## Equity Debt and Net Present Value

In the project described above, assume that Aracruz had used all equity to finance the project, instead of its mix of debt and equity. Which of the following is likely to occur to the NPV?

a. The NPV will go up, because the cash flows to equity will be much higher; there will be no interest and principal payments to make each year.

b. The NPV will go down, because the initial investment in the project will much higher c. The NPV will remain unchanged, because the financing mix should not affect the NPV

d. The NPV might go up or down, depending upon

Properties of the NPV Rule

The net present value has several important properties that make it an attractive decision rule.

1. Net present values are additive

Assets in Place: These are the assets already owned by a

The net present values of f- ■ . , , . , firm, or projects that it has already taken.

individual projects can be aggregated to arrive at a cumulative net present value for a business or a division. No other investment decision rule has this property. The property itself raises a number of implications.

• The value of a firm can be written in terms of the net present values of the projects it has already taken on as well as the net present values of prospective future projects

Value of a Firm = ! Present Value of Projects in Place + ! NPV of expected future projects

The first term in this equation captures the value of assets in place, while the second term measures the value of expected future growth. Note that the present value of projects in place is based on anticipated future cash flows on these projects.

• When a firm terminates an existing project that has a negative present value based on anticipated future cash flows, the value of the firm will increase by that amount. Similarly, when a firm takes on a new project, with a negative net present value, the value of the firm will decrease by that amount.

• When a firm divests itself of an existing asset, the price received for that asset will affect the value of the firm. If the price received exceeds the present value of the anticipated cash flows on that project to the firm, the value of the firm will increase with the divestiture; otherwise, it will decrease.

• When a firm invests in a new project with a positive net present value, the value of the firm will be affected depending upon whether the NPV meets expectations. For example, a firm like Microsoft is expected to take on high positive NPV projects and this expectation is built into value. Even if the new projects taken on by Microsoft have positive NPV, there may be a drop in value if the NPV does not meet the high expectations of financial markets.

• When a firm makes an acquisition, and pays a price that exceeds the present value of the expected cash flows from the firm being acquired, it is the equivalent of taking on a negative net present value project and will lead to a drop in value.

2. Intermediate Cash Flows are invested at the hurdle rate

Implicit in all present value calculations are assumptions about the rate at which intermediate cash flows get reinvested. The net present value rule assumes that intermediate cash flows on a projects —, i.e., cash flows that occur between the initiation and the end of the project

— get reinvested at the hurdle rate, which is the cost of capital if the cash flows are to the firm and the cost of equity if the cash flows are to equity investors. Given that both the cost of equity and capital are based upon the returns that can be made on alternative investments of equivalent risk, this assumption should be a reasonable one.

Hurdle Rate: This is the minimum acceptable rate of return that a firm will accept for taking a given project.

3. NPV Calculations allow for expected term structure and interest rate shifts

In all the examples throughout in this chapter, we have assumed that the discount rate remains unchanged over time. This is not always the case, however; the net present value can be computed using time-varying discount rates. The general formulation for the NPV rule is as follows where

CFt = Cash flow in period t rt = One-period Discount rate that applies to period t N = Life of the project The discount rates may change for three reasons:

• The level of interest rates may change over time and the term structure may provide some insight on expected rates in the future.

• The risk characteristics of the project may be expected to change in a predictable way over time, resulting in changes in the discount rate.

• The financing mix on the project may change over time, resulting in changes in both the cost of equity and the cost of capital.

Illustration 5.15: NPV Calculation With Time-Varying Discount Rates

Assume that you are analyzing a 4-year project, investing in computer software development. Further, assume that the technological uncertainty associated with the software industry leads to higher discount rates in future years.

CiLsh Flow S 300 S 400 S 500 S 600

Investirent <5 IOOO>

The present value of each of the cash flows can be computed as follows -PV of Cash Flow in year 1 = \$ 300 / 1.10 = \$ 272.72

PV of Cash Flow in year 2 = \$ 400/ (1.10 * 1.11) = \$ 327.60

PV of Cash Flow in year 3 = \$ 500/ (1.10 * 1.11 * 1.12) = \$ 365.63

PV of Cash Flow in year 4 = \$ 600/ (1.10 * 1.11 * 1.12 * 1.13) = \$ 388.27 NPV of Project = \$ 272.72+ \$ 327.60+ \$ 365.63+ \$ 388.27 - \$ 1000.00 = \$354.23

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