elec5212 module3 cost of capital(1)

8/17/2019 Elec5212 Module3 Cost of Capital(1)

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ELEC5212 Power SystemPlanning & Power Market

Module 3 Cost of Capital

Prof. Z. Y. Dong, Dr. Jin Ma


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Outlines

What is the cost of capital?

InvestmentsNet Present Value


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Why is the cost of capitalimportant

Cost has direct impacts on the price and investments;

Under regulation, the regulator must determine (1) whichoperating expenses are appropriate (2) whether customers arepaying prices that ensure sufficient long-run security of supply.Based on these two considerations, the regulator could decidewhether the price is appropriate;

Under regulation, a utility is allowed to recover reasonable costsincurred in the provision of service;

Under deregulation, generators are not guaranteed cost recovery,but most transmitters and distributors remain regulated; So theregulator must have a clear idea on the cost and how this costcan be recovered so as to encourage investments;

However, one of the most difficult tasks of an electricity utility isto determine its cost of capital.


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Cost of capital (I) Financing the capital cost of new investment

can involves two sources: Borrow funds from financial institutions, this is

called debt capital;

•

For debt capital, determining the appropriate cost ofcapital is easy: the rate of interest charged by financialinstitutions;

Provided by the owners or shareholders of the

firm or from profits earned by the firm, this iscalled equity capital;

• The rate of return is the rate that the owners of the

firm earn on their equity;


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Cost of capital (II)

When a firm is a regulated electric utility, theregulator must decide the appropriate rate ofreturn to charge customers to remunerate theproviders of equity capital. So the service canbe sustainable.


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Capital market

For simplicity, we assume there is a singlemarket for financial capital;

Firms who want to borrow money enter this

market and announce how much they arewilling to borrow at each rate of interest.

Investors also enter this market and announcehow much they are willing to lend at each rate ofinterest;


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Market equilibrium

The equilibrium rental(interest) rate and totallevel of capitaldemanded aredetermined by the

intersection of demandfor financial capital byfirms and the supply offinancial capital by

investors. If the interest rate is

low, supply would beless and demands on

capital would be high.


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Demand behaviour In a capital market, capital is a commodity;

If a firm purchases a unit capital, he must make surethat the increase in his revenue that this unit capitalproduces at least no less than the cost of that unit

capital; So it is worthwhile to attract the capital in; If the increase of the revenue is higher than the cost

of capital that produces this increase of the revenue,that firm will continue to demand capital inputs until

the revenue increase that the capital produces is justequal to the price of the capital (that is its marginalrevenue product)


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Investor

Assume that individual investors attempt tomaximize their well-being; They are rationalinvestors;

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We assume investors prefer certainty touncertainty;

Giving a choice between an uncertain outcome and an equivalent

certain outcome, most individuals would prefer the equivalentcertain outcome.

For example, consider the choice between (1) receiving 100$ withprobability one half and 0$ with probability one half and (2) 50$

with probability 1. Most individuals would choose the latter.


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So decisions of investors

Investors would be willing to invest less inprojects that are more risky.

Thus an electric utility decision maker has to

determine: First, the risk class of each investment;

Second, the appropriate rate of return on

capital for the appropriate risk classes It can be expected that for high risk project,

the investor would look for high rate of

return to protect them from the risk.


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Structure of rate of return(I) The basic component of rate of return is risk-

free interest rate;

Risk-free interest rate is also called (nominal)rate of interest on the risk-free investment,i.e., one investment that always pays aknown return to the lender; such as thesecurities sold by the government; For a

stable government, this investment can beseen as no risk;


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Risk-free interest rate (I) There are two components to the risk-free

interest rate R f :

One component compensates investors for inflationrate i

The other component compensates investorsbecause they are unable to use the funds while the

capitals are being used by the borrower; This iscalled real risk-free interest rate rf


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Risk-free interest rate (II)

(1+ R f ) = return/capital

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If inflation is low (e.g. less than 5%) and thereal risk-free rate is low (e.g. less than 3%),

will be small, e.g. , we oftenapproximate


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Structure of rate of return (II)

For all risky projects, investors will charge a riskpremium (RP) to compensate them for the unknownrate of return


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An example of an interest rateof return

The real (risky) interest rate r is 10%, whichis equivalently, for example, to a risk-freerate rf =5% and a risk premium RP=5%;

If the rate of inflation is 10%, then thenominal (risky) interest rate would be at least20% with stable inflation.

If the rate of inflation is high, this item cannotbe neglected.


