Financial management is that managerial activity which is concerned wi planning and controlling of the firm’s financial resources. In other words is concerned with acquiring, financing and managing assets to accompli: the overall goal of a business enterprise (mainly to maximise tl shareholder’s wealth). “Financial Management comprises of forecasting, planning, organizin directing, coordinating and controlling of all activities relating acquisition and application of the financial resources of an undertaking | keeping with its financial objective.” Raymond Chambers Another very elaborate definition given by Phillippatus is “Financial Management is concerned with the managerial decisions th result in the acquisition and financing of short term and long term credi Jor the firm.” rl ;wlldministration and = ] ) " aa a pe te |FINANCIAL MANAGEMENT Narrow Concept - PROCUREMENT OF FUND - MANAGEMENT OF CASH - MAINTENANCE OF THE LIQUIDITY OF FUNDSFINANCIAL MANAGEMENT BROAD CONCEPT - INVESTMENT DECISIONS - FINANCING DECISIONS - DIVIDEND DECISIONS ie ee eeimportance of Financial Management The best way to demonstrate the importance of good financial management is t: describe some of the tasks that it involves:- > Taking care not to over-invest in fixed assets > Balancing cash-outflow with cash-inflows » Ensuring that there is a sufficient level of short-term working capital > Setting sales revenue targets that will deliver growth > Increasing gross profit by setting the correct pricing for products or services > Controlling the level of general and administrative expenses by finding more cost efficient ways of running the day-to-day business operations, and > Tax planning that will minimize the taxes a business has to pay.Scope of Financial Management Based on Ezra Solomon's concept of financial management, following are the scope of financial management: (a) Determination of size of the enterprise and determination of rate of growth. (b) Determining the composition of assets of the enterprise. (c) Determining the mix of enterprise’s financing i.e. consideration of level of debt to equity, etc. (d) Analysis, planning and control of financial affairs of the enterprise. Frarcal ManagementOBJECTIVES OF FINANCIAL MANAGEMENT Maximisation of profits of a firm Maximisation of wealth of a firm Survival and Growth of the firm Minimisation of financial charges eeProfit maximisation: Stresses only the efficient use of capital resources efor) rep ites precise, allows bivsittsgu carton} Not specific time Heslop Colm elcoi cate) be measured beater ear ithg Etre arnt iatedShareholders’ wealth maximisation: According to Van Home, “Value of a firm is represented by the market price of t company's common stock. The market price of a firm's stock represents the focal judgme of all market participants as to what the value of the particular firm is. It takes into accou present and prospective future earnings per share, the timing and risk of these earnings, t dividend policy of the firm and many other factors that bear upon the market price of t stock. The market price serves as a performance index or report card of the firm’s progre: It indicates how well management is doing on behalf of stockholders.Comparison between Wealth Maximisation and Profit Maximisation Cs [Advantages Dieat vantages ss Large amount of (i) Easy to calculate profits (i) Emphasizes the short term c profits — (ii) Easy to determine the Bains (maximise) link between financial ii) Ignores risk or uncertainty decisions and profits. (iii) Ignores the timing of retu (iv) Requires immediate resources. er Highest market (i) Emphasizes the long term (i) Offers no clear relationshi value of gains between financial decisions ar . shares. (ii) Recognises risk or share price. uncertainty (ii) Can lead to management (iii) Recognises the timing of @PXiety and frustration. retums (iv) Considers shareholders’ return. _ _ aConflicts in Profit versus Value Maximisation or Wealth Maximisation Principle ESS STEIN Cs Ma Au CREE WS NYSDEC) It measures the performance of a It measures the performance of business firm only on the basis of a business firm on the basis of the profits. shareholder's wealth. It is based on the assumption of perfect —_ It assumes efficient capital market. competition in the product market. This goal ignores the Time Value of This goal considers the Time Value of money. moncy. It does not take into account the risk It takes into account the risk involved in involved in achieving this goal. any particular investment project. LLLCapital Budgeting Decisions |}... | Capital Budgeting Decisions |} _. syodernisation Internal Funds ——— \ |= Expansion Debt Funds <= Need to Raise Funds '__. Diversification External Equity. ——! Capital Structure Decisions f L Existing Capi StructureRole of a Chief Financial Officer (a) Financial analysis and planning: Determining the proper amount o funds to employ in the firm, i.e. designating the size of the firm and it: rate of growth. (b) Investment decisions: The efficient allocation of funds to specific assets. (c) Financing and capital structure decisions: Raising funds on favourable terms as possible i.e. determining the composition of liabilities. (d) Management of financial resources (such as working capital). (e) Management of Retained Earnings (f) Risk management: Protecting assets. eeeTime Value of MoneyTIME VALUE OF MONEY The different value per unit of money at different time periods is called as the time value of money. The value of money received today is more than the value of same amount receivable at some other time in future. “A RUPEE TODAY IS WORTH MORE THAN A RUPEE TOMORROW”REASON BEHIND THE TIME VALUE OF MONEY (i) Preference for Present Consumption: Individuals have a preference for current consumption in comparison to future consumption. In order to forego the present consumption for a future one, they need a strong incentive. Say for example, if the individual's present preference is very strong then he has to be offered a very high incentive to forego it like a higher rate of interest and vice versa. Interest Income Inflation: Inflation means when prices of things rise faster than they actually should. When there is inflation, the value of currency decreases over time. If the inflation is more, then the gap between the value of money today to the value of money in future is more. So, greater the inflation, greater is the gap and vice versa. (iv) Risk: Risk of uncertainty in the future lowers the value of money. Say for example, nonreceipt of payment, uncertainty of investor's life or any other contingency which may result in non-payment or reduction in payment.USES OF TIME VALUE OF MONEY It is used to calculate : ¢Future Value of Cash Flow * (Compounding Technique) * Present Value of Cash Flow * (Discounting Technique)Future Value and Present Value Accrued amount or Future Value at nth year (FV.)on a principal P after n payment periods at i (in decimal) rate of interest per payment period is given by: FV, = PV x(i+i)" Where, = FV, = Future Value after nth year FV, Po (FVIF.n) PV = Principal amount/Present value of amount Where, FVIF,, is the future value i = rate of interest in decimal interest factor at i % for n periods n= number of years equal (1+ i)” FV n Cima For Present Value PV = d4+i"Future Value of Single Cash Flow - Annual Compounding FV, = PV Where, FY, = Future Value after nth year PV = Principal amount/Present value of amount i=rate of interest in decimal n= number of years Prob 1: An individual invests %4,000 at 10% interest rate compounded annually for 5 years. Find out the amount that he would receive after 5 years. Solution: A= 4,000(1 + 0.10)° 4,000 (1.6105) =% 6,442 x (1+ i)" FV, = Py (FVIFin ) Where, FVIF;, is the future value interest factor at i % for n periods equal (1 + i)"Future Value of Single Cash Flow - Annual Compounding FV, = PV x(i+i)" Where, FV, = Future Value after nth year PV = Principal amount/Present value of amount irate of interest in decimal n= number of years FV, = Py (FVIF,y) Where, FVIF;, is the future value interest factor at i % for n periods equal (1 + i)" Prob 2: Determine