Quantitative Method and Financial Economics


QuantitativeMethod and Financial Economics


Part1: Quantitative Methods

NetPresent Value

Netpresent value is the present value of cash inflows subtracted thepresent value of the cash outflows (Berk,DeMarzo, &amp Harford, 2012).If the net present value of an investment opportunity is negative,the investment is not worth and should thus, be rejected by theinvestor. In other words, net present value (NPV) is the decrease orincrease in affluence accumulating to an investor when she or heinvests. Net Present value is donated as NPV. Positive NPV projectsincrease wealth while negative NPV projects decrease wealth.


N= holding period

n=each period

C=cash flows

r=investor’s rate of return

Alternatively,NPV can be calculated as the difference between at least one inboundcash flows and at least one outbound cash flows.

NPV= Present value (PV) of cash inflows – present value (PV) of thecash outflows

Netpresent value is generally an imperfect tool for analysis as it hasmany problems:

  • There is no valid quantitative derivation of discount rate adjustment to account for risk. In fact, it is normally a presumption or guess.

  • Projected cash flows hardly match the real results, particularly when the original approximations are extremely positive.

  • An investment mainly depending on the NPV analysis merely assess the conditions of a particular investment instead of looking at the entire system of generating profit hence, the investment utilizing NPV can be sub-optimized.

NPVnormally falls into three categories

  • Zero NPV—implies that one is paying exact price of the asset

  • Negative NPV—implies that one is paying more than exact price of the asset

  • Positive NPV—implies that one is paying less than the actual price of the asset


Perpetuityis a fundamental concept in corporate finance. The perpetuity conceptallows for the valuation of real estates, stocks, as well as otherinvestments prospects. Theoretically, perpetuities valuation isquite easy and not complicated.

Inthe field of business finance, people try to compare the value ofvarious streams of cash flows. Now and again people exchange a givenamount of value for a known stream of future payments. Nevertheless,for perpetuity case, the payments endless. A perpetuity is an endlessor endless stream of cash flows. It implies that if one purchase orbuy a perpetuity rights after paying the stated amount, an endlessrepayment is expected.

Eventhough perpetuity valuation may not appear instinctive, it is needed.Many types of investments that have features similar to perpetuity.For instance, common stocks, which are investments in companyoperations. In theory, companies have infinite life. Thus, theshareholders by currently paying the price of the stick will receivean endless stream of future dividends. This is why common stocks areconsidered a perpetuity. Besides real estates are valued as aperpetuity because after purchasing the real estate, the owner willreceive a ceaseless torrent of rental payments.

Themost contradicting part of perpetuity is its finite value. One maywonder why a chain of inestimable cash stream have a finite orlimited valuation. However, it is because the real value of futurecash flows normally keeps on dropping. In early years, the PV(present value) is high, but the amount of payment is fixed under aperpetuity (Berk, DeMarzo, &amp Harford, 2012).

Theformula for perpetuities valuation is given as


C= the cash flow amount received every period

PV=Perpetuity present value

R=requiredreturn rate


BondValuation is a method used to determine the fair value of a givenbond. The valuation of bond includes calculating the value of thebond upon maturity (par value or face value) and the present value(PV) of the future interest payments on the bond (its cash flow)(Berk, DeMarzo, &amp Harford, 2012).

Bondvaluation is among the key factors that investors must considerbefore opting to invest in a given bond. Other key considerationsinclude issuing the creditworthiness of the company, whichestablishes if a bond is junk or investment-grade price appreciationpotential of the bond and the prevailing interest rates of themarket and whether they are projected to increase or decrease in thefuture (Berk, DeMarzo, &amp Harford, 2012).

Formulafor bond valuation is given by:

Valuationof common stock

Valuationof common stock is a process that determines the value of shares ofstock in a given company. An individual with one share in a companywith 1-million shares outstanding is the owner of the one-millionthof the company the share value must represent the percentage worthof the company. Stock valuation is performed using either of the twobasic approaches (Berk,DeMarzo, &amp Harford, 2012).The first method looks at the fundamentals including earning analysisand discounted cash flow. It is the same as bond valuation however,the cash flows are harder to predict making the stock a hazardousinvestment. The second method is studying the conditions of themarket—demand and supply for the stock as well as general trends ofthe financial markets. It is quite difficult to value common stock.The cash flows are not easily identified or are unstable. One of themost common models used in the valuation of stock is the Gordondividend valuation Model (Berk,DeMarzo, &amp Harford, 2012).


