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Examples Frequetly used MS-Excel fuctios Add-Is

1 Paos Kostati Power ad Eergy Systems Egieerig Ecoomics Itroductio ad Istructios Cotets List of Files with Examples Frequetly used MS-Excel fuctios Add-Is developed by the Author Istallatio Istructio of the Excel Add-I

2 Frequetly used MS-Excel fuctios I the followig some of frequetly used MS-Excel fuctios are listed ad explaied. Withi brackets the ame of the fuctio i the Germa Excel versio is icluded. Compoudig ad discoutig fuctios Future value fuctio FV (ZW): Returs the future value of a ivestmet based o periodic costat paymets ad a costat iterest rate. Sytax: FV(Rate, Nper, Pv, Fv, Type) Preset value fuctio PV (BW): Returs the preset value of a series of periodic future equal paymets ad a costat iterest rate. Sytax: PV(Rate; Nper; Pmt; Fv, Type) Net preset value fuctio NPV (NBW): Calculates the et preset value of future paymets usig a costat discout rate. I cotrast to the PV fuctio the paymets ca be equal or uequal, positive (cash iflows) or egative (cash outflows). Sytax: NPV(Rate, value 1, value 2,.value ) If the values 1 to value are arraged i series, just mark the rage of series (e.g. A2:A20) istead of isertig the values oe by oe. Aual equivalet amouts (auities) fuctio PMT (RMZ): Calculates the aualized costat amouts of the preset value of a iitial paymet (pricipal) at a costat iterest rate. Sytax: PMT(Rate; Nper; Pv; Fv; Type) Rate: iterest rate i % per period Nper: Number of periods Fv: Future value (i the examples i this book it is usually zero) Type: For paymets at the year s ed zero, at the year s begiig 1 (i the examples i this book it is usually zero) Pmt: The costat future paymets Pv: The preset value of CAPEX or pricipal Note: Excel assumes paymets to be cash-outflows ad returs them as egative amouts. I the Cost Models i this book all series are costs, hece it does ot make sese to desigate them egative values. All paymet series have positive values therefore a mius sig must be iserted i frot of the fuctio to get positive values. Other Excel fuctios Iteral Rate of Retur fuctio IRR (IKV): Returs the Iteral rate of retur of a periodic series of paymets cosistig of cash i-flows (positive values) ad cash-outflows (egative values). The paymets must occur i regular itervals (e.g. yearly) but they do ot have to be equal. Sytax: IRR(rage of values; guess) Rage of values: Just mark the rage of paymet series (e.g. A2:A20) Guess: Give a estimated IRR otherwise Excel will assume 10%.

3 Modified Iteral Rate of Retur fuctio MIRR (QIKV): As IRR, however, the returs are reivested. MIRR cosiders both the IRR of the iitial ivestmet ad the iterest rate of the reivestmet. Sytax: MIRR(Rage of values; fiace rate; reivest rate) Rage of values: Just mark the rage of paymet series (e.g. A2:A20) Fiace rate: The iterest rate used i the iitial ivestmet Reivest rate: The iterest rate expected for reivestmets Exceedace Probability calculatio PXX: Exceedace probability is calculated usig the NORM.INV fuctio as follows. Sytax: X P=100 - Norm.Iv(Probability; mea; stadard deviatio) Probability: PXX, a umber betwee 0 ad 1 (or PXX/100); this is the probability correspodig to ormal distributio. Mea: This is the arithmetic mea of the distributio Stadard deviatio : This is a positive umber. Example: Exceedace Probability Mea value = 50 GWh/a PXX =5 =10 GWh / a GWh / a P P P Note: The cells PXX are customized: e.g. cell with 90; Format cells, custom, P90 ; isert Probability i the fuctio P90/100 istead of 0.9. Goal seek ad Table are frequetly used i examples. They ca be foud uder Data, what if aalysis. Goal seek will fid the right iput to obtai a certai result (e.g. fid rate to get NPV=0, this is the IRR). Data Tables allow calculatios of may differet possible iputs at the same time. This is a very useful tool for sesitivity aalysis.

