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Present value cash flows

Plot purchase âˆ’1,450,000

D&A âˆ’92,593

Build âˆ’701,228

Sell 2,381,497

NPV of build project 137,676

So we can see that, based on the current assumptions, there is an NPV of

$137,676. This means that provided we were happy with the assumptions we

would be content that the project was worthwhile. We might well reflect on

the relatively low NPV in relation to the initial cost of the plot. If we were

constrained by the money available to purchase plots then our investment

efficiency would be calculated as NPV divided by purchase price. The figure

for this project is just 9.5%. We might also consider the delay between initial

plot purchase and obtaining permission to build. A ten month increase in

this would result in a slight negative NPV.

This project is one where there are many cash outflows and just one posi-

tive cash flow at the end. We should appreciate that this means the impact of

any increases in the discount rate would be negative. If we were to increase

the discount rate to 11% the project would have a very small negative NPV.

This shows that to the nearest 0.1%, the IRR is 11%.

Our original purpose was to calculate what the required selling price was

for any given set of assumptions such that the project would achieve a zero

NPV. A spreadsheet model will make this type of calculation quite simple.

So, for example, it would show that:

â€¢ For the base case assumptions the break-even selling price is $2,826,568.

â€¢ An increase in the initial purchase price of $50,000 would mean the selling

price had to rise by approximately $63,000 to achieve a break-even NPV.

24 The five financial building blocks

â€¢ A decrease in the D&A time of half a year (and hence also the associated

D&A cost) would mean the break-even selling price would fall by approxi-

mately $100,000.

These are the kind of insights which should help anybody with responsibility

for the project not only to decide on the simple question of â€˜goâ€™ or â€˜no goâ€™ but

also to identify ways of making the overall economic result better.

We will return to this example in the next building block when we want to

illustrate the impact of borrowing money to finance a project.

Example 3: Paving the way to the future

In this final example we will investigate a more typical project. This involves

a heavy initial investment followed by several years of positive cash flows.

The investment is in building a factory that manufactures paving slabs. The

investment will cost $10m in the first year and $8m in the second year. The

new plant comes on stream at the beginning of year 3 and will then operate

for ten years. In the year after closure there will be a net negative cash flow as

clean-up costs and redundancy payments are expected to exceed the resale

value of the land. When the site is operational the key assumptions will con-

cern sales price, sales volume (measured as a % of maximum sales capacity)

and operating costs. In order to simplify things we will ignore inflation, tax

and also timing effects related for example to any credit period given to cus-

tomers. Cash flows will all be assumed to occur mid year.

Our assumptions are as follows:

ASSUMPTIONS

Year 1 capex $m 10

Year 2 capex $m 8

Capacity 1,500,000

Selling price $ per slab 5.00

Inflation rate 0%

Year 0 1 2 3 4 5 6 7

Sales rate â€“ % of maximum 0% 0% 70% 75% 80% 85% 90%

Fixed costs $m 0.8

Variable costs $ per slab 0.75

Shut down cost $m 2

Cost of capital 10%

Note that further assumptions are made concerning the sales rate. This is

maintained at 90% throughout the remaining operating period which is

years 3â€“12. Shutdown happens in year 13.

25 Building block 1: Economic value

The resulting cash flow model looks like this:

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Sales 5.3 5.6 6.0 6.4 6.8 6.8 6.8 6.8 6.8 6.8 0.0

Fixed costs 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.0

Variable 0.8 0.8 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0

costs

Capex 10.0 8.0

2.0

Close

down

cost

Cash flow âˆ’10.0 âˆ’8.0 3.7 4.0 4.3 4.6 4.9 4.9 4.9 4.9 4.9 4.9 âˆ’2.0

The next step is to convert the annual flows into present values:12

Cash flow âˆ’10.0 âˆ’8.0 3.7 4.0 4.3 4.6 4.9 4.9 4.9 4.9 4.9 4.9 âˆ’2.0

Discount 1 0.953 0.867 0.788 0.716 0.651 0.592 0.538 0.489 0.445 0.404 0.368 0.334 0.304

factor

âˆ’9.5 âˆ’6.9 2.9 2.9 2.8 2.7 2.7 2.4 2.2 2.0 1.8 1.7 âˆ’0.6

Present

value

cash

flow

0 âˆ’9.5 âˆ’16.5 âˆ’13.6 âˆ’10.7 âˆ’7.9 âˆ’5.2 âˆ’2.5 âˆ’0.1 2.1 4.1 5.9 7.5 6.9

Cumu-

lative

present

value

The NPV of the project is the number in the far right hand column of the cumula-

tive present value row, i.e. $6.9m. The other economic indicators are as follows:

â€¢ IRR â€“ 18%;

â€¢ discounted payback â€“ beginning of year 9;

â€¢ investment efficiency â€“ 38%.13

Many sensitivities can be calculated. For example, zero NPV cases

would be:

â€¢ sales price of $3.96 per slab;

â€¢ fixed costs of $2.1m;

â€¢ capacity of 1,135,000 slabs per year.

I have used mid year discount factors. For the first year the figure is 1 Ã· âˆš1.1 = 0.953. For subsequent years

12

the factor is the previous yearâ€™s factor divided by 1.1. Note also that I refer to a year 0 in the cash flow

model. To be strictly correct this is not a year. It is better referred to as â€˜time zeroâ€™ which is then present.

In this case investment efficiency is NPV per unit of initial investment, i.e. 6.9/18.

13

26 The five financial building blocks

Note that at this stage these sensitivities are purely arithmetic calculations

which show the impact on the result of flexing a single assumption in the

spreadsheet. One of the key skills of business concerns the ability to assess

assumptions. So, for example, a wise manager would understand how lower-

ing the selling price might well result in higher sales. For the present at least

we have a model that will allow the value impact of changes in assumptions

to be assessed.

Finally, note that this example was used to provide the cash flow data for

the value profile chart shown earlier in this building block. It is important that

readers should have a good understanding of this chart as we will be return-

ing to it again later in the book. I suggest, therefore, that readers for whom

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