D1= 1st year Dividends ks =&nbspExpectedreturn rate of investorsg =&nbsprate of growth in Dividends.

D1=currentdividends x (1+g)

Constantgrowth Formula

Constantgrowth model is employed to calculate the current price of a shareproportionate to its dividend payments, the projected dividends’growth rate, and the expected rate of return by the investors withinthe market (Berk,DeMarzo, &amp Harford, 2012).

Timevalue of money (Present discounted Value)

TVM(Time Value of Money) stipulates that the value of money now is morethan the value of the same amount of money in several years to come.This is attributed to the earning capacity of money. It implies thatprovided money can generate interest, it is more worth if it isreceived soonest (Berk,DeMarzo, &amp Harford, 2012).

Basedon the actual condition in question, the formula of TVM may varyslightly. For instance in the case of perpetuity or annuity, thegeneralized formula has less or additional factors/elements. However,the most basic TVM formula considers the following variables:

i=interest rates

PV= Present value of money

FV= Future value of money

t= number of years

n= total compounding periods per year

Basingthe TVM formula on these variables:


TheInternal rate of return (IRR) of is a rate of discount making the NetPresent Value (NPV), equals zero (Berk,DeMarzo, &amp Harford, 2012).Similar to Net Present value technique, the Internal Rate of Returnconsiders all cash streams for a given projects as well as well asadjustments for the time value of money. The IRR estimation arealways expressed in percentage. When IRR technique is employed tomake decisions on capital budgeting, the proposed venture’s IRR iscompared with the rate of return that organization expect for theventure. The expected return rate is known as the hurdle rate. Theventure will be accepted only if the IRR of the venture is equal toor more than the hurdle rate.The formula for IRR is (Berk,DeMarzo, &amp Harford, 2012):


P0,P1, P2.. . Pn is the cash flows for 1st, 2nd, 3rd. . . nth periods respectively

C=the internal return of the project.


APR(the annual percentage rate) is the yearly rate earned through aninvestment or rate charged for borrowing. It is expressed as apercentage representing the actual annual cost of funds over the loanterm. It includes any additional expenses or fees with thetransaction however, do not consider compounding.

TheProfitability index rule

Theprofitability index ruleis basically varying the Net present value rule. Generally is NetPresent Value (NPV) is negative, the profitability index would beless than 1 and if NPV is positive, the Profitability index (PI)would be greater than 1 (Cuthbertson&amp Nitzsche, 2014).

Profitabilityindex (PI) is method for evaluating an investment. It is determinedby dividing the Present Value of future cash streams of a givenproject by the initial investment needed for the project.

Theprofitability Index rule give guidelines of whether or not to acceptthe project. If PI is greater than 1 then a project is accepted,stay indifferent if the PI is equivalent to zero, and reject aproject if the PI is less than 1.ThePayback Rule

Thepayback rule is the time duration needed to recover an investmentcost.

Thepayback period is given by the formula:

Part2: Financial economics

Financialeconomics is a branch of economics that explores the utilization aswell as the resources distribution within markets where decisions arenormally made under uncertainty (Cuthbertson&amp Nitzsche, 2014).Financial decisions must consider future events, whether those beassociated with individual portfolios, stocks or the general market.Financial economics utilizes theory to assess how time, uncertainty(risk), information, and opportunity costs can create disincentivesor incentives for a particular decision (Cuthbertson&amp Nitzsche, 2014).

Financialeconomics in most cases involves developing sophisticated models tohelp test various variables influencing certain decisions. Suchmodels assume that institutions or persons making decisions actrationally although it is not certainly the case. In FinancialEconomics, irrational behavior of individuals or parties isconsidered as a potential risk factor. Financial economics putsemphasis on the interrelation of financial variables includinginterest rates, shares, and prices. Financial economics focusesmainly on two areas corporate finance and asset pricing: the firstbeing users of capital while the second being capital providers(Cuthbertson&amp Nitzsche, 2014).

