Accounting Business Reporting for Decision Making

CHAPTER 12 Capital investment 509

the present value of the net cash flows. The discount rate is the interest rate at which a future cash flow

is converted to a present value.

PV = CF 1 /(1 + r) + CF 2 /(1 + r)^2 + CF 3 /(1 + r)^3 ... CFn/(1 + r)n

NPV + CF 1 /(1 + r) + CF 2 /(1 + r)^2 + CF 3 /(1 + r)^3 + ... + CFn/(1 + r)n – INV

where CF = the net cash flow at the end of period n

r = the selected discount rate per period

n = the number of periods, and

INV = the initial investment.

Decision rule for NPV

The cash flows are assumed, for simplicity, to have occurred at the end of each relevant period. This

point is discussed in more detail later in this section.

The investment decision rule based on the financial analysis is to invest in projects (assets) if the NPV

is positive (i.e. PV net CF > initial investment). This is because the positive value indicates a project that

is potentially able to yield a higher return than the opportunity cost of funds (whose value is incorpo-

rated in the discount rate). Calculating NPV is demonstrated in illustrative example 12.4.

ILLUSTRATIVE EXAMPLE 12.4

Calculating net present value

Let us now return to the Coconut Plantations example and assume that potential manufacturers require

a 10 per cent investment return. Denominated in thousands of dollars, the NPV is calculated as follows.

NPV = CF 1 /(1 + r) + CF 2 /(1 + r)^2 + CF 3 /(1 + r )^3 + ... + CFn/(1 + r )n − INV

= 30/1.1 + 60/(1.1)^2 + 50/(1.1)^3 + 100/(1.1)^4 − 120

= 27.27 + 49.58 + 37.57 + 68.30 − 120

= 62.72

Remember, the $100 000 in year 4 is the $40 000 from the sale of coconut oil, plus the $60 000 from

the sale of the secondhand machinery. The result of $62 720 is positive and indicates that, on this

measure, the contract to manufacture coconut oil should be undertaken, as it will enhance the manufac-

turer’s wealth. While a positive value for the NPV indicates that the manufacturer would be better off if it

took on this project, a negative value, on the other hand, indicates that the project would not generate

sufficient surplus and the manufacturer would not increase their wealth through this project.

To solve the NPV equation, with r valued at 10 per cent so that (1 + r) equals 1.1, a financial calculator

can be used in place of the manual steps above. Refer to appendix 12B for the calculator steps.

Discount tables

An alternative to using the formula and calculation method shown in illustrative example 12.4 is to

use discount tables. A discount table showing the present value of $1 received in n periods of time is

included in appendix 12A at the end of this chapter.

Look at the discount table in this chapter. For period 1 and a 10 per cent discount rate, the table tells us

that the discount factor is 0.909. In our example, $30 000 × 0.909 gives $27 270; and, for period 2 and a

10 per cent discount rate, the table tells us that the discount factor is 0.826. Multiplying $60 000 by 0.826

gives $49 560. The difference between that value and the $49 580 is due to rounding to three decimal places.

Determining the discount rate

There are a number of factors that affect the discount rate used in investment decisions, including infla-

tion, risk and the opportunity cost of capital.