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5 R$ 66,004 R$ 3,465 R$ 9,643 R$ 13,108 R$ 56,361
6 R$ 56,361 R$ 2,959 R$ 10,149 R$ 13,108 R$ 46,212
7 R$ 46,212 R$ 2,426 R$ 10,682 R$ 13,108 R$ 35,530
8 R$ 35,530 R$ 1,865 R$ 11,243 R$ 13,108 R$ 24,287
9 R$ 24,287 R$ 1,275 R$ 11,833 R$ 13,108 R$ 12,454
10 R$ 12,454 R$ 654 R$ 12,454 R$ 13,108 R$ 0

Note that while the total payment remains unchanged, the break down into interest and
principal payments changes from year to year.
Exhibit 5.3 summarizes the net income from plant investment to Aracruz each
year for the next 10 years. Note that all of the projections are in real cashflows.
Consequently, the price of paper (which grows at the same rate as inflation) is kept
constant in real terms, as is any other item having this characteristic.
In Exhibit 5.4 we estimate the cash flows to equity from the plant to Aracruz. To
arrive at these cash flows, we do the following:
Subtract out the portion of the initial capital expenditures that comes from equity; of

the initial investment of 250,000 BR, only 150,000 BR comes from equity. In year 5,
there is an additional investment of 50,000 BR.
Add back depreciation and amortization, since they are non-cash charges.

Subtract the changes in working capital; since investments in working capital are

made at the beginning of each period, the initial investment in working capital of 35.1
million BR is made at time 0 and is 15% of revenues in year 1. The changes in
working capital in the years that follow are 15% of the changes in revenue in those
years. At the end of year 10, the entire investment in working capital is recovered as


Subtract the principal payments that are made to the bank in each period, since these

are cash outflows to the non-equity claimholders in the firm.
Add the salvage value of the plant in year 10 to the total cash flows, since this is a

cash inflow to equity investors.
The cash flows to equity measure the cash flows that equity investors at Aracruz can
expect to receive from investing in the plant.

5.6. ˜: The Effects of Debt Financing on Cashflows to Equity
In the analysis above, we assumed an additional capital expenditure of 50 Million BR in
year 5, financed entirely with funds from equity; the cash flow to equity in year 5 (from
exhibit 5.4) is “5,411 Million BR. If, instead, we had assumed the 50 Million BR had
come from new borrowing, the cash flow to equity in year 5
a. will increase by 50 Million BR
b. will decrease by 50 Million BR
c. will remain unchanged

This spreadsheet allows you to estimate the cash flows to equity on a project


Exhibit 5.3: Estimated Net Income from Paper Plant Investment: Aracruz Cellulose
1 2 3 4 5 6 7 8 9 10
Capacity (in '000s) 650 700 750 750 750 750 750 750 750 750
Utilization Rate 90% 90% 90% 95% 95% 95% 95% 95% 95% 95%
Production 585 630 675 713 713 713 713 713 713 713
Price per ton 400 400 400 400 400 400 400 400 400 400
Revenues 234,000 252,000 270,000 285,000 285,000 285,000 285,000 285,000 285,000 285,000
Expenses 178,700 188,600 198,500 206,750 206,750 206,750 206,750 206,750 206,750 206,750
Depreciation 35,000 28,000 22,400 17,920 14,336 21,469 21,469 21,469 21,469 21,469
Operating Income 20,300 35,400 49,100 60,330 63,914 56,781 56,781 56,781 56,781 56,781
- Interest 5,250 4,837 4,403 3,946 3,465 2,959 2,426 1,865 1,275 654
Taxable Income 15,050 30,563 44,697 56,384 60,449 53,822 54,355 54,916 55,506 56,127
- Taxes 5,117 10,391 15,197 19,170 20,553 18,300 18,481 18,671 18,872 19,083
Net Income 9,933 20,171 29,500 37,213 39,896 35,523 35,874 36,244 36,634 37,044

Beg. Book Value 250,000 215,000 187,000 164,600 146,680 182,344 160,875 139,406 117,938 96,469
- Depreciationa 35,000 28,000 22,400 17,920 14,336 21,469 21,469 21,469 21,469 21,469
End Book Value 215,000 187,000 164,600 146,680 182,344 160,875 139,406 117,938 96,469 75,000
Depreciation is 20% of depreciable value (Remaining book value “ Salvage) until year 6. In year 6, we switch to straight line for the remaining depreciable
value over the remaining life because it yields a higher depreciation ($11,469). We also depreciate the second investment in year 5 straight line over 5 years.