the compound interest for an investment of & 7,500 at 3 % compounded yearly for 12 years. Given that (1+i)” for i = 0.03 and n = 12 is 1.42576. Solution: Compound Amount = @ 7,500 (1 + 0.03) =% 7,500 x 1.42576 = 10,693.20 Compound Interest = = 10,693.20 — 27,500 = % 3,193.20FV of Single Cash Flow - Multi-Period Compounding FV=Pvx(1+4/,,)™ Where, FV = Future Value PV = Principal amount/Present value of amount i= rate of interest n— number of years m = number of compounding Prob 3: Suppose the deposit is 5,000 in a bank for 6 years at 12% interest and the number of compounding is 4 times in a year. Find out the Future Value of the deposit at the end of the 6" year. Solution: FV = %5,000(1 + 0.12/4)**6 =%5,000 (2.0328) = 10,164FV of Single Cash Flow - Multi-Period Compounding = t /; mn. FV =PV x(1+ Jn) Where, FV = Future Value PV = Principal amount/Present value of amount i= rate of interest n= number of years m = number of compounding Prob 4: Determine the compound interest for an investment of % 7,500 at 6 % compounded Half-yearly for 12 years. Given that (1+i)" for i = 0.03 and n = 12 is 1.42576. Solution: Compound Amount = % 7,500 (1 + 0.03) =% 7,500 x 2.0328 = 15,245.96 Compound Interest = % 15,245.96 - %7,500 =% 7,745.96Prob 5: What annual rate of interest compounded annually doubles an 1 investment in 7 years? Given that 27= 1.104090. Solution If the principal be P, FVn = 2P Since, FVn = P(1 + i)” 2P=P(1 +i)” or,2=(1+i)7 1 or, 27=1+i or, 1.104090 = 1 +i or, i= 0.10409 Required rate of interest = 10.41%P b 6: A person opened an account on April, 2020 with a deposit of & 800. The account fetched 6% interest compounded quarterly. On October 1, 2020, he closed the account and added enough additional money to invest in a 6-month Time Deposit for €1,000 earning 6% compounded monthly (a) How much additional amount did the person invest on October 1? (b) What was the maturity value of his Time Deposit on April 1, 2021? (c) How much interest was earned in total? Given that (1 + i)!" is 1.03022500 for i = 1’ %, m = 2 and is 1.03037751 for t Solution (a) The initial investment eamed interests for April - June and July ~ September quarter, ic. for 2 quarters or ¥2 year. In this case, interest is compounded quarterly for 2 quarters and the principal amount was ¥ 800. FV=PVx (1+ ‘/m)™ 800 x (1+ %/,)*% 800 «(1+ 1 1/2)? % 800 = 1.03022500 =% 824.18 The additional amount = 2 (1,000 ~ 824.18) = 175.82 4 % and n = 6, (b) In this case, the Time Deposit eared interest compounded monthly for 2 quarters. P= 1,000 FV=PV= (1+ %m)™ = 21,000 (1+ 94) = 1,000 x (1+ 4/,)8 = % 1,000 x 1,03037751 = 21,030.38 (c) Total interest carned = % (24.18 + 30.38) = 2 54.56Effective Rate of Interest It is the actual equivalent annual rate of interest at which an investment grows in value when interest is credited more often than once a year. If interest is paid m times in a year it can be found by calculating: Ei=(1+i/m)"-1Prob 7: Mr. D deposits 10,000 in a bank for a period of 1 year. The bank offers Sollowing two options — i) To receive interest at 12% p.a. compounded monthly, or ii) To receive interest at 12.25% p.a. compounded half-yearly. Which option should Mr. D accept? Solution: For Option (a) For Option (b) Ei=(1 +0.12/12)!? -1 Ei = (1+ 0.1225/2)? -1 = 1.1268-1 = 1.12625—1 = 0.1268 = 0.1263 = 12.68% = 12.63%Prob 8: Mr. X deposits the following amounts SE Fi 50,000 90,000 70,000 40,000 Calculate the maturity value at the end of the given cash flows Rate of interest is 7%. Solution : tre merry Roary ong ay ee Compounded 1 50,000 3 1.2250 61,252 2 90,000 2 1.1449 1,03,041 3 70,000 1 1.0700 74,900 4 40,000 0 1 40,000 Total 2,79,193 CVIF — Compound Value Interest Factor Maturity Value — & 2,79,193 FV ~ Future ValueANNUITY ‘An annuity is a stream of regular periodic payment made or received for a specified period of time. In an ordinary annuity, payments or receipts occur at the end of each period. It is a sequence of equal cash flows, occurring at the end of each period and is also known as an ordinary annuity. Future Value of an Annuity is expressed as FVAn = a{oeorat} i Where, FVAn = Future Value of annuity A= Annuity amount i= rate of interest n= number of yearsProb 9. Mr. Roy contributed 270,000 per year to PPF account in SBI for 15 consecutive years at 8% interest rate. What is the Future Value of the annuity at the end of the 15h year? (1+0.08)"8 -1 0.08 = % 70,000 (27.1525) = % 19,00,675 Solution: FVAn = 70,0 Prob 10. & 200 is invested at the end of each month in an account paying interest 6% per year compounded monthly. What is the amount of this annuity after 10th payment? (1+ 0.06/12)? "°F -1 0.06 /12 = 2 200 (10.2280) = % 2,046 Solution: py4, = 200{Sinking Fund A sinking fund is the fund created for a specified purpose by way of sequence of periodic payments over a time period at a specified interest rate. The utility of this fund is to deposit and save money to repay a debt or replace a wasting asset in the future. In other words, its like a savings account that you deposit money in regularly and can only be used for a set purpose. Sinking Fund Factor ijt — A=FVAn/ {event} Where, FVAn = Future Value A= Annuity amount i= rate of interest number of vearsProb 11. Mr. R wants to buy a flat in Kolkata worth %25,00,000. The payment has to be made after 5 years from now. For this purpose, he wants to save an annual fixed amount in the form of bank deposit. The bank pays an interest of 9% p.a. How much should he save per year if his total deposit along with interest is sufficient to buy the flat after 5 years? Solution: (atiy A= FvAn/{* 140.09) —1 A= 2s,00,000/{"* Sr) — = 25,00,000 / 5.9844 = %4,17,753Annuity-due A sequence of periodic cash flows occurring at the beginning of each period. Examples of Annuities-due > Monthly Rent payments: due at the beginning of each month. > Car lease payments. > Cable & Satellite TV and most internet service bills. FV of Series of Equal Cash Flow - Annuity Due FVAn = {o-oo Where, FVAn = Future Value A> Annuity amount i= rate of interest n= number of yearsProb 12. Mr: J deposits £50,000 at the beginning of each year for 5 years in a public sector bank and the deposit earns a compound interest of 8% p.a. Calculate how much money he will have at the end of 5 years $ Solution: FVAn = s0,000{ 49.09) Ha 40.08) = % 50,000 (6.3359) =%3,16,795 Prob 13, XYZ Company is creating a sinking fund to redeem its preference capital of ¢ 10 lakhs issued on April 6, 2021 and maturing on April 5, 2031. The first annual payment will be made on April 6, 2021. The company will make equal annual payments and expects that the fund will earn 12 percent per year. How much will be the amount of sinking fund payment? Solution: XYZ Company wants to accumulate a future sum of € 10,00,000. Since the annual payments will be made in the beginning of the year, the formula for the compound value of an annuity can be used. ‘0 10,00,000 = a{¢ sony ta +0.12) or 8 10,00,000 = A (19.6546) or A % 10,00,000 / 19.6546 or A =%50,879Present Value “Present Value” is the current value of a “Future Amount”. It can also be defined as the amount to be invested today (Present Value) at a given rate over specified period to equal the “Future Amount” If we reverse the flow by saying that we expect a fixed amount after n number of years, and we also know the current prevailing interest rate, then by discounting the future amount, at the given interest rate, we will get the present value of investment to be made. - Future Value Present Value a Discounting future amount converts it into present value amount. Similarly, compounding converts present value amount into future value amount. Therefore, we can say that the present value of a sum of money to be Teceived at a future date is determined by discounting the future value at the interest rate that the money could ‘cam over the period. This process is known as Discounting.Future Value and Present Value mmm> For Future Value FV, = PV x (1+i)" Where, FY, = Future Value after nth year PV = Principal amount/Present value of amount i = rate of interest in decimal n= number of years => For Present Value FV, (1+ i)” PV =Prob 14. If the discount rate is 12%, calculate the present value of 25,000 to be received by Mr. Joy at the end of the 5 years. FV , Solution: Py = —— (1+ i)" 5,000 Yo = P (1+ 0.12)° 000 PVv= 5 °°°/ 4 7623) PV = % 2837.20PV of Single Cash Flow - Multi-Period Discounting PV = w{ a} (1+i/m)™" Where, FV = Future Value PV = Principal amount/Present value of amount i= rate of interest n= number of yearsProb 15. What is the present value of 250,000 receivable after 5 years from now if the discount rate is 8% and discounting is done quarterly? Solution: PV = 50,000, ———_ {a +0.08/4)** | PV = 50,000 / (1.4859) PV = % 33,649.64Prob 16. Mr. X has made real estate investment for % 12,000 which he expects will have a maturity value equivalent to interest at 12% compounded monthly for 5 years. If most savings institutions currently pay 8% compounded quarterly on a 5 year term, what is the least amount for which Mr. X should sell his property? Solution: It is a two-part problem. First being determination of maturity value of the investment of 812.000 and then finding of present value of the obtained maturity value. Maturity value of the investment may be found from FV=PV = (14 Ym) FV = 12,000 * (1 + ©42/,,)32*5 FV ~ 12,000 x (1 + 0.01) FV = 12,000 (1.8167) FV =2 21,800.40 Thus, maturity value of the investment in real estate = % 21,800.40 The present value, P of the amount FVn due at the end of n interest periods at the rate of i % interest per period is given by 1 py=Fvi__!__| py =21,800.40/_ _1__ (1+i/m™ @+0.08/4)"* PV = 2 21,800.40 (0.6730) or PV = 14.671.67 Mr. X should not sell the property for less than % 14,671.67PV of Series of Unequal Cash Flows Prob 17: The life span of an investment project is 6 years. During its life span, it creates an inflow of cash as follows— [ES TETS a 550 750 800 850 900 950 Calculate the present value of the series of cash inflows considering a discounting rate of 6%. Solution : DORMS ree ee cra) aac a E550 1 0.9434 $18.87 = 750 2 0.8900 667.50 800 3 0.8396 671.68 Za 850 4 0.7921 673.29 900 5 0.7473 672.57 Rm 90 6 0.7050 669.75 3873.66Present Value of an Annuity Sometimes instead of a single cash flow the cash flows of the same amount is received for a number of years. The present value of an annuity may be expressed as follows : py =a} id+i)" Prob 18. Find out the present value of a 4 year annuity of %20,000 discounted at 10per cent. Solution: 4 ween PV = 20,000 Q+0.)"=1 0.101+ 0.1) _ (1.4641-1 _ (0.4641 * PY = 20.000 ail oP = 70.00 ae } or — PV=% 20,000 x (3.1699) or — PV =% 63,398Prob 19. ¥ bought a TV costing ® 13,000 by making a down payment of ° 3,000 and agreeing to make equal annual payment for 4 years. How much would be each payment if the interest on unpaid amount be 14% compounded annually? Solution In the present case, present value of the unpaid amount was (13,000 — 3,000) = 10,000. The periodic payment, A may be found from “vn 4 py -aata" a1 or —210,000= 4 A041 id+i" 0.1401+0.14) or %10,000= (on or = 10,000 = A (2.9133) 0.14x1.6890 or A=210,000/2.9133 or A= 3432.55Prob 20. Mr. X borrows from a commercial bank a loan of 88,00,000 at 8% interest rate to be paid in equal annual instalments. The repayment period is 10 years. What would be the size of annual instalment? Solution: PV =A d+ i” -1 i(1+i)" _ ,f +0.08)" -1 or £800,000 Sa +0.08)"° 2.1589-1 = A, —————_—_ “r %8,00,000 (as sal or A= 28,00,000 * 0.1727 / 1.1589 or A= %8,00,000 x 0.1490 or A= 21,19,200Perpetuity / Perpetual Annuity Perpetuity is an annuity in which the periodic payments or receipts begin on a fixed date and continue indefinitely or perpetually. Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities. It is a series of continuous cash flows of an equal amount over a limited period is known as Annuity which continues forever. PV of a Perpetual Annuity A v PV Where, PV = Present Value A= Annuity amount i=rate of interestProb 21: Calculate the present value of a perpetual annuity of @1,00,000 per year at a discount rate of 8%. Solution: py = & i PV =2 1,00,000/0.08 = 2 12,50,000 Prob 22. Ramesh wants to retire and receive & 3,000 a month. He wants to pass this monthly payment to future generations after his death. He can earn an interest of 8% compounded annually. How much will he need to set aside to achieve his perpetuity goal? Solution: py = & i i= 0.08 / 12 = 0.0067 PV = 2 3,000 / 0.0067 =7450.000A bond is a debt instrument that provides a steady income stream to the investor in the form of coupon payments. At the maturity date, the face value of the bond is repaid to the bondholder. The characteristics of a regular bond include: (a) Par Value: Value stated on the face of the bond. It is the amount a firm borrows and promises to repay at the time of maturity. () Coupon rate: A bond carries a specific interest rate known as the coupon rate. The interest payable to the bond bolder is par value of the bond x coupon rate. The coupon rate is the fixed return that an investor ears periodically until it matures. The frequency of payment of interest is also specified (e.g. payable annually, semi-annually, quarterly or monthly) (© Maturity date: All bonds have maturity dates, some short-term, others long-term. When a bond matures, the bond issuer repays the investor the full face value of the bond. The face value is not necessarily the invested principal or purchase price of the bond. Corporate bonds have a maturity period of 3 to 10 years, while government bonds can have maturity periods extending up to 30 years. (@) Yield to Maturity (YIM): The YTM is defined as that discount rate (“ky”) at which the present value of frture cash flows from a Bond equals its Market Price. (©) Current price: Depending on the level of interest rate in the environment, the investor may purchase a bond at par, below par, or above patBond Valuation rr Bond valuation is a technique for determining the theoretical fair value of a particular bond. Bond valuation includes calculating the present value of a bond’s future payments, also known as its cash flow, and the bond's value upon maturity, also known as its face value or par value. The holder of a bond receives a fixed annual interest payment for a certain number of years and a fixed principal repayment (equal to par value) at the time of maturity. So the value of a bond is: _yn I F Va dha Gakat * Gkayn Where, V = value of the bond I= annual interest payable on the bond, assuming annual interest payments F = principal amount (par value) of the bond repayable at the time of maturity n= maturity period of the bond.Problem 1. A % 1,000 par Ve] Oe coupon rate of 14 per cent eR AMM] eR LLL RCM) MOLL this bond is 13 per cent. alculate the value of the aires Solution: -yn,_!_,_F V= hea (1+kd)t + (1+kd)” 140 1,000 or V= Di =1 (40.13) (1+0.13)5 or V =(140x3.5172) + (1000x0.54276) Or V = 492.41 + 542.76 = 21035.17Bonds pay interest semi-annually. This requires the bond valuation equation to be modified as follows: (a) The annual interest payment, I, divided by two to obtain the semi-annual interest payment. (b) The number of years to maturity is multiplied by two to get the number of half-yearly periods (c) The discount rate divided by two to get the discount rate applicable to half-yearly periods The basic bond valuation equation thus becomes: _y2n __V/2 F Vode Geka” Gk V = Value of the bond 1/2 = Semi-annual interest payment K,/2 = Discount rate applicable to a half-year period F = Par value of the bond repayable at maturity 2n = Maturity period expressed in terms of half-yearly periods.Problem 2: If a = 100 par value bond carries a coupon rate of 12 Fa RL Ree Peete Pre ae me value of the bond when the required ea Arn ew Le Solution The value of the bond is yon __V/2 FE V= Xt (a+kd/2)t 7 (+kd/2)2" - 16 12/2 + 100 Orv Lee1 Groat (4+0.14/2)'* Or V = (6 x 9.4466) + (100 x 0.3387) Or V = 56.68 + 33.87 = 290.55Yield to Maturity (YTM) The rate of return one earns is called the Yield to Maturity (YTM). The YTM is defined as that value of the discount rate (“ky”) for which the Intrinsic Value of the Bond equals its Market Price. If we ignore the issue related expenses, k, equals the relevant cost of (debt) capital for the company. YTM or k, can be calculated by ‘Trial and Error’ method or by using Short Cut method. By using Simple Interpolation under Trial and Error method YTM can be calculated more accurately as compared to Shortcut method which provides an approximate YTM or ky rate. # Shortcut method ingbiin 160 ax — TH(F=P)/n 14(F-P)/n YTM ~ 04Fs0.6P (F+P)/2 Where I = Annual Interest payment F = Par value or redemption value of the bond P= Current market price of the bond and n= number of years to matun BeProblem 3: If the price per bond is ? 