4 Add-Is developed by the Author BWSesc: Calculates the preset value (PV) of a series of paymets escalatig with a costat escalatio rate. The Add-I is based o the equatio show below. Sytax: BWSesc(escalatio rate%; Discout rate%; Number of periods, startig value without escalatio). t= t p PV = P = P _ esc 0 t 0 t= 1 q q p q q p P 0 : the costat paymet each period before escalatio q=1+i : the discout factor, i : aual iterest rate p = 1+j : escalatio factor, j : escalatio rate (may be also <0!) : umber of years of the discoutig period Whereby: q p; q 0; p 0 If j > 0 the PV of the series is icreasig, if j < 0 it is decreasig! See Example 2 12, Preset value of Persoel costs over lifetime. ANesc: Coverts a series of paymets escalatig with a costat escalatio rate i costat aual equivalet amouts (auities). The fuctio calculates first the NPV of the series ad uses the PMT fuctio to covert the NPV i auities. The Add-I is based o the equatio show below. The fuctio is used for levelizig escalatig paymet series. Sytax: ANesc(escalatio rate%; Discout rate%; Number of periods, startig value without escalatio). q p p q 1 CU PAN _ esc = LC = P0 q p q 1 a P AN_esc : Auity of a series of escalatig paymets P 0: The costat paymet without escalatio q= 1+i : Discout factor, with i" discout rate (iterest rate) p= 1+j : Escalatio factor or geometric gradiet, with j escalatio rate : Number of periods (years) See Example 2 15, levelized aual persoel costs. ItCo: Calculates the iterest durig costructio assumig disbursemet of loa i costat istallmets over the costructio time. The A-I is developed based o the FV fuctio of Excel. Sytax: ItCo(Capex; loa % of CAPEX; years of costructio, iterest for loas, periods per year). See Example 2 8, iterest durig costructio.

Istallatio Istructio of the Excel Add-I If you just wat to use the authors Excel Add-I AddI_BWSesc_ANesc_ItCo.xlam without istallig the Add-I follow this istructios: 1.

5 Istallatio Istructio of the Excel Add-I If you just wat to use the authors Excel Add-I AddI_BWSesc_ANesc_ItCo.xlam without istallig the Add-I follow this istructios: 1. Copy the Excel Add-I file AddI_BWSesc_ANesc_ItCo.xlam ito the same directory where you also store your book examples (e.g. Ch2_FiacialMaths_Examples.xlsx) 2. To check if the Add-I is recogized accordigly ope the Example from Chapter 2: Ch2_FiacialMaths_Examples.xlsx ad verify if i work sheet Ex_2.12_PVesc_PersoelCosts the cell F13 is calculated propely. 3. If this is the case you ca ow ope the book example you would like to work with. If you would like to istall the authors Excel Add-i AddI_BWSesc_ANesc_ItCo.xlam permaetly use either the flowig istructio or use the official Microsoft homepage for guidace ( 1. Save the Excel Add-I file AddI_BWSesc_ANesc_ItCo.xlam as well as all examples (Ch*.xlsx) i the directory of your choice (e.g. "c:\data\book\") 2. After you have saved the file, click the Microsoft Office Butto withi Excel, ad click Excel Optios. 3. I the Excel Optios dialog box, click the Add-Is category. 4. I the Maage drop-dow list, select Excel Add-Is. The click the Go to butto. 5. I the Add-Is dialog box, select the butto Browse ad select the Excel Add-I AddI_BWSesc_ANesc_ItCo.xlam stored i your directory of choice (e.g. "c:\data\book\") ad select Ok. 6. Now the Excel Add-I Addi_Bwsesc_Aesc_Itco is show a ca be slected with the check box ifrot of the ame (as show below with the Add-I Myfuctios ). 7. After you follow these steps, your custom fuctios will be available each time you ru Excel 8. Available Add-Is: BWSesc (Preset value, of series with escalatio) ANesc (Auität eskaliereder Zahluge / Auity of a series with escalatio) ItCo (Bauzise / Iterest durig costructio)

2. The Time Value of Money

2. The Time Value of Money 2. The Time Value of Moey Problem 4 Suppose you deposit $100 i the bak today ad it ears iterest at a rate of 10% compouded aually. How much will be i the accout 50 years from today? I this case, $100 ivested