Economic Evaluation of Projects: Principles of Financial Math PDF - 2024/2025

AUIC A.A. 2024/2025 Course of Economic Evaluation of Projects prof. Giulia Datola Principles of financial math 3_October 2, 2024  Program of the course ECONOMIC EVALUATION OF PROJECTS A.Y. 2024/2025 18-set-24 8:15 - 11:15 L1_ Introd...

AUIC A.A. 2024/2025 Course of Economic Evaluation of Projects prof. Giulia Datola Principles of financial math 3_October 2, 2024  Program of the course ECONOMIC EVALUATION OF PROJECTS A.Y. 2024/2025 18-set-24 8:15 - 11:15 L1_ Introduction to the course and project work L2_The Nature of the Real Estate Market. Information on Real Estate Market. How to Theoretical + practical 25-set-24 8:15 - 11:15 T1 develop Market Analysis example Theoretical + exercise 02-ott-24 8:15 - 11:15 L3_ Basics of financial math and exercises in class L4_Market Value definitions and Market Value estimation: Sales Comparison Theoretical + exercise 09-ott-24 8:15 - 11:15 Approach (SCA) + Income Approach in class Theoretical + exercise T2 16-ott-24 8:15 - 11:15 L5_Market Value estimation: Cost approach + cost analysis in class Theoretical + practical 23-ott-24 8:15 - 11:15 L6_Private feasibility: Criteria and decision rules example 30-ott-24 8:15 - 11:15 L7_Project work revision I: Cost Analysis I revision Workshop in class for 06-nov-24 8:15 - 11:15 L8_Private feasibility: Business Plan - workshop "how to develop a business plan" PW Theoretical + practical T3 13-nov-24 8:15 - 11:15 L9_Public feasibility: Stakeholders Analysis and Multicriteria Analysis example 20-nov-24 8:15 - 11:15 L10__Project work revision II: Business plan II revision Workshop in class for 27-nov-24 8:15 - 11:15 L11_Public feasibility: Community Impact Evaluation (CIE) method + workshop PW 04-dic-24 8:15 - 11:15 L12_Project work revision III: final review III revision 18-dic-24 8:15 - 11:15 L13_Project work revision IV: final review IV revision  Principles of Financial L3 02/10 Math  Outline ▪ Introduction ▪ Definitions ▪ Interest ▪ Discounting and postponement ▪ Annuity ▪ Exercises  Introduction (1/3) Financial mathematics deals with the study of financial operations. The financial calculation consists in adding, subtracting or, comparing, monetary values referred to different times. It is essential to solve certain economic and estimative problems. It provides the tools needed to compare financial performance related to different time periods  Introduction (2/3) Within numerous estimation methods it is necessary to work with values that have different time frames (for examples costs and revenues of a transformation project) This values can change during the time (growth/decay) This imposes the use of tools that allow operating with values differently positioned over time We refers to financial operations  Introduction (3/3) The complexity of financial mathematics tools can certainly not be summarized in 1 lesson! Therefore, the objective is to focus our attention on some tools that allow some important estimation operations  Definitions Principal (P) = Initial money that you will invest Interest (I) = the price for using the monetary capital. (It represents the remuneration due to the subject who loans a capital money for a determined period of time). Accumulated amount (A) = Principal plus interest Interest rate (r) = interest accrued per capital unit and per unit of time. It can be expressed in percentage terms (e.g. 3%) or unit terms (0.03).  Interest, Principal, Accumulated amount The interest (I) is defined as the price for the use of the monetary capital. (It represents the remuneration due to the subject who loans a capital money for a determined period of time). P + I = A T0 T1  Interest Simple interest Compound Interest  Interest Simple interest It is directly proportional to the principal and time. Interest is simple when the accrued interest does not in turn accrue further interest. It is used when considering a period of time less than 1 year I = Prt p= principal r = interest rate t = time (num of days, months) Example: P= 2,000€ I = (2,000)(0.05)(4/12)= 33.3€ r = 5% t = 4 months  Interest Example: Simple interest Every year the interest earned are Determine the Accumulated amount of capital of 120,000 not summed to the principal € considering a simple interest for a period of 4 months with and interest rate of 3%. I= Prt A= P+I A= P+Prt A= P(1+rt) P= A/(1+rt)  Interest Example: Simple interest Every year the interest