0:13

So we saw in the previous segment

that costs and benefits of resource conservation projects

commonly follow a pattern.

Costs tend to be high early on the project

and benefits tend to be high later on in the project.

And this matters for our economic analysis,

because benefits and costs occurring at different times

are not equivalent.

So today we're going to look at how we can tell whether or not

the benefits exceed the cost overall

when we allow for this difference in the timing

of benefits and costs.

We're going to look at two different ways

to address this problem.

In this session we're going to look at a way that's probably

more intuitive for most people, and that

is to imagine that there's a bank account devoted solely

to the conservation project that we're doing,

and that the bank charges interest when the account is

in deficit or in debt, and pays interest

when the account is in credit.

All of the benefits and costs from the project

go in and out of this account, and interest

is charged or paid.

And the question is, how does the account

look after the project's finished,

at the end of the project?

So does it have a positive or negative balance

at the end of the time period that we're interested in?

And that's the basis that we're going to use,

that's the criteria we're going to use

to judge whether the project is a good or a bad project.

So if it accumulates a lot of interest costs,

that may outweigh some of the benefits,

and we'll have to see whether that's the case.

So let's look at an example or two.

Suppose that a cost is incurred of $100 in year 1.

And that then there's an interest rate

that a farmer has to pay of 5%.

What this means is that in year two

the cost will have grown two $105.

And then in year three we pay another 5% of interest on that,

and it grows to $110.25.

And that keeps going each year, and the cost compounds.

And eventually, after 20 years the cost has grown to $265.

So although the increase doesn't seem much in the early years,

by 20 years or more, the accumulated cost of interest

is really substantial.

So anybody with a home loan is familiar with the way

that the cost that they have to repay

is much higher than the amount that they borrow

in the end because of these interest costs

compounding over time.

So what this means is that if we have

a cost of say, $100 in the first year,

and we want to offset or outweigh it

with a benefit in year 20, the benefit in year 20

has to be much bigger-- $265 compared to $100

cost upfront-- if the benefit's going to outweigh the cost.

So it sets a high bar.

It makes it relatively difficult for resource conservation

projects to be beneficial overall

once we factor in these interest costs on the upfront costs.

4:02

So let's look at an example where a farmer borrows $1,000

now and the interest rate is 7% per year.

And this is an unusual loan.

It's going to be repaid in total as a lump sum after five years.

So how big will that repayment need to be?

We plug those numbers into the formula.

$1000 is the present value, 7% is r, and 5 is t, the time.

And we can do the calculation and it turns out to be $1,402.

So we borrow money now, $1,000, and the cost

after five years is a bit over a $1,400.

So again, it shows that time really

matters once you have recognized the fact that upfront

costs have an interest cost.

So which time frame to use?

I've used five years and I've 20 years earlier on in the tree

planting example.

Which is the right time frame?

Well, there's no single right or wrong answer to this question.

It depends on the particular project, on the circumstances,

and on the preferences of who's making the decision.

So for farmers, for example, a realistic time frame

might be five years if they're on the verge of retiring

and they're not interested in benefits and costs

after that time.

Or 10 years or 20 years.

But for governments, they probably

have a longer time frame, maybe 20, 50.

Even as long as 100 years might be a realistic time frame

for governments to worry about.

Similarly, there's a question about which

interest rate to use.

I've used 5% and 7% in the example I've give so far,

but again, the right rate to use depends on the circumstances

and on who's making the decision.

For a farmer, borrowing funds might be more expensive,

risks might be more important, and risk

can be built into interest rates,

so the interest rate might be say, between 7% and 12%.

For government, funds are probably cheaper,

and their investments are highly diversified.

They've got so many different types of investment

that risk is less of a concern.

So the appropriate interest rate might be 5%, 6%, 7%,

in nominal terms.

So I'm going to explain what I mean

by nominal terms in a moment, but before I get to that,

I'm just going to comment that I'm talking here

about interest rates.