Financialeconomics deals with the allocation as well as the distribution ofeconomic resources spatially and across time in an environment thatis uncertain. It focuses on making of decision under uncertainty inthe financial markets context, and the resultant financial andeconomic models and principles. It also involves deriving policyimplications or testable from satisfactory assumptions. Financialeconomics is built on decision theory and microeconomics theory.

MathematicalFinance provides numerical or mathematical models suggested byfinancial economics. Financial econometrics is one of the financialeconomics branches that employs econometric methods to parameterizethese relationships. Financial economics is often taught at thepostgraduate level. However, specialist undergraduate degree programsare now offered in this field.

Financialeconomics generally focuses on the decision making where two elementsor concerns are mostly significant: firstly, parts of the outcomesare uncertain (risky) secondly, both the outcomes and decisions maytake place at different times. Financial economicmics is oftenapplicable to investment decisions especially in financial markets,but it is also closely linked to parts of microeconomics associatedwith saving and insurance. Financial economics has many differentaspects, and this include and not limited to (Lengwiler,2013):

Discounting—Makingof decision over time recognizes that the value of $1 now is greaterthe value of $1 several years to come. Therefore, the value of $1 inthe future need to be discounted to take into account inflation, riskand the future. Ignoring or failing to discount correctly can lead toissues and hitches including systematic underfunding of pensionschemes experienced recently.

Managementand Diversification of Risk—most ads for financial goods based onstock market act as a reminder to potential purchasers that theinvestments value could rise or drop. Thus, even though stocks yielda return that is averagely high, it is principally to compensate foruncertainty or risk. As a result, all financial institutions normallylook for means to insure or hedge the risk. However, uncertainty mustremain low for overall risk. If share X performs excellently whenshare Y performs poorly and the inverse is true then the two sharesperform a perfect ‘hedge.` (Lengwiler,2013).

Financialeconomics rely mainly on basic accounting concepts andmicroeconomics. Besides, it demands that one has full knowledge aboutstatistics and basic probability techniques, since these are thestandard tools employed to measure as well as evaluate risk(Lengwiler,2013).

HowFinancial Economics Work or operate

Financialeconomics is a field that is highly quantitative. It studies theasset’s fair value by assessing the linked risk factors cashgenerated by the asset as well as whether the generation of the cashflow is dependent on another asset or an event. In addition, it takesinto account the market price of the asset as compared to that ofparallel assets while studying the fair value of the asset(Lengwiler,2013).

Besides,financial economics studies financial instruments including stocksand commodities, bonds, market regulations, financial institutions,and the markets in which these instruments are traded. The basicconcepts of financial economics often revolve around the CapitalAsset Pricing Model and Portfolio Theory.

TheCAPM (Capital Asset Pricing Model) aids to determine the price of arisky security by assessing the related risks and expected returns.The model depends on the point that investors must be compensated forall the risks they undertake and the time value of money. The CAPMstates that the expected return from security is the sum of the rateon a risk premium and a risk-free security (Lengwiler,2013).

ThePortfolio Theory proliferates the reduction of the risk profile of aninvestment portfolio by diversifying an investment capital. Byassuming that investors are averse to risk, the theory concentrateson the assets (resources) allocation, valuation securities,measurement of portfolio performance and portfolio optimization.

FinancialEconomics Benefits

Financialeconomics assist investors to make very informed decisions regardinginvestment options.


Berk,J., DeMarzo, P., &amp Harford, J. (2012). Fundamentalsof corporate finance.Boston: Prentice Hall.

Cuthbertson,K., &amp Nitzsche, D. (2014). Quantitativefinancial economics: Stocks, bonds and foreign exchange.Chichester, England: Wiley.

Lengwiler,Y. (2013). Microfoundationsof financial economics: An introduction to general equilibrium assetpricing.Princeton, N.J: Princeton University Press.