earned are Determine the Accumulated amount of a capital of not summed to the principal 120,000 € considering a simple interest for a period of 4 months with and interest rate of 3%. I= Prt I=Prt A= P+I A=P+I A= P+Prt I=120,000*0.03*4/12 = 1,200 € A= P(1+rt) A= 120,000+1,200 = 121,200 € P= A/(1+rt)  Simple Interest The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. A= P(1+rt) Postponement P A 0 n Discounting Method for calculating the present value of a future amount of money, taking into consideration the interest rate. P= A/(1+rt) When determining how much should be paid today for an investment that is expected to produce income in the future we have to apply an adjustment called discounting to income received in the future to reflect the true value of money. Simple interest and discounting: example Suppose that an individual is considering an investment that promises a return of 15,000 € after 6 months at the interest rate of 5%, what would be the present value of the capital? P = A /(1+rt) = = 15,000 €/(1+0.05*6/12) = 14,634 €  Interest Compound interest It is used for those investments that are over 1 year. In this case the interest is calculated year by year. In the case of compound interest, the interest that accrues within a certain period (t) is added to the initial capital and accrues new interest. Example: Investment of 100 euros for 2 years at the interest rate of 5% per year. 1- after the first year you earn 5 euros. 2- In the second year, you will earn 5% on 105 euros (100 euros + 5 euros), 3- so you earn 5.25 euros.  Interest Compound Interest P= 2000 € I= Prt r = 5% t = 3 year P1= P0+P0r P1= P0 (1+r) P2= P1+P1r I= Prt I1= (2,000)(0.05)(1)= 100 € P2= P1(1+r) P1= 2,000+100= 2,100 € P2= P0(1+r) (1+r) = P0(1+r)2 I2= (2,100)(0.05)(1)= 105 € A= P0(1+r)t P2= 2,100+105= 2,205 € P0= A/(1+r)t I3= (2,205)(0.05)(1)= 110.25 € P3 = 2,205 + 110.25 = 2,315. 25 €  Compound Interest The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. A= P(1+r)t Postponement P A 0 n Discounting Method for calculating the present value of a future amount of money, taking into consideration the interest rate. P= A/(1+r)t When determining how much should be paid today for an investment that is expected to produce income in the future we have to apply an adjustment called discounting to income received in the future to reflect the true value of money.  Coefficient of discounting / postponement Simple interest Compound Interest Postponement = (1+rt) Postponement =(1+r)t q= (1+rt) qt = (1+r)t Discounting= 1/(1+rt) Discounting= 1/(1+r)t 1/qt =1/(1+r)t 1/q= 1/(1+rt)  Annuity A sequence of equal payment made at equal periods of time The time between payment is called Payment period The time from the beginning of the first payment period to the end of the last period is called Term of the annuity A1 A2 A3 A4 A5 A6 A7 A8 0 1 2 3 4 5 6 7 8 Used to: 1) To accumulate funds (when you make regular deposits in a saving account) 2) To pay out funds (eg. when you receive regular payment from pension after you retire)  Annuity Not limited annuity: an infinite number of annuity Number Limited annuity: limited number of annuity An ordinary annuity is an annuity where payments are made at the end of each period and the frequency of payment is the same as the frequency of compounding interest Date of payment A annuity due is an annuity where the payment are made at the beginning of each period  Ordinary annuity not limited a a a a a a a 1 2 3 4 5 6 7 n a A = r Formula for the capitalization This formula is of fundamental importance in real estate evaluation and it is employed for determining the market value of a building on the basis of the income that it produces over its economic life.  Recall Annuity: series of equal payments at equal interval of time Examples: Saving for retirement Getting paid from a pension plan Paying a rent for a house Ordinary annuity: payment are made at the end of the period Due annuity: payment are made at the beginning of the period  Conclusion The following principles must be taken into account when solving any estimative question that requires the application of financial mathematics: 1) each value cannot be moved over time without taking into account the relative interest or discount; 2) Addition/subtraction and comparisons between values referring to different periods cannot be performed: to do this the values must first be made homogeneous, that is, they are reported at the same time.