Finance and Market

rule of 72: x% compounding annually takes 72/x years to double the money

economic feasibility of a project or an investment opportunity

Definitions for exams:

Nominal interest rate vs Effective interest rate -Nominal interest rate is the advertised rate stated by the lender without taking compounding into consideration -Effective interest rate takes compounding into consideration and is the true rate at which the invested or burrowed money would grow if interest were compounded annually
MARR: -MARR stands for Minimum Acceptable Rate of Return is the rate at which project must earn to be acceptable -MARR represents the required return on investment that justifies the use of capital and covers the risk of the investment
1. Cost of capital, minimum return to satisfy the stakeholderws
2. Opportunity cost, is the return that could be earned from investing in an alternative project or opportunity
3. Inflation
4. Risk
5. Norms and policies
IRR vs ERR: IRR: -Exprssed as a percentage that represents the discount rate that makes the net present value of the project equal to zero - ERR: -Expresed as a percentage that represents the investment opportunities outside the firm

Engineering economics: -It is a subset of economics concerned with the use and application of economic principles in the analysis of engineering decisions -Precisely, it involves the systematic evaluation of the economic merits of proposed solutions to engineering problems -To be economically acceptable (i.e. affordable), solutions to engineering problems must demonstrate a positive balance of long-term benefits over long-term costs

Engineers in economic decisions: -Engineers are called upon to participate in a variety of decisions, ranging from manufacturing, through marketing, to financing decisions -Their primary tasks is to plan for the acquisition of equipment (i.e. capital expenditure) that will enable the firm to design and produce products economically -Also they must consider the effective user of capital assests such as buildings and machinery -With each purchase of any fixed asset, we need to estimate the profits (more precisely, cash flows) that the asset will generate during its period of service, in other words, we have to make capital expenditure decisions based on predictions about the future -An inaccurate estimate of the need for assets may have serious consequences, if you invest too much in assets, you incur unnecessarily heavy expenses, on the other hand, spending too little on fixed assets, however, is also harmful, for then the firm’s equipment may be too obsolete to produce products competitively

Fundamental principles of engineering economics: -The fundamental principles of engineering economics unite the concepts and techniques used in practice 1. A dollar earned today is worth more than a dollar earned in the future: -Money has a time value associated with it, as we can earn interest on money received today, it is better to receive money earlier than later -Example: If you receive $100 now, you can invest it and have more money available six months from now

2. All that counts are the differences among alternatives:
	-An decision should be based on differences among the alternatives considered, as all that is common is irrelevant to the decision
	-Example
		Buy:	$100	$120	$100
		Rent:	$100	$120	$120
		
3. Marginal revenue must exceed marginal cost:
	-Any increased economic activity must be justified on the basis of the fundamental economic principle that marginal revenue must exceed marginal cost, where marginal revenue means the additional revenue made possible by increasing the activity by one unit (or small unit) and marginal cost has an analogous definition
	-Example:
		Gross Revenue	   | $4 (1 unit)
		Cost of goods sold | $2 (1 unit)
		
4. Additional risk is not taken without expected additional return:
	-If compensation is not enough for anticipated inflation and the perceived investment risk, investors would purchase whatever goods they desire ahead of time or invest in assests that would provide a sufficient reutrn to compensate for any loss from inflation or potential risk
	-Example:
		Saving account	| Low risk	| 1.5%
		Bond		| Moderate	| 4.8%
		Stock		| High		| 11.5%

Accounting: The basis of decision making 1) Balance sheet: -What is company’s financial position at the end of the reporting period? The answer lies in balance sheet -Reports three main categories of items: assets, liabilities and stockholders’ equity -Accounting equation: Assets = Liability to owners (equity) + Liability to others (liablity)

	ASSETS (order of their liquidity)
		
		Current assets:
		1. Cash
		2. Accounts receivable
		3. Inventories
		
		Fixed assets:
		4. Propertiies, plant and equipments
		
		Other assets:
		5. Investment made in other companies, copyrights, franchises etc.