90 and the bond has a par value of & 100, Ne ee ae) ee eC ORL Re Rn eee RAC LLa Tat Solution By using Trial and Error method Ifky=17% Ihkg= 14% 14 100 =1 (140.17) +0.17)8 V = (14 * 3.5892) + (100 * 0.3898) F v-dh ‘aaa (1+kd)! 4 100 tt 4 = “Zh Gy 14)” (140.1496 90 = Y6_,— + +} Or V = (14 x 3.8887) + (100 « 0.4556) (atk)! (1+kedy" Or V = 50.25 + 38,98 = & 89.23 OrV = 54.44 + 45.56 = 100 By Simple Interpolation x-14 90-100 17-14 ~ 8923-100 Therefore YTM (kd) = 16.79% or (x — 14) = 0.9285 x 3 = 2.7855 or x = 16.7855%ee ee a oe Ae Mee Se aU coupon rate of 14 per cent, and a maturity period of 6 years, calculate it’s BUA} era # Shortcut method _1+(F-P)/n YIM = [@Pyn YIM 04F+0.6P x 0.4F+0.6P 14+( 100 - 90)/6 14+(F-P)/n “(0.4 x100)+(0.6 x90) (F+P)/2 _ 1441.67 _ 15.67 40454 (94 = 0.1656 Where I = Annual Interest payment F = Par value or redemption value of the bond P = Current market price of the bond and or ky = 16.56% n= number of years to maturityProblem 3: If the price per bond is % 90 and the bond has a par value of € 100, a coupon rate of 14 per cent, and a maturity period of 6 years, calculate it’s yield to ara # Shortcut method vIn 1+(F— P)/n YTM = I+(F-P)/n or 0.4F+0.6P 0.4F+0.6P __14+( 100 - 90)/6 I+(F-P)/n ~ (0.4 x100)+(0.6 x90) (F+P)/2 _ 1441. 15.67 Where I = Annual Interest payment >of od. F = Par value or redemption value of the bond = __ 0.1656 P= Current market price of the bond and or ky = 16.56% n= number of years to maturity K, Under Trial and Error method = 16.79% 1+(F- P)/n YTM = (F4P)/2 _14+(100 ~ 90)/6 ~~ (100+90)/2 1441.67 _ 15.67 “9595 = 0.1649 or ky = 16.49%Bond Value Theorems / Rules CAUSE EFFECT Required rate of return Bond sells at par value or YTM = coupon rate Required rate of return Bond sells at a discount or YTM > coupon rate Required rate of return Bond sells at a premium or YTM < coupon rate Longer the maturity of Greater the bond price abond change with a given change in the required tate of return. Zero Coupon Bond ‘As name indicates these bonds do not pay any coupon during the life of the bonds. Instead, Zero Coupon Bonds (ZCBs) are issued at discounted price to their face value, which is the amount a bond will be worth when it matures or comes due. It is sold at a deep discount to par when issued. The difference between the purchase price and par value is the investor’s interest earned on the bond. To calculate the value of a zero-coupon bond, we only need to find the present value of the face value. The maturity dates on ZCBs are usually long term. These maturity dates allow an investor for a long-range planning. ZCBs issued by banks, government and private sector companies. However, bonds issued by corporate sector carry a potentially higher degree of tisk, depending on the financial strength of the issuer and longer maturity period, but they also provide an opportunity to achieve a higher return.De) Teer a ee rd sr ee interest deep discount bonds of face value of & PRU ram 5 ae] a after 25 years. Compute MN ye Le Peay ona ae Solution: Here, Redemption Value (RV) = 71,00,000 Net Proceeds (NP) = 2.500 Interest = 0 Life of bond = 25 years ‘There is huge difference between RV and NP therefore in place of approximation method we should use trial & error method. FV=PVx(1 +r)" 1,00,000 = 2,500 x (1+)? 40 =(1+1)"8 Trial 1: r= 15%, (1.15) 32.919 Trial 2: r= 16%, (1.16)?5 = 40.874 By using Simple Interpolation: 2-15 40 — 32.919 16-15 40.874—32.919 or x = 15 + 0.890 or x = 15.89%In order to undertake equity valuations, an analyst can use different approaches, some of which are classified as follows (1) Dividend Based Models (2) Earning Based Models (3) Cash Flows Based Model Dividend Based Models Valuation of equity shares based on dividend are based on the following assumptions: a. Dividend to be paid annually. b. Payment of first dividend shall occur at the end of first year. c. Sale of equity shares occur at the end of a year and that to at ex- dividend price. The value of any asset depends on the discounted value of cash streams expected from the same asset. Accordingly, the value of equity shares can be determined on the basis of stream of dividend expected at Required Rate of Return or Opportunity Cost ie. Ke (Cost of Equity).Valuation Of 1 Sfe [eta msde (1) Valuation Based holding period of One Year : Tfan investor holds the share for one year then the value of equity share is computed as follows: = Pr Pa Daa 0 (a+Ke)? (1+Ke)!— (1+Ke)* (2) Valuation Based on Multi Holding Period: In this type of holding following three types of dividend pattern can be analysed (i) Zero Growth: Also, called as No Growth Model, as dividend amount remains same over the years infinitely. The value of equity can be found as follows: _D Por ke (ii) Constant Growth: Constant Dividend assumption is quite unrealistic assumption. Accordingly, one very common model used is based on Constant Growth in dividend for infinitely long period. In such situation. the value of equity shares can be found by using following formula: Di DO(1+g) Po Ke-g Keg It is important to observe that the above formula is based on Gor don Growth Model of Calculation of Cost of Equity.DEFINITION + According to Charles T. Horngren, “Capital Budgeting is long-term planning for making and financing proposed capital outlays. As per Richards and Greenlaw, “The capital budgeting generally refers to acquiring inputs and long-run returns.” In the words of G. C. Phillippatus, “Capital budgeting is concerned with the allocation of the firm's scarce financial resources among the available market —_ opportunities. The consideration of investment opportunities involves the comparison of the expected future streams of earnings from a project; with the immediate and subsequent stream of, expenditures for it.”(Long-term Applications: implies that capital budgeting decisions are helpful for an organization in the long rim as these decisions have a direct impact on the cost structure and future prospects of the organization, In addition, these decisions affect the organization's growth rate. Therefore, an organization needs to be careful while making capital . . decisions as any wrong decision can prove to be fatal for the Significance of organization. For example, over-investment in various . assets can cause shortage of capital to the organization, Cc ‘apital whereas insufficient investments may hamper the growth of Budgeting the organization. (b) Competitive Position of an Organization: Refers to the fact that an organization can plan its investment in various fixed assets through capital budgeting. In addition, capital investment decisions help the organization to determine its profits in future. All these decisions of the organization have a major impact on the competitive position of an organizationSignificance of Capital Budgeting ©) Cash Forecasting: Implies that an organization needs a large amount of funds for its investment decisions. With the help of capital budgeting, an organization is aware of the required amount of cash, thus, ensures the availability of cash at the right time. This further helps the organization to achieve its long-term goals without any difficulty d)Maximization of Wealth: Refers to the fact that the long-term investment decisions of an organization helps in safeguarding the interest of shareholders in the organization. If an organization has invested in a planned manner, sharcholders would also be keen to invest in the organization. This helps in maximizing the wealth of the organization. Capital budgeting helps an organization in many ways. Thus, an organization