Accounting Business Reporting for Decision Making

508 Accounting: Business Reporting for Decision Making

the $1000 received then worth the same amount to you as it is now? The answer is no. This is because

the $1000 will buy less in a year’s time because of the change in the level of prices (inflation, which is

currently about 3 per cent per year). In addition, you could invest your $1000 received today elsewhere

and earn a return without taking on much risk, making the future value of the $1000 higher.

Let us say you had invested at 4 per cent, the return of $40 on your $1000 would have covered the

effect of inflation if it was about 3 per cent for the year, and would mean you would have received a net

increase in funds as well. Here is a timeline showing this situation:

$1000 (present value) $1040 (future value)

T 0 = now T 1 = 1 year’s time

Here is the formula you used to do this calculation in your head.

FV = PV (1 + i )n

where FV = future value

PV = present value

i = interest rate/period

n = no. of periods.

For example, FV = 1040 = 1000 (1 + 0.04)^1.

We could look at this situation from the other end — in one year’s time. If Andrew pays back the

$1000 then, what is the dollar value of that $1000 now, given that you could have earned 4 per cent

return for the year? The answer is $961.54, which is the present value (PV) of $1000 in one year’s time,

given a discount rate of 4 per cent. The $961.54 is called a discounted cash flow. The discounted cash

flow or PV is calculated by dividing the future sum by a discount factor.

PV =

FV

(1 + i)n

PV =

1000

= 961.54

1.04

Here, that factor is 1.04 (i.e. 1 + the relevant interest rate for the year). You can check to find if

$961.54 is correct by multiplying it by 1.04 to see if you get $1000.

$961.54 (present value) $1000 (future value)

T 0 = now T 1 = 1 year’s time

This shows that receiving $1000 in one year is the equivalent of receiving $961.54 today, assuming a

rate of return of 4 per cent.

The reason for calculating the present values of all the cash flows is so that the initial investment may

be matched with the expected inflows in terms of the same units of money with the same purchasing

power. A dollar that is received now has the same purchasing power as a dollar paid out now. In addition,

the cash flows are adjusted for risk and the opportunity cost of capital. The cash flows used in the anal-

ysis are the net cash inflows (either positive or negative) for each period. This means that the final net

cash inflow also includes any salvage value that might be gained by selling the infrastructure or materials

that are left over at the completion of the project. Normally, the initial investment is taken to occur now

and its value is thus a PV, unless it is a major project where development spans more than one period.

The investment decision techniques involving discounting cash flows that we discuss in this chapter

are net present value (NPV) and internal rate of return (IRR). The PV of a project is the sum of the

PVs of all the expected cash flows from all the individual periods. These PVs of the cash flows are cal-

culated just as we saw above. Then, the NPV measure compares the sum of the present values (PVs) of

all of the expected cash inflows from the project with the PVs of the expected cash outflows. The NPV is