	LIABILITIES (order of their press)
		
		Current liabilities:
		1. Accounts payable, salaries, interest etc.
		
		Long-term:
		2. Bonds, mortgages etc.

2) Income statement:
	-Indicates whether the company is making or losing money during a stated period, usually a year
	-Equation:
		(Net) revenue = revenue - returns and discounts - (returns and allowances)
		Gross margin = net revenue - labour and materials
		Net margin = operating margin - taxes

Time value of money:

Purchasing power is the value of a currency expressed in terms of the number of goods or services that one unit of money can buy. It can weaken over time due to inflation. That’s because rising prices effectively decrease the number of goods or services you can buy.

Earning power of money refers that money can be put to work, earning more money for its owner, as the way interest operates reflects the fact that money has a time value

Cash flow diagrams: End-of-period convention: 0 is today;

Simple Interest: F = P + I = P(1 + iN) is the total amount at the end of N periods

Compound Interest: F = P(1 + i)

Economic equivalence: 1. Equivalence Calculation Made to Compare Alternatives Require a Common Time Basis 2. Equivalence Depends on Interest Rate 3. Equivalence Calculations May Require the Converion of Multiple Payment Cash Flows to a Single Cash Flow

Formulas for Equivalence Calculations:

Single Cash Flow: F = P(1.i)^{ N} = P(F/P, i, N) P = F(1.i)^{-N} = F(P/F, i, N) (N bhaneko chai gap ho yesma)
Equal-Payment (Uniform) Series: F = A[{(1.i)^n-1}/i] = A(F/A, i, N) (dui tarika le herna milxa: surudekhi nai start hunu paryo 0 ma empty huna paryo OR, bich dekhi start xa bhane N is the towers) (P/A) = (1-(1.i)^{-n})/i
Linear-Gradient Series: F = G[{(1.i)^N-iN-1}/i^2] = G(F/G, i , N) (o ma empty huna paryo plus 1 ma zero huna paryo, ra tesari garda equivalent chai 0 position ma aauxa OR, N bhaneko suru ko zero count garera towers ho ra equivalent chai empy wala point ma aauxa naki zero wala point ma) --- yo future ma aauxa muji gwach ---
Geometric Series: P = A1 [1/(i-g)[1-[(1+g)/(1+i)]^N]] P = A1 [N/(1.i)] P = A1(P/A1, g, i, N) (yesma ma zero huni haina feri A1 huni ho g chai A1 dekhi auni haru ma lagni percent increase ho) ---- yo chai present ma aauxa ---

Interest Rates: -Implicit assumption that payments are received at the end of interest period (usually anually) -If the institution uses of unit of time other than a year -say, month or quater when calculating interest payments, the institution usually quotes the interest rate on an annual basis -APR 18% compounded montly means that each month the bank will charge 1.5% interest on an unpaid balance -The 18% is the nominal interest rate, and the compounding frequency is 12 -The APR does not explain more precisely the amount of interest that will accumulate in a year -Effective annual interest rate is the one that truly represents the interest earned in one year -Assuming that the nominal interest rate is r, and M compounding periods occur during the year, APY is ia = (1+r/M)^M - 1

-(yeta ta cash flow haru year based ma banako thiye, frequency change bhayo bhane what?)
-To compute interest rate for periods of any duration:
	i = (1+r/CK)^C - 1
where,
	K is the number of payment periods per year
	C is the number of compounding per payment period
-For continuous compoudning:
	ia = e^(r/K)-1
-NOTE: The interests are per payment periods
-(jastai harek mahina cashflow banauni ho bhane K = 12 hunxa, hai ani tyo 1 mahina ma kati choti compound garni ta? 1 choti ki 0.5 choti)

Equivalence Calculations with Effective Intrest Rates: -Whenever payment and compounding periods differ from each other, one or the other must be transforemd so that both conform to the same unit of time

