Net present value (NPV) and internal rate of return (IRR)

CFA level I / Quantitative Methods: Basic Concepts / Discounted Cash Flow Applications / Net present value (NPV) and internal rate of return (IRR)

Capital budgeting is the allocation of funds to long-term projects and investments. The company allocates the capital depending on certain profitability criteria. The most used criteria are the net present value (NPV) and the internal rate of return (IRR).

The net present value of an investment is equal to the present value of its cash inflows minus the present value of its cash outflows or the present value of cash inflows net the present value of cash outflows.

Steps in computing the NPV and apply the NPV rule are given below:

• Identify all the cash inflows and cash outflows associated with the investment.
• Determine the appropriate discount rate per the risk of the investment
• Calculate the present value of cash inflows and cash outflows using the discount rate
• Subtract the sum of the present value of all cash outflows from the sum of the present value of all cash inflows to get the NPV
• Apply the NPV rule and take the appropriate action of selecting/rejecting the investment

NPV rule: There are primarily two kinds of projects: independent projects and mutually exclusive projects.

For independent projects, select all the projects where the NPV of the investment is positive and reject all the projects where it is negative.

For mutually exclusive projects, select the project which has the maximum positive NPV among the given projects. A mutually exclusive project is a project where only one project can be selected out of many projects.

The NPV of an investment adds up to the total shareholders' wealth of the company. If the NPV is positive, then the shareholders' wealth increases. If the NPV is negative, then the shareholders' wealth decreases.

NPV =∑CF_t/(1+r)^t from 1 to N

where

CF_t = the expected net cash flow at time t
N = the investment's projected life
r = the discount rate

Calculating NPV using the financial calculator: We need to follow the following steps to calculate the NPV of a project with three annual cash flows of 100, 200 and 300. The initial cash outflow is $400. Assume the discount rate is 8 percent.

Key Strokes	Explanation	Display Output
[CF][2nd][CLR WORK]	Clear CF memory registers	CF0 = 0
400[+/-][ENTER]	Initial cash outlay	CF0=-400
[↓]100[ENTER]	Period 1 cash flow	C01=100
[↓][↓]200[ENTER]	Period 2 cash flow	C02=200
[↓][↓]300[ENTER]	Period 3 cash flow	C03=300
[NPV]8[ENTER]	8 percent discount rate	I/Y=8
[↓][CPT]	Calculate NPV	NPV=94.64

Example 1: Calculating the net present value

TVF Inc. is considering an investment in a project. The initial outlay of the project is $250,000. The expected cash inflows in the first two years are $30,000 and $40,000 respectively. The expected cash inflow from year 3 to year 8 is the same in each year and equal to $50,000. The project duration is eight years. Compute the NPV of the project and specify whether the project should be selected or rejected per NPV rule. The discount rate is 10 percent. Solution: The cash flows are given below: CF0 = -250,000 CF1 = 30,000 CF2 = 40,000 CF3 to CF8 = 50,000 Using the financial calculator: Key Strokes Explanation Display Output [CF][2nd][CLR WORK] Clear CF memory registers CF0 = 0 250000[+/-][ENTER] Initial cash outlay CF0= -250000 [↓]30000[ENTER] Period 1 cash flow C01=30000 [↓][↓]40000[ENTER] Period 2 cash flow C02=40000 [↓]6[ENTER] Putting frequency as six as the same cash flow occurs for six periods F3=6 [↓]50000[ENTER] Period 3 to 8 cash flows C03=50000 [NPV]10[ENTER] 10 percent discount rate I/Y=10 [↓][CPT] Calculate NPV NPV=-8,818.16 Since the net present value is a negative number, the company should reject the investment in the project.

The internal rate of return (IRR) is another measure to check the profitability of a project. It is the discount rate that makes net present value equal to zero. It equates the present value of cash outflow to the present value of the cash inflows. It is called "internal" rate of return because it is dependent only on the cash flows of an investment and no external data are needed.

PV(Outflows) = PV(Inflows)

Calculating IRR using the financial calculator: Let's calculate the IRR of a project having an initial outlay of $300 and two cash inflows of $200 and $150 at the end of the first and second year respectively.

Key Strokes	Explanation	Display Output
[CF][2nd][CLR WORK]	Clear CF memory registers	CF0 = 0
300[+/-][ENTER]	Initial cash outlay	CF0= -300
[↓]200[ENTER]	Period 1 cash flow	C01=200
[↓][↓]150[ENTER]	Period 2 cash flow	C02=150
[IRR][CPT]	Calculate IRR	IRR=11.51

IRR Rule: If the IRR is greater than the cost of the project, then accept the project. If IRR is less than the cost of the project, then reject the project.

Example 2: Calculating the internal rate of return

Kotak Inc. is thinking of investing in a project that would generate cash flows of $200 each year for five years. The initial cash outlay for the project is $600. The cost of the project is 12.50 percent. Calculate the IRR of the project and interpret it. Solution: The cash flows are given below: CF0 = -600 CF1 to CF5 = 200 Using the financial calculator: Key Strokes Explanation Display Output [CF][2nd][CLR WORK] Clear CF memory registers CF0 = 0 600[+/-][ENTER] Initial cash outlay CF0= -600 [↓]200[ENTER] Period 1 cash flow C01=200 [↓]5[ENTER] Entering the frequency of the first year cash flow as 5 F01=5 [IRR][CPT] Calculate IRR IRR=19.86 The internal rate of return is 19.86 percent, and it is greater than the cost of the project (12.50 percent). Hence, the project should be selected.

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