But we need to use this sort of thinking

of inflating upfront costs even if we're not paying interest,

because the funds that we are using

could have been invested in a bank account

and generated interest.

So we may not actually receive or pay interest,

but we could have done, and so we need to factor that in.

Nominal terms-- economists talk about nominal and real interest

rates, and nominal and real costs and benefits.

So we often adjust costs and benefits to allow for inflation

before we do other calculations, such as calculating

the present value or the future value.

So if we factor out inflation, that

means we're expressing our benefits and costs

in real terms.

If the inflation's left in, then we're

expressing the benefits and costs in nominal terms.

And we need to make sure that we use the right interest

rate for the right types of costs and benefits.

If we leave inflation in, then we're

using nominal benefits and costs and we

need to use a nominal interest rate, which leaves inflation

in.

If we factor inflation out of our benefits and costs,

we need to factor inflation out of our interest rate,

as well, which means using a real interest rate.

So the interest rate has to match the benefits and costs.

So here's this diagram we've seen before for the tree

example, where we have these upfront costs and benefits that

mainly occur later on.

And here's a table that shows exactly the numbers that

were in that diagram.

So the table also shows the calculation

of interest in the fifth column, and the future value

of the tree planting, which is at the bottom

of the sixth column.

But before we get to that, I'll just

point out that the first four columns are the same numbers as

appeared in earlier graphs.

So those first four columns are the year, the benefits,

the costs, and the net benefits.

And we've already seen those in one of the other of the graphs

that we've used previously for this example.

The last column shows the balance of this imaginary bank

account.

And the bottom of the last column

shows the balance at the end of the time period of 20 years.

So that's the criteria we're going to use.

If that's positive, it's good.

If that's negative, it's not good.

And in the fifth column, we can see the interest that's

paid or received on that balance in each of the years,

and that gets included in the balance.

So the benefits, the costs, and the interest

costs all go into determining the balance for that year.

9:08

Now, if we happen to ignore the interest costs and benefits--

interest paid and interest received--

then the net benefits for this project

would be $1,318, so a bit over $1,300

If we allow the interest costs to be included,

all the interest receipts, and our interest is 10% per year,

then the net benefits is $291 at the end of year 20.

So you can see $291 at the bottom of the sixth column.

That's the final net benefit.

It's positive, so that means that the benefits somewhat

outweigh the costs.

They don't outweigh it by a huge amount,

but they outweigh it by a bit.

So because we accounted for interest costs and benefits,

then we can see that the final net benefit is it

about $300 instead of $1,300.

So it makes a big difference to our assessment of

whether or not this is a good project.

It's still a good project, but it's nowhere near as good

as we thought it was when we ignored interest.

It's also interesting to note that if you

look at the net balance down that column,

the net balance is negative until year 19.

So our costs and interest costs outweigh the benefits

until we get right towards the end of the time period.

So a farmer may well be concerned

about that, because it feeds into their assessment

of the riskiness of the project.

10:40

This next table shows exactly the same example

with one difference.

This time we've increased the upfront cost from $450 to $600.

So you can see that's been circled.

And having increased that upfront cost,

the net benefit is now minus $718.

So that's the number at the bottom

of the final column, the balance column.

So this time the balance is negative

throughout the whole period.

So what we've done by increasing the upfront cost by $150

is we have decreased the net benefit at the end

by about $1,000.

So that additional $850 is due to interest.

So really, it's very important to recognize that the interest

cannot be ignored when you're weighing up benefits and costs

that occur at widely different times.

If you ignore interest costs, you'll

be making a big mistake, very likely,

when you evaluate such long term projects.

So in summary, interest means that time is money.

And when benefits and costs occur at different times,

you need to allow for interest payments

so that we can compare the benefits and costs validly.

One valid approach to do this is to imagine a bank account

for the project with interest paid in or charged out

depending on the balance each year.

And the criteria we're going to use

to evaluate the project when we use this approach

is to look at the account balance

at the end of the planning period.

If it's positive, it's good.

If it's negative, then the investment is not worthwhile.

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