1) When payment period is equal to compounding period:
	M = K = ?, C = 1
	i = r/K - r/M
	N = M * no. of years
	
2) Compounding is more frequent than payments
	M = ?, K = ?, C = ?
	For discrete:
		i = (1+r/M)^C-1
	For continuous:
		i = e^(r/K)-1
	N = K * no. of years

3) Compounding is less frequent than payments

Evaluation of business and engineering assets:

Independent vs Mutually exclusive investment projects: -Most firms have a number of unrelated investment opportunities availale. In some projects economic attractiveness can be measured, and a decision to accept or reject the project can be made without reference to any of the other projects. In other words, the decision regarding any one project has no effect on the decision to accept or reject another project. Such projects are said to be independent. -In many engineering situations, we are faced with selecting the most economically attractive project from a number of alternative projects, all of which solve the same problem or meet the same need. It is not desirable to choose more than one project in this situation, and the acceptance of one automatically entails the rejection of all of the others. Such projects are said to be mutually exclusive

PAYBACK METHOD: -Screens projects on the basis of how long it takes for net receipts to equal investment outlays -Whether to pursue a project is if its payback period is shorter than some specified period >Conventional payback method: ignores time-value-of-money considerations

	Advantages:
		-Simple and easy to calculate
		-Interpreted in tangile term of years
		-Does not require any assumptions about the project in terms of timing, life-time or interest rate
		-Eliminate the non-potential alternatives
		
	Disadvantages:
		-Fails to measure profitability
		-Takes no account of time value of money
		-Does not allow for the possible advantages of a project with a longer economic life
		
>How to solve?
	Ans: Make a tabular chart with cumulative cash flow, then the one which has the first positives lie the answer, from there do the linear interpolation to get just 0. Say 3 ma negative ra 4 ma positive aayo then the payback period lies between 3 and 4th year.
		y - y1 = (y2-y1)/(x2-x1) * (x-x1)

>Discounted payback method: includes them
	
	Advantages:
		-Considers TVOM
		-Considers riskiness of project's cash flow
	
	Disadvantages:
		-Does not give cleare data whether investment increases firm's value or not
		-Requires estimate of the cost of capital in order to calculate the payback
		-Ignores cashflows beyond the discounted payback period
				
>How to solve?
	Ans: The same but here cash flow column will be discounted to the present

DISCOUNTED CASH FLOW ANALYSIS: -Takes into account the time value of money over the entire project life

NET-PRESENT WORTH CRITERIA: -Present worth of all cash inflows is compared against the present worth of all cash outflows associated with an investment project -Difference between the present worth of these cash flows is referred to as the net present worth (NPW), whose value determines whether the project is an acceptable investment -NPW analysis further allows us to select the best project by comparing their NPW figures -STEPS: 1. Determine the interest rate that the firm wishes to earn on its investments. The rate you determine represents the rate at which the firm can always invest the money in its investment pool (MARR). Usually, selection of the MARR is a policy decision made by top management. 2. Estimate service life of project. 3. Estimate cash inflow and outflow for each period over the service life 4. Determine the net cash flows 5. Find PW of each net cash flow at the MARRR
```
 PW(i) = NPW calculated at i MARR
 	= A0/(1+i)^0+ A1(1+i)^1 + ... + AN(1+i)^N
 	= sum_{n=0}^{N} An/(1+i)^n
 	= sum_{n=0}An(P/F,i,n)	
 	
 where, 
 	An = Net cash flow at end of period n
 	i = MARR (or cost of capital)
 	N = Service life of the project
 	
```
Single project evaluation: -A postive NPW means that the equivalent worth of the inflows is greater than the equivalent worth of outflows, so the project makes a profit. -Therefore, if the PW(i) is positive for a single project, the project should be accepted; if the PW(i) is negative, the project should be reject i.e. If PW(i) > 0, accept the investment If PW(i) = 0, remain indifferent If PW(i) < 0, reject the investment