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Net Present Value (NPV) Net Present Value maximization is the

most widely accepted method of project

evaluation in modern finance; The most important concept around NPV

maximization is: “time value of money”,

i.e., that money in hand today has adifferent value than the same amount oneyear ago or one year from now.

So when we talk about money to beinvested, we should discount all of themfrom future into the present.


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Discounting to Present (I) To focus on the most important idea, we

neglect the transaction costs, i.e., the rentalrate on financial capital (money) is the samefor the borrower and the lender.

For example, if the real (risk) interest rate is10% per year, the firm pays 10% per year tothe investor; There are no extra cost.

Actually, this is an assumption of a perfectcapital market.


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Discounting to Present (II)

So

Or we rewrite it into:

is denoted as the discounting factor


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Discounting to Present (III)

For year t

Here we use compounding: the return earned from a

previous period will be put into investment to earn thereturn in the next period.


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Discounting to Present (IV)


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Discounting to Present (V)

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Discounting to Present (VI)

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Discounting to Present (VII)

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If we discount by breaking the periods into sub-periods, for example, into months.

Under monthly discounting, the annual rate of 10%is divided by 12, or, 0.833% per month.

If we compound monthly, the annual rate would be:

The effective annual rate is 10.47%, a little higher than10% annual rate;


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Discounting to Present (VIII)

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If we discount by breaking the periods into days. Under daily discounting, the annual rate of 10% is

divided by 365, or, 0.0274% per day.

If we compound daily, the annual rate would be:

The effective annual rate is 10.515%, even higher thancompounding monthly;


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Discounting to Present (IV)

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Now we discount by breaking the periods into evensmaller time intervals.

We separate one year into m periods, the annualrate of 10% is divided by m and when , we

actually compound continuously

That is the limit that we can have for an effective annual rate;

It should be noted in this case monthly compounding approaches continuous

compounding and daily compounding is almost indistinguishable from continuouscompounding.


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Investment (I)

Now consider we investment yearly. For simplicity, weassume we invest uniformly each year.

We discount our investments into the present value:

If we invest until year T, we can add all the terms together and get:


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Investment (II)

Question: If we make an investment PV in the present,what amount must be collected each year to recover ourinvestment?

Since


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Investment (III)

Example: we make an investment of 1000$ today, ifr=10% and we want to recover our investment in 30 years(say, the life cycle of this product that we invest in) , use

106.08$ must be collected each year for 30 years. Thatmeans our average annual profit cannot be less than $106.08;

If it is less than this value under reasonable cause, theregulator should consider compensation if necessary toencourage the investments in this product.


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Investment (IV)

If T goes to the infinity, the equivalent payment that wehave to collect at every period in the foreseeable futurebecomes

Since

In this case, r=10% and the present investment is $1000;the annual payment would be $100. It gives a very closeestimate to the annual payment for long recovery periods

(e.g., 30 years) but with much simpler calculation.


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Net Present Value (I)

In our last module, we discussed the fact that firms

maximize their profits in each period; But firms, particular those owning physical capital

with long productive lives, such as electricitygeneration capacity, must make decision based onfuture profits.

So we have to extend our behavioural assumption

from single-period profit maximization to multi-periodprofit maximization.


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Net Present Value (II)

Considering profits (net cash flow) in two future

periods, Since

and we discount the future profits into the present value

of future revenues TR minus (net of) future costs TC.


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Net Present Value (III)

Since TC includes the variable cost (VC) and the fixed

cost (FC), this approach assumes that costs includingFC are incurred in each future period.

In most cases, some costs, such as capital costs,

must be spent in the current period so revenues canbe received in the future.

If the fixed cost is incurred in the first period and

variable costs are spent in the future periods, then.

in each future period, discounted at the relevant cost of capital r, to thepresent.


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Net Present Value (IV)

Obviously, we may earn profit in some years, such as

PR t>0 or we may lose money in some years, such asPR t 0, we earn profits inaverage. A positive NPV implies positive discountedprofit to the present.


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Net Present Value (V)

Net Present Value Rule: The investors invest in

projects (e.g., power plants) with positive NPVbecause all projects with positive NPV imply positivediscounted profits.

The investors will

first rank possible projects by NPV;

then begin by investing in the project with the highestNPV;

This is often referred to as maximizing Net Present Value

principle in multi-periods framework.


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Summary In this module, we learned methods to

evaluate cost of capital, which is veryimportant at the planning stage;

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When we evaluate the cost of capital, we should keep the time

value of money in mind;

We have learned one most important method on investmentevaluations, i.e., net present value method.


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Thank you!

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elec5212 module3 cost of capital(1)

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