Exhibit 5.4: Cash Flows to Equity from Paper Plant: Aracruz Cellulose
0 1 2 3 4 5 6 7 8 9 10
Net Income 9,933 20,171 29,500 37,213 39,896 35,523 35,874 36,244 BR 36,634 BR 37,044 BR
+ Depreciation &
Amortization 35,000 28,000 22,400 17,920 14,336 21,469 21,469 21,469 21,469 21,469
- Capital Expenditures 150,000 0 0 0 0 50,000 0 0 0 0 0
- Change in Working
Capital 35,100 2,700 2,700 2,250 0 0 0 0 0 0
- Principal Repayments 7,858 8,271 8,705 9,162 9,643 10,149 10,682 11,243 11,833 12,454
+ Salvage Value of Assets 117,750
Cashflow to Equity (185,100 ) 34,375 37,201 40,945 45,971 (5,411 ) 46,842 46,661 46,470 46,270 163,809
Salvage Value of Assets = Salvage value of Plant and Equipment (75,000) + Salvage value of working capital (42,750)


In Practice: Estimating Expected Revenues and Cash flows
How do we estimate a project™s expected revenues and expenses? The key word
in this question is “estimate”. No one, no matter what his or her skill at forecasting and
degree of preparation, can forecast with certainty how a project will do. There are
generally three ways in which we can make these forecasts:
a. Experience and History: The process of estimating project revenues and expenses is
simplest for firms that consider the same kind of projects repeatedly. These firms can
use their experience from similar projects that are already in operation to estimate
expected values for new projects. Disney, for instance, can use its experiences with its
theme parks in the United States, Tokyo Disney and Euro Disney in making its
estimates for Disney Bangkok.
b. Market Testing: If the project being assessed is different from the firm™s existing
business, we may need a preliminary assessment of the market before actually
investing in the project. In a market survey, potential customers are asked about the
product or service being considered, to gauge the interest they would have in
acquiring it. The results usually are qualitative and indicate whether the interest is
strong or weak, allowing the firm to then decide whether to use optimistic forecasts
for revenues (if the interest is strong) or pessimistic forecasts (if the interest is weak).
Companies that need more information will often test market the concept on smaller
markets, before introducing it on a larger scale. Test marketing not only allows firms
to test out the product or service directly, but also yields far more detailed
information about the potential size of the market.
c. Scenario Analysis: There are cases in which a firm is considering introducing a
product to a market it knows well, but there is considerable uncertainty introduced by
external factors that the firm cannot control. In such cases, a firm may decide to
consider different scenarios, and the revenues and expenses on the project under each
scenario. While the concept is a simple one, it has four critical components. The first
is the determination of which factors the scenarios will be built around. The second
component is determining the number of scenarios to analyze for each factor. While
more scenarios may be more realistic than fewer, it becomes more difficult to collect
information and differentiate between the scenarios in terms of project revenues. The


third component is the estimation of project revenues and expenses under each
scenario. The final component is the assignment of probabilities to each scenario.
While we have laid out three ways of estimating revenues and expenses for projects, none
of these approaches yields perfect estimates. While some project risk may come from
estimation error, a large portion of risk comes from real uncertainty about the future.
Improving estimation techniques, using more market testing and doing scenario analysis
may reduce estimation error but cannot eliminate real uncertainty. This is why we
incorporate a risk premium into the discount rate.