Break-even interest rate: -MARR at which PW is zero

Tf is MARR? -If the firm did not invest in the project and left the amount in the pool the fund would grow at MARR -Fund can borrow all of its capital from a bank at an interest rate of MARR Basis for selecting the MARR: -First element if the cost of capital, which is the required return necessary to make an investment project worthwhile -Includes both the cost of dept (the interest rate associated with borrowing) and the cost of equity (the return that stockholders require for a company) -The cost of capital determines how a company can raise money (through issuing a stock, borrowing, or a mix of the two), so this is normally considered as the rate of return that a firm would receive if it invested money someplace else with a similar risk -Second elemtn is a consideration of any additional risk associated with the project, if is a normal risk category, the cost of capital may already reflect such a risk premium
FUTURE-WORTH ANALYSIS:
ANNUAL EQUIVALENT ANA:
CAPITALIZZED EQIV ANW: -When the life of a proposed project is perpetual or the planning horizon is extremely long (say, 40 years or more) -Capitalized cost represents the amount of money that must be invested today to yield a certain return A at the end of each and every period forever, assuming an interest of i, on limits: -(so k ho ta bhanda euta infinite annuity xa bhane teslai agadi leuni ta ho) CE(i) = A/i = AW/i (annuity of twakka ek step agadi aauxa hai)

Note: if there is gap wala annuity then teslai smooth wala annuity ma convert garnxa milxa CC wala numerical ma plus gap bata continue bhako annuiy lai agadi leuni kura ta bhaihalyo
RATE-OF-RETURNS: -The rate of return is the break-even interest rate i* that equates the present worth of a project’s cash outflows to the present worth of its cash inflows, PW(i*) = PW_{Cash inflows} - PW_{Cash outflows} = 0 -IRR is the fund that remain internally invested in the projected, means that the equipment project under consideration brings in enough cash to pay for itself and slo provide the firm with a return of IRR% on its invested capital -If the IRR exceeds the MARR, assure that the company will more than break even
```
 If IRR > MARR, accept the project
 If IRR = MARR, remain indifferent
 IF IRR < mARR, reject the project
 
```
-(SOLVE GARNA TA GAAD HUNXA TA:) -find PW for some number of i’s that you want until you find just postivies and negatives -smaller i ko lagi positve hunxa ani ghatdai negative tira janxa -the do interpolation as i* = i1 + PW1/(PW1-PW2)(i2-i1) -ek thau negative ra postive bhayo bhane yo simple investment, multiple thau ma change bhayo bhane mixed investemests

-Mixed investments, when firm acts as a burrower, requires ERR -If any of the project balance calcuated at project’s i* is positive, the project is not a pure investment -(i* bhaneko ta balance negative negative huni ani last ma gayera break otu huni ho ni ta sathi) -A positive project balance indicates that, at some time during the project life, the firm acts a burrower [PB(i*)n > 0] rather than an investor in the project [PB(i*)n < 0] -(SOLVE GARNI YESARI:) -negative haru lai disscount garni MARR rate ma (which is external investment rate) -Positive haru lai compound garni MARR rate ma -ani postiive haru lai discount garni i* rate ma, equate garera i* nikalni
LIFE-CYCLE COST ANALYSIS: -LCCA is a process of evaluating the economic performance of various design options that have differing initial costs, operating costs, maintainence costs, and possibly different life cycles -Estimates will cover the entire life span from the early conceptual stage, through the design and development stages, throughout the operating stage, and even the disposal stages -Public sector projects are usually evaluated using BC analysis, rather than LCC analysis, because estimates to the citzenry are difficult to make with much accuracy -LCC estimates may be categorized into a simplified format for the major phases of acquisition, operation and phaseout and their respective stages:
1. Acquisition phase: (see slides)
’
BENEFIT-COST ANALYSIS: -BC is a decision making tool that is used to systematically develop useful information about the desirable and undesirable effects of public projects. In other words, benefit–cost analysis attempts to determine whether -Let B and C be the present values of benefits and costs:
```
 B = sum{n=0 to N}bn(1+i)^{-n}
```
and, C = sum{n=0 to N}cn(1+i)^{-n} where, bn, cn = benefit at the end of period n N = project life i = sponsor’s interest rate Accept if BC(i) > 0;

