Calculating the net present value (NPV) and/or internal rate of return (IRR) is virtually identical to finding the present value of an uneven cash flow stream (see example).

**Suppose that you were offered the investment in Example 3 at a cost of $800. What is the NPV? IRR?**

To solve this problem we must not only tell the calculator about the annual cash flows, but also the cost (previously, we set the cost to 0 because we just wanted the present value of the cash flows). Generally speaking, you’ll pay for an investment before you can receive its benefits so the cost (initial outlay) is said to occur at time period 0 (i.e., today). To find the NPV or IRR, first clear the cash flow registers and then enter -800 into CF0, then enter the remaining cash flows exactly as before. For the NPV we must supply a discount rate, so enter 12 into i, and then press f and PV. You’ll find that the NPV is $200.17922. Solving for the IRR is done exactly the same way, except that the discount rate is not necessary. This time, you’ll press f and FV to find that the IRR is 19.5382%.

Example: Project X has the following expected after-tax net cash flows. The firm’s cost of capital is 10%. (Note: Clear all previous work.)

Expected Net After-Tax Cash Flows Project X

Year

Cash Flow

0 (initial outlay)

$2,000

1

1,000

2

800

3

600

4

200

The IRR for Project X is:

{2,000} [CHS] [g] [PV] CF_{0}

{1,000} [g] [PMT] CF_{j}

{800} [g] [PMT] CF_{j}

{600} [g] [PMT] CF_{j}

{200} [g] [PMT] CF_{j}

[f] [FV] IRR gives the result, 14.48884.

A note on Net Present Value (NPV): For NPV calculations on the examination, we recommend computing the present value of each individual cash flow and adding them together. No need to memorize more calculator functions - you’ve got enough to memorize for the exam! However, for the curious, the keystrokes to calculate NPV are provided below:

The NPV of Project X is:

{2,000} [CHS] [g] [PV] CF_{0}

{1,000} [g] [PMT] CF_{j}

{800} [g] [PMT] CF_{j}

{600} [g] [PMT] CF_{j}

{200} [g] [PMT] CF_{j}

{10} [i]

[f] [PV] NPV gives the result, $157.63951

Remember: The [PV] is the [WHITe] name of the key. We use this convention because the white keys are easier to read and identify.

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Updated On: 15.07.14