needs to take into consideration various aspectsCapital Budgeting Process be formalised and systematic procedures established depends on the size of the organisation; number of projects to be considered: direct financial benefit of each project considered by itself: the composition of the firm's existing assets and management's desire to change that composition; timing of expenditures associated with the projects that are finally accepted @ Planning: The capital budgeting process begins with the identification of potential investment opportunities. The opportunity then enters the planning phase when the potential effect on the firm's fortunes is assessed and the ability of the management of the firm to exploit the opportunity is determined. Opportunities having little merit are rejected and promising opportunities are advanced in the form of a proposal to enter the evaluation phase. (WEvaluation: This phase involves the determination of proposal and its investments, inflows and outflows. Investment appraisal techniques, ranging from the simple payback method and accounting rate of return to the more sophisticated discounted cash flow techniques, are used to appraise the proposals. The technique selected should be the one that enables the manager to make the best decision in the light of prevailing circumstances.Capital Budgeting Process (iii) Selection: Considering the returns and risks associated with the individual projects as well as the cost of capital to the organisation, the organisation will choose among projects so as to maximise shareholders’ wealth. (iv) Implementation: When the final selection has been made, the firm must acquire the necessary funds, purchase the assets, and begin the implementation of the project. (¥) Control: The progress of the project is monitored with the aid of feedback reports. These reports will include capital expenditure progress reports, performance reports comparing actual performance against plans set and post completion audits. (vi) Review: When a project terminates, or even before, the organisation should review the entire project to explain its success or failure. This phase may have implication for firms planning and evaluation procedures. Further, the review may produce ideas for new proposals to be undertaken in the future.Types of Capital Investment Decisions Generally capital investment decisions are classified in two ways. One way is to classify them on the basis of firm’s existence. Another way is to classify them on the basis of decision situation. On the basis of firm's existence: The capital budgeting decisions are taken by both newly incorporated firms as well as by existing firms. The new firms may be required to take decision in respect of selection of a plant to be installed. The existing firm may be required to take decisions to meet the requirement of new environment or to face the challenges of competition. These decisions may be classified as follows: () Replacement and Modernisation decisions: The replacement and modernisation decisions aim at to improve operating efficiency and to reduce cost. Both replacement and modemisation decisions are called cost reduction decisions. (i) Expansion decisions: Existing successfull firms may experience growth in demand of their product line. If such firms experience shortage or delay in the delivery of their products due to inadequate production facilities. they may consider proposal to add capacity to existing product line. (iti) Diversification decisions: These decisions require evaluation of proposals to diversify info new product lines, new markets etc. for reducing the risk of failure by dealing in different products or by operating in several markets. Both expansion and diversification decisions are called revenue expansion decisions.Types of Capital Investment Decisions ¢ On the basis of decision situation: @ Mutually exclusive decisions: The decisions are said to be mutually exclusive if two or more alternative proposals are such that the acceptance of cone proposal will exclude the acceptance of the other alternative proposals. For instance, a firm may be considering proposal to install a semi-automatic or highly automatic machine. If the firm installs a semi-automatic machine it excludes the acceptance of proposal to install highly automatic machine. (ii) Accept-reject decisions: The accept-reject decisions occur when proposals are independent and do not compete with each other. The firm may accept of reject a proposal on the basis of a minimum return on the required investment. All those proposals which give a higher return than certain desired rate of retum are accepted and the rest are rejected (iif) Capital Rationing Decisions - is normally applied to situations where the supply of funds to the firm is limited in some way. As such, the term encompasses many different situations ranging from that where the borrowing and lending rates faced by the firm differ, to that where the funds available for investments are strictly limited. In other words, it occurs when a firm has more acceptable proposals than it can finance. At this point, the firm ranks the projects from highest to lowest priority and, as such, a cut-off point is considered. Naturally, those proposals witich are above the cut-off point will be accepted and those which are below the cut-off point are rejected. ie., ranking ts necessary to choose the best altematives.Project Evaluation TechniquesMethods of Investment Appraisal Payback period (PRP) ‘The length of time: cash proceeds recover the initial capital expenditure Accounting Rate of Return (ARR) Aretum measurement by using average annual profits Net Present Value (NPV) The present value of the net cash inflows less the initial investment Internal Rate of Return (IRR) A return measurement takes into account the time value of money ‘Modified IRR (MIRR) ‘The decision criterion of MIRR is same as IRR i.e. you accept an investment if MIRR is larger than required rate of retum and reject if it is lower than the required rate of return. Profitability Index (PI) A ratio that consists of the present value of future cash flows over the initial investment. Discounted Pay Back Period ( Discounted PBP) Discounted Payback is more appropriate way of measuring the payback period since it considers the of money.Depreciation Tax Shield Depreciation is not a cash outflow but for income tax depreciation can be reduced from profit and compute tax. Depreciation tax shield is the tax benefit or tax saved that we derive from deducting depreciation from profit. It is the reduction in tax liability that results from admissibility of depreciation expense as a deduction under tax laws. In capital budgeting calculations, net operating cash flows are reduced by the amount of depreciation tax shield available each year. The Net Present Value and Internal Rate of Retum are calculated using the after-tax cash flows which are determined using either of the following formula: CF=(CI-CO-D)x(1-)+D CF=CI-CO-(CI-CO-D)xt Where CF is the after-tax operating cash flow, Cl is the pre-tax cash inflow, CO is pre-tax cash outflow, tis the tax rate and D is the depreciation expense. ‘These two equations are essentially the same. The expression (CI — CO — D) in the fist equation represents the taxable income which when multiplied with (1 ~ 0) yields afier-tax income. Depreciation is added back because it is a non-cash expense and we need to work with after-tax cash flows (instead of income). The second expression in the second equation (CI - CO — D) = t calculates depreciation tax shield separately and subtracts it from pre-tax net cash flows (CI - CO).Problem: ABC Ltd is evaluating the purchase of a new project with a depreciable base of 21,00,000: expected economic life of 4 years and change in earnings before taxes and depreciation of 245,000 in year 1. 