C. Time-Weighted versus Nominal Cash Flows
Very few projects with long lifetimes generate earnings or cash flows evenly over
their life. In sectors with huge investments in infra structure, such as telecommunications,
the earnings and cash flows might be negative for an extended period (say ten to twenty
years) before they turn positive. In other sectors, the earnings may occur earlier in time.
Whatever the reason for the unevenness of cash flows, a basic question that has to be
addressed when measuring returns is whether they should reflect the timing of the
earnings or cash flows. We will argue that they should, with earlier earnings and cash
flows being weighted more than earnings and cash flows later in a project life.

Why cash flows across time are not comparable
There are three reasons why cash flows across time are not comparable, and a cash
flow in the future is worth less than a similar cash flow today:
(1) Individuals prefer present consumption to future consumption. People would have to
be offered more in the future to give up present consumption - this is called the real rate
of return. The greater the real rate of return, the greater will be the difference in value
between a cash flow today and an equal cash flow in the future.
(2) When there is monetary inflation, the value of currency decreases over time. The
greater the inflation, the greater the difference in value between a cash flow today and a
cash flow in the future.
(3) Any uncertainty (risk) associated with the cash flow in the future reduces the value of
the cashflow. The greater the uncertainty associated with the cash flow, the greater will


be the difference between receiving the cash flow today and receiving an equal amount
in the future.
The process by which future cash flows are adjusted to reflect these factors is called
discounting, and the magnitude of these factors is reflected in the discount rate. Thus the
present value of a cash flow (CFt) at a point in time ˜t™ in the future, when the discount
rate is r, can be written as follows:
Present Value of Cash Flow = CFt #
" (1+ r)t %
Note that the second term in the brackets # is called the discount factor and
" (1+ r)t %
effectively weights the cash flow by when it occurs. The differences in weights across
time will depend entirely upon the level of the discount rate. Consequently, when
discount rates are high, which could be due to high real rates, high inflation and/or high
uncertainty, returns that occur further in the future will be weighted less. Appendix 1
includes a more complete discussion of the mechanics of present value.

The Case for Time-weighted Returns
If we accept the arguments that cash flows measure returns more accurately than
earnings, and that the incremental cash flows more precisely estimate returns than total
cash flows, we should logically follow up by using discounted cash flows (i.e., time-
weighted returns) rather than nominal cash flows for two reasons.
1. Nominal cash flows at different points in time are not comparable, and cannot be
aggregated to arrive at returns. Discounted cash flows, on the other hand, convert all
cash flows on a project to today™s terms and allow us to compute returns more
2. If the objective in investment analysis is to maximize the value of the business taking
the investments, we should be weighting cash flows that occur early more than cash
flow that occur later, because investors in the business will also do so.

5.7. ˜: Time Horizons and Time Weighting
Calculating present values for cash flows leads to a greater weighting for cash flows that
occur sooner and a lower weighting for cash flows that occur later. Does it necessarily


follow that using present value (as opposed to nominal value) makes managers more
likely to take short-term projects over long term projects?
a. Yes
b. No
Why or why not?

Investment Decision Rules
Having estimated the accounting earnings, cashflows and time-weighted
cashflows on an investment, we are still faced with the crucial decision of whether we
should take the investment or not. In this section, we will consider a series of investment
decision rules and put them to the test.

What is an investment decision rule?
When faced with new investments and projects, firms have to decide whether to
invest in them or not. While we have been leading up to this decision over the last few
chapters, investment decision rules allow us to formalize the process and specify what
condition or conditions need to be met for a project to be acceptable. While we will be
looking at a variety of investment decision rules in this section, it is worth keeping in
mind what characteristics we would like a good investment decision rule to have.
First, a good investment decision rule has to maintain a fair balance between allowing

a manager analyzing a project to bring in his or her subjective assessments into the
decision, and ensuring that different projects are judged consistently. Thus, an
investment decision rule that is too mechanical (by not allowing for subjective inputs)
or too malleable (where managers can bend the rule to match their biases) is not a
good rule.
Second, a good investment decision rule will allow the firm to further our stated

objective in corporate finance, which is to maximize the value of the firm. Projects
that are acceptable, using the decision rule, should increase the value of the firm
accepting them, while projects that do not meet the requirements would destroy value
if the firm invested in them.
Third, a good investment decision rule should work across a variety of investments.


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