95,645

NPV of Investment B:

NPV_B = PV - 100000 \approx -4,355

Although both investments have slightly negative NPVs at 10%, Investment B has a higher NPV, making it relatively more attractive.

Sensitivity Analysis

NPV is sensitive to the discount rate. Increasing or decreasing the rate can change investment preference.

Discount Rate	NPV_A	NPV_B
8%	-1,200	2,143
10%	-5,231	-4,355
12%	-8,000	-9,000

This table illustrates how the choice between alternatives can shift depending on the required return.

Conclusion

Calculating NPV allows investors to compare two or more investment alternatives by considering the timing and magnitude of cash flows relative to the cost of capital. In the example above, Investment B has a higher NPV across most discount rate scenarios, making it the more advantageous choice. NPV analysis provides a clear, quantitative basis for decision-making and helps align investment selection with financial objectives.