230,000 in year 2, 825,000 in year 3 and %35,000 in year 4. Assume straight-line depreciation and a 20% tax rate. You are required to compute relevant cashflows. Solution: 1@ r BIS Earnings before tax and depreciation 45,000 30,000 25,000 35,000 Less: Depre 25,000 25,000 25,000 25,000 Earnings before tax 20,000 5,000 0 10,000 4,000 1,000 0 2,000 16,000 4,000 0 8,000 RCCen De ate 25,000 25,000 25,000 25,000 Net Cash flow 41,000 29,000 25,000 33,000PAY-BACK PERIOD (PBP) Payback periods are an integral component of capital budgeting and should always be incorporated when analyzing the value of projected investments and Payments made at a later date still have an opportunity cost attached to the time that is spent, but the payback period disregards this in favor of simplicity.Computation of PBP The first step in calculating PBP is determining the total initial capital investment. The second step is estimating the annual expected after tax net cash inflows over the useful life of the investment. The payback period can be calculated in two different situations a) When annual cashflow is uniform investment PEP jonstant Annual Cash inflows b) When annual cashflows are not uniform The Payback period = the point in time at which cash flows tum from negative to positive Payback period = change in cash flow required to reach zero/total cash flow in year + year in which cash flows turn from negative to positive oePay Back Period Advantages > It is easy to compute. > It is easy to understand as it provides a quick estimate of the time needed for the organization to recoup the cash invested. > The length of the payback period can also serve as an estimate of a project’s risk; the longer the payback period, the riskier the project as long-term predictions are less reliable. In some industries with high obsolescence risk like software industry or in situations where an organization is short on cash, short payback periods often become the determining factor for investments. Limitations >It ignores the time value of money. As long as the payback periods for two projects are the same, the payback period technique considers them equal as investments, even if one project generates most of its net cash inflows in the early years of the project while the other project generates most of its net cash inflows in the latter years of the payback period A second limitation of this technique is its failure to consider an investment’s total profitability: it only considers cash flows from the initiation of the project until its payback period and ignores cash flows after the payback period > Lastly, use of the payback period technique may cause organizations to place too much emphasis on short payback periods thereby ignoring the need to invest in long-term projects that would enhance its competitive position.Problem: Project A Project B Initial investment % 100,000 100,000 The depreciation is 220,000 per year. Cash inflows The residual value for both projects is the ‘Year 1 245,000, $30,000 same, £20,000. ‘Year 2 240,000 230,000 CALCULATE PBP ‘Year 3 235,000 244,000 ‘Year 4 Solution: The Payback period = the point in time at which cash flows tum from negative to positive Project | Cash flows| _ Cumulated cash flow | Cash flows | Cumulated cash flow ‘Year 0 -100,000 -100,000 -100,000 -100,000 ‘Year 1 45,000 ___-55,000 30,000 -70,000 ‘Year 2 40,000 -15,000 30,000 -40,000 Year 3 35,000 +20,000 44,000 +4,000 Year 4 50,000 +70,000 66,000 +70,000 Payback period (A) = change in cash flow required to Payback period (B) = 40,000/44,000 = 0.91 + 2 years = reach zero/toal cashflow in year 2.91 years = 0.43 + 2 years = 2.43 years> Payback Reciprocal Itis the reciprocal of payback period. A major drawback of the payback period method of capital budgeting is that it does not indicate any cut off period for the purpose of investment decision. It is, however, argued that the reciprocal of the payback would be a close approximation of the internal rate of retum if the life of the project is at least twice the payback period and the project generates equal amount of the annual cash inflows. In practice, the payback reciprocal is a helpful tool for quickly estimating the rate of return of a project provided its life is at least twice the payback period. The payback reciprocal can be calculated as follows:Problem: Suppose a project requires an initial investment of 20,000 and it would give annual cash inflow of %4,000. The useful life of the project is estimated to be 5 years. Calculate Payback Reciprocal. Solution: Payback reciprocal will be : Average annual cash in HOW 199 £4000 199 = 399 ~%20,000 100 = 20% [The above payback reciprocal provides a reasonable approximation of the internal rate of return, Le. 19%.] =Accounting Rate of Return (ARR) The accounting rate of return of an investment measures the average annual net income of the project (incremental income) as a percentage of the investment. = Average annual net income * Accounting rate of return (ARR) Investment 100 The numerator is the average annual net income generated by the project over its useful life. The denominator can be either the initial investment or the average investment over the useful life of the project. Some organizations prefer the initial investment because it is objectively determined and is not influenced by either the choice of the depreciation method or the estimation of the salvage value. Either of these amounts is used in practice but it is important that the same method be used for all investments under consideration ‘The accounting rate of retum is quite useful for providing a clear picture of a project’s potential profitability, satisfying a firm’s dese to have a clear idea of the expected return on investment. This method also acknowledges earnings after tax and depreciation, making it effective for benchmarking a firm’s current level of performance.Advantages > This technique uses readily available data that is routinely generated for financial reports and does not require any special procedures to generate data. > This method may also mirror the method used to evaluate performance on the operating results of an investment and management performance. Using the same procedure in both decision-making and performance evaluation ensures consistency. > Lastly, the calculation of the accounting rate of return method considers all net incomes over the entire life of the project and provides a measure of the investment’s profitability. Limitations > The accounting rate of retum technique, like the payback period technique, ignores the time value of money and considers the value of all cash flows to be equal. > The technique uses accounting numbers that are dependent on the organization’s choice of accounting procedures, and different accounting procedures, e.g., depreciation methods, can lead to substantially different amounts for an investment’s net income and book values. » The method uses net income rather than cash flows; while net income is a useful measure of profitability, the net cash flow is a better measure of an investment’s performance. » Furthermore, inclusion of only the book value of the invested asset ignores the fact that a project can require commitments of working capital and other outlays that are not included in the book value of the project.Step 1: Step 2: Step 3: Step 4: Calculate Annual Profit Annual Profit = Net Cash Inflow - Depreciation Calculate Average Profit Average Profit = Total Profits / Number of Years Calculate Average Capital Invested Average capital invested = {(Initial Cost - Residual Value) / 2} + Salvage Value + Net Working Capital Calculate ARR ARR = Average Profit/Average Capital Invested x 100Problem: Project A Project B Initial investment 2 100,000 100,000 Cash inflows ‘Year I 245,000 230,000 Year 2 240,000 230,000 ‘Year 3 235,000 244,000 ‘Year 4 230,000, 246,000 Solution: Project A ‘The depreciation is 220,000 per year. ‘The residual value for both projects isthe same, %20,000. CALCULATE ARR ‘Average profit = & (25,000 + 20,000 + 15,000 + 10,000)/4 = 70,000/4 = & 17,500 Average capital invested = [8(100,000 - 20,000) /2] +8 20,000 = % 60,000 ARR = 217,500 / % 60,000 x 100 = 29% Project B Average profit = = (10,000 + 10,000 + 24.000 + 26.000)/4 = 217,500 Average capital invested = [2(100,000 + 20,000)/2] +8 20,000 = ¢ 60,000 ARR = 217,500 / 2 60.000 x 100 = 29%Net present value (NPV) is used for