From our book:
1. Conventional BC ratio: BC ratio = PW(B) / (PW(I) + PW(O and M) - PW(S))
2. Modified BC ratio: BC ratio = [PW(B) - PW(O and M)] / (I - PW(S))

DISCLAIMER: -While comparing more than two (2 ta lai ta hunxa) projects, you cannot use IRR or MRR, BCR, because they are relative measures 1. First calculate all the IRR, MARR of all of it (reject the one with less than MARR) 2. Now sort them based on initial investment and subtract successively to form n-1 rojects 3. Do the IRR analysis again then for A-B if greater than MARR then accept A and reject B, else reject A and accept B

Life cycle costing:

Aile samma ta same life ko barema kura bhayo, different life xa bhane k garne bro?

Repeatability assumption: -Duita ko LCM lini aru teta samma cash flow lai extend garni -Investment, revenue, salvage? -Investment lai ni copy garni at equal intervals -Annuity (annual E and O) lai chai same tarika le expand garni -Salvage lai k garni? investment jasari nai repeat garni NOTE: salvage value lai 10% of investment bhanxa, tyo chai present worth nai hunxa
Coterminated: A. Useful life > study period: (need to truncate) -Investment lai j ko tei form ma PW ma lini -Reveneue lai ni j ho tei, mathi samma nai huna sakxa tara we truncate it -Salvage value? yes, bich ma project rokyo bhane market value bhanxa teslai -ALSO we need to do is: find market value at the end of n years: sum of PW of remaining capital recovery cost at the end of n years which comes by converting the [initial investment+salvage value] to annuity and then taking from 4 to useful life + PW of salvage value at the end of useful life (N) at the end of nth years

B. Useful life < study period: (need to extend) -Either you do like repeatibility argument if possible -Or invest it to the future meaning that calculate the FW then only PW

REPLACEMENT THEORY: when could be a good time to replace defender?

-AEC is the annual equivalent cost to maintain the asses in operation (jun chai costs ra capital recovery ko sum hunxa for some reason)
-The reason is that the capital recovery goes into the project as the cost meaning that we are not absorbing CR from the project means taht we are putting that amount into the project itself

	AEC(i) = CR(i) + OC(i); is an annuity though
	
-The year at which AEC is minimum is the economic life of the asset, at which point we consider the replacement
1. Capital recovery niikalni tarika:
	CR(i) which is the anniuity 
		= I * (A/P, i%, N) + S * (A/F, i%, N) if asset is N years long
	
		= (I-SN) (A/P, i%, N) + SN(i%)
		= (I-SN) (A/F, i%, N) + I(I%)
		here investement is at 0 and salvage is at the end

2. Operating cost nialni:
		= deko operating costs haru sablai ekmusta single flow ma laijani ani annuity ma convert garni
		
Finall, euta table banayera sum garni jun minimum hunxa tei nai ho answer

-Euta asset lai arko le replace garda better ki nai
-Aile chalirako project lai assume it the total new project starting from the current time
-In cost analaysis, its market value is transferred to another replacer asset and then evaluated
-Now can find PW, AW or whatever of your choice for comparison
-opportuity cost ma chai current market value lai negative cash flow banauni, meaning that that amount is invested onto the existing project itselfxs

<ajahi arko> combination garera assets haru chalauni, certain years yo certain yo

-Find AEC of each if not already given then limit the age of each asset upto that year only
-ani AEC rakhera cashflow banauni ani tyo AEC ko matra PW nikalni (investsment ta same ho) so yesari 4-5 ota cases herni ani value nikalni

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Aile samma ta same life ko barema kura bhayo, different life xa bhane k garne bro?