analyzing the projected returns for a potential investment or project. The net present valuc represents the difference between the current value of money flowing into the project and the current value of money being spent. The value can be calculated as positive or negative, with a positive net present value implying that the earings generated by a project or investment will exceed the expected costs of the venture and should be pursued. Also, unlike other capital budgeting methods, like the ARR and Payback Period, NPV accounts for the time value of money, so opportunity costs and inflation are not ignored in the calculation. To achieve this, the net present value formula identifies a discount rate based on the costs of financing an investment or calculates the rates of return expected for similar investment options.Unlike some capital budgeting methods, NPV also factors in the risk of making long- term investments. Therefore, the formula for net present value is longstanding and effective, but professionals in the industry must still recognize the potential room for error that arises when relying on calculations like investment costs, rates of discount, and projected returns, all of which rely heavily on assumptions and estimates. As accounting for unexpected expenses can be difficult when budgeting for capital investments, it is important to consider using payback period metrics and the internal rate of retum as possible alternatives to net present value calculations when evaluating a project or investment. NPV is computed as the difference between the Present Value of the Cash Inflows and the Cash Outflows (Initial Investment)Advantages >NPV method takes into account the time value of money. »The whole stream of cash flows is considered. > The net present value can be seen as the addition to the wealth of share holders. The criterion of NPV is thus in conformity with basic _ financial objectives. >The NPV uses the discounted cash flows ie., expresses cash flows in terms of current rupees. The NPVs of different projects therefore can be compared. It implies that each project can be evaluated independent of others on its own merit Limitations > wolves difficult calculations. > The application of this method necessitates forecasting cash flows and the discount rate. > Thus accuracy of NPV depends on accurate estimation of these two factors which may be quite difficult in practice. > The ranking of projects depends on the discount rate.Problem: | ___ Pretest’ Project B The depreciation is 220,000 per year. Initial investment 100,000 100,000 : The residual value for both projects is Cash inflows the same, 220,000. Cost of Capital is Year 1 245,000 330,000 10%. Year 2 240,000 230,000 CALCULATE NPV Year 3 35,000 244,000 Year 4 330,000 246,000 Solution: Project A | Cash Discount Disc. cash Project B | Cash Discount Disc cash flow | factor (10%) | flow flow | factor (10%) | flow ‘Year 0 -100,000 1.00 (100.000) ‘Year 0 -100,000 1.00 (100,000) Year! | 45,000 0.909/ 40.905 Year 1 30,000 909] 27.270 Year2 | 40,000 0.826] 33,040 Year2 | 30,000 0.826| 24,780 Year3 | 35,000 0.781] 26.285 Years | 44,000 0.751 33,044 ‘Year 4 50,000, 0.683 34,150 ‘Year 4 66,000 0.683 45,078 ‘NPV 334,380 NPV 30,172INTERNAL RATE OF RETURN (IRR) Internal rate of retum for an investment proposal is the discount rate that equates the present value of the expected net cash flows with the initial cash outflow. This IRR is then compared to a criterion rate of return that can be the organization’s desired rate of return for evaluating capital investments. The internal rate of return calculation is used to determine whether a particular investment is worthwhile by assessing the interest that should be yielded over the course of a capital investment. It is determined by using a particular formula that must be calculated through trial-and- error (SIMPLE INTERPOLATION). As the internal rate of return helps aid investors in measuring the profitability of their potential investments, the ideal internal rate of return for a project should be greater than the Cost Of Capital required for the project. as it can be assumed o that the project will be a profitable one.INTERNAL RATE OF RETURN (IRR) Acceptance Rule: The use of IRR, as a criterion to accept capital investment decision involves a comparison of IRR with the required rate of return known as cut off rate . Then project should be accepted if IRR is greater than cut-off rate. If IRR is equal to cut off rate the firm is indifferent. If IRR less than cut off rate the project is rejected. The Reinvestment Assumption : The Net Present Value technique assumes that all cash flows can be reinvested at the discount rate used for calculating the NPV. This is a logical assumption since the use of the NPV technique implies that all projects which provide a higher return than the discounting factor are accepted. In contrast, IRR technique assumes that all cash flows are reinvested at the projects IRR. This assumption means that projects with heavy cash flows in the early years will be favoured by the IRR method vis-a-vis projects which have got heavy cash flows in the later years.Advantages >This method makes use of the concept of time value of money. Y All the cash flows in the project are considered > IRR is easier to use as instantaneous understanding of desirability can be determined by comparing it with the cost of capital > IRR technique helps in achieving the objective of maximisation of shareholders wealth. Limitations > The calculation process is tedious, the interpretation of which is difficult > The IRR approach creates a peculiar situation if we compare two projects with different inflow/outflow patterns. It is assumed that under this method all the future cash inflows of a proposal are reinvested at a rate equal to the IRR. It is ridiculous to imagine that the same firm has a ability to reinvest the cash flows at a rate equal to IRR. If mutually exclusive projects are considered as investment options which have considerably different cash outlays. A project with a larger fund commitment but lower IRR contributes more in terms of absolute NPV and increases the sharcholders’ wealth. In such situation decisions based only on IRR ctiterion may not be correct v %‘roblem: ProjectA__| Project | The depreciation is 220,000 per year. Initial investment | 2 100,000 | 2100,000_| The residual value for both projects is the same, Cash inflows 220,000. ‘Year 1 245,000 230,000 CALCULATE IRR ‘Year 2 240,000 230,000 ‘Year 3 235,000 244,000 Year 4 230,000 | 246,000 Solution: Project A Year | Cash Flows Disc.(10%) PV 15% Pv 20% PV 25% PV 0 -1,00,000 1, -100000 1.0000 -100000| 1.0000 -100000 a -100000 45,000 0.9091, 40909.091 0.8696] 39130.43} 0.8333 37500 0.8000 36000, 40,000 0.8264 33057.851 0.7561] 30245.75, 0.6944 27777.78__0.6400__-25600 2 3 35,000 0.7513 26296.018 0.6575) 23013.07 0.5787 2025463 0.5120 17920, 4 50,000 0.6830 34150.673 0.5718 28587.65 0.4823 2411265 0.4096, 20480, NPV 34413.633 | 2097691 9645.062 0 IRR of Project A= 25%Year |Cash Flows Dise.(10%)| PV | 15% | PV | 20% | PV | 21% =1,00,000 27273) 0.8696, 25000_0.8264 24793, 0.7561, 22684) 0.6944) 0.7513 33058, 0.6575 _28931| 0.5787) 0.6830 45079 0.5718 37736, 0.4823] 30203 _ 15438 25463, 0.5645 31828.7, 0.4665 3125 By Simple Interpolation: IRR-22 ____ 0+ 1230.5 21-22 910.13+ 1230.5 1230.5 2140.63 IRR = 22 - 0.5748 = 21.4252 % = 0.5748 =100000, 1.0000, -100000, 1.0000, -100000_ 1.0000 -10000 24793) 0.8197) 20833.3, 0.6830, Pv | 22% 1.00 20490| 0. on 24837] 0.550 30789| 0.4514 910.1. Py 100000 245902 201559, 242311 29792.3, -1230.5IRR tells us... * How much risk (inflation, rise in interest rates, delays in project implementation, delays in getting accounts receivables) a business can absorb. * More the IRR, it is better for business as it can survive even during bad timesIn NPV, the present value of all future expectant cash flows are discounted at the firms cost of capital. The decision rule under NPV is that the project yielding negative NPV is rejected. However, in case of IRR no such discount rate is pre-determined. It is to be determined in such a way, so that the present value of all future cash inflows is exactly equal to the initial investment amount. A project whose IRR is less than the Cost of Capital, is rejected. Actually, if IRR is less than the Cost of Capital, the NPV in that case happens to be negative. Thus the project will be rejected under both the methods and there happens to be no conflict in decision making. However, in case of ranking of multiple mutually exclusive projects, there may arise a conflict in decision between NPV and IRR.NPV assumes that all intermediate cash flows are re-invested at its cost of capital while IRR assumes all intermediate cash flows earned, are re-invested at the IRR. Of these two assumptions, the assumption of NPV about re-investment is more logical and tealistic. Cost of Capital represents the opportunity cost where one can borrow and lend at that rate; while IRR is the projects own rate of return and there is no guarantee that the cash flow will be re-invested at that rate. Moreover the NPV method maximises wealth which is in line with the objective of shareholder wealth maximisation. Thus when there is a conflict under both these methods, the decision will be taken on the basis of NPV. The main reason for this is the difference in the new investment rate.The profitability index is a capital budgeting tool designed to identify the relationship between the cost of a proposed investment and the benefits that could be produced if the venture was successful. The profitability index employs a ratio that consists of the present value of future cash flows over the initial investment. As this ratio increases beyond 1.0, the proposed investment becomes more desirable to companies. When this ratio does not exceed 1.0, the investment should be rejected, as the project’s present value is less than the initial investment. Sum of discounted cash in flows Profitability Index (PT) ~ Tnitial cash outlay or Total discounted cash outflowAdvantages >The method also uses the concept of time value of moncy and is a better project evaluation technique than NPV. Limitations > Profitability index fails as a guide in resolving capital rationing where projects are indivisible. > Once a single large project with high NPV is selected, possibility of accepting several small projects which together may have higher NPV than the single project is excluded. > Also situations may arise where a project with a lower profitability index selected may generate cash flows in such a way that another project can be taken up one or two years later, the total NPV in such case being more than the one with a project with highest Profitability Index.Problem: Project A Project B ‘The depreciation is 20,000 per year Initial investment | __@ 100,000 100,000 ‘The residual value for both projects ix the same, Cash inflows 220,000. Cost of Capital is 10%. Year 1 245,000 330,000 CALCULATE PL Year2 340,000 330,000 Which project is the better one based on PI? Year 3 335,000 44,000 Year 4 230,000 246,000 Solution: Project A Disc factor(10%) | Disc. CF PV of cath inft of cash inflows ‘Year 0 1.00 100,000) a car £100,004) PI= Cash Ouiflows Year 1 0.909| 40,905 Year 2 0.826| 33,040 PI= 1,34,380/1,00,000 Year3 7st] 26285 = 1.3438 Year 4 0,683] 34,150 Total PV of Cl %1,34,380Problem: ProjectA | Project B [Initial investment | % 100,000 | 210,000 Cash inflows ‘Year 1 245,000 30,000 ‘Year 2 40,000 330,000 Year 3 244,000 Year 4 330,000 246,000 Project B Cash flow | Discount factor | Disc Cash Flow Year 0 ~100,000 1.00 (100,000) Year 1 30,000 0.909 27.270 Year 2 30,000 0.826 24.780 Year 3 44,000 0.751 33,044 Year 4 66,000 0.683 45,078 Total PV of CI 2130172 ‘The depreciation is £20,000 per year. ‘The residual value for both projects is the same, 220,000. Cost of Capital is 10%. CALCULATE PL ‘Which project is the better one based on PI? PV of cash inflows Cash Ouiflows PI= 1,30,172/1,00,000 = 1.30172 As PI > 1 Project is accepted PiDiscounted Payback Period Method Some accountants prefers to calculate payback period after discounting the cash flow by a predetermined rate and the payback period so calculated is called, ‘Discounted payback period’. One of the most popular economic criteria for evaluating capital projects also is the payback period. Payback period is the time required for cumulative cash inflows to recover the cash outflows of the project.Problem: A company has to choose between two altemative machines for which the following details are available, the year wise cash flows for 5 years are as follows: [AMOUNT IN THOUSANDS] Year 0 Year1 ‘Year 2 Year 3. Year 4 Year 5 Machine A -25 - 3 20 14 24 ‘Machine B =40 10 14 16 17 15_| ‘The finance manager tries to appraise the machine by calculating the following: a b. © d. Discounted Payback Period NPV Profitability Index (PI) Payback Period ‘With reasons advise the finance manager. Cost of capital = 10% Solution: Machine A Machine B Year | CF PV Year | CF Disc Factor. PV o | 25 25, 0 -40 1.0000, -40.00 © AS_ per NPV 1 o 0. 1 10 0.9091 9.09 Machine A is 2 5 4.13) 2 14 0.8264. 11.57 to be selected za el ae am ae as de NPVs 4 5 y . 5 24 14.9 3 1s 0.6209 931 higher. NPV 18.62, | NPV 13.61Machine A Year AERO PV Inflows Machine A CF 25 0 5 20 14, 24 Disc Factor 1.0000, 0.9091 0.8264, 0.7513, 0.6830 0.6209 43.62 Profitability Index (PI) =33~ =1L74 PV -25.00) 0.00) 4.13) 15.03} 9.56) 14.90) 43.62, Machine B Year CF 0 -40 1 10 2 14 3 16 4 17 5 15 PV Inflows _ Sum of Discounted Cash Inlows: Profitability Index (PI) = TaigaT Cash Outlay or Total Discounted Cash Outflow Machine B Profitability Index (PI) = 53.64 = 134 Disc Factor 1.0000 0.9091) 0.8264, 0.7513} 0.6830, 0. a PV -40.00 9.09) 1157, 12.02 11.61 931 53.61| Machine A is to be selected as PI of Machine A is higher than that of Machine BCalculation of PBP Machine A Machine B Year CA Cum. C/I Year cA Cum. C/l 1 > : 1 10 10 2 5 5 2 14 24 3 20 25 3 16 40 4 14 39 4 17 37 5 24 63 5 15 72 PBP = 3 years PBP = 3 years Both the machines have PBP of 3 yearsMachine A Year CF Disc Fact 025 1 0 (2s 3 20 414 5S 24 Discounted Payback Period for Machine A =3+ 3 O56 ~ 3.61 years 25 -19. 0.9091 0.8264 0.7513, 0.6830, 0.6209 16 Machine B | Year CF Wewreelo 40 10 | 14 | 16 | 7 1s 40 ~32.68 11.61 = 3.63 years jisc Factor] PY | 1.0004 0.9091) 0.8264 0.7513 0.6830 0.6209 v_Com CF "0 00) - 9.09 9.09 1157, 20.66] 32.68 44.2! 931] 33.60 Discounted Payback Period for Machine B Based on Discounted Payback Period Machine A is to be selected.Problem : X Ltd. wants to replace its old machine with a new one. Two models, A and B, are available at the same cost of %5,00,000 each. Salvage value of the old machinery is 71,00,000. The utilities of the existing machine can be used, if X Ltd. purchases Machine A. Additional cost of utilities to be purchased in that case where the amount is %1,00,000. If the company purchases Machine B, all the existing utilities are to be replaced with new utilities costing %2,00,000. The salvage value of the old utilities will be %20,000. The salvage value at the end of 5 years for machine A will be 750,000 and that of machine B will be 260,000. The cash inflows that are expected, are as follows: Machine 1,00,000 1,50,000 1,80,000 2,00,000 1,70,000 pve nnta 2,00,000 2,10,000 1,80,000 1,70,000 40,000 Find out which machine is more profitable (Under NPV, Discounted Payback and Desirability Factor method . Given, cost of capital = 15%.Machine A ory Da Flows [Factor 15 Pv 1.0000 -500000.00 0.8696 86956.52 0.7561 113421.55 0.6575 11835292 .f 0.5718 114350.65 BI 70. 0.4972 EB 84520.05 5 (Salvage) 0.4972 24858.84 NPV 42460.52 Initial Cash outflow Cost 25,00,000 Less: Salvage value of old Mach —_21,00,000 Add: Additional cost of utilities __21.00,000 Total cash outflow 35,00,000 Machine B Cor a es pig had -5,80,000 2,00,000 Factor 15%| PY 1.0000 -580000.00 0.8696 173913.04 2,10,000 0.7561 158790.17 1,80,000 0.6575 —118352.92 1,70,000 0.5718 — 97198.05 0.4972 19887.07 0.4972 — 29830.60 17971.86 Initial Cash outflow %5,00.000 salvage value of old Mach —1,00,000 Add: Additional cost of utilities %2,00,000 Less: Salvage of old utilities &20,000 Total cash outflow %5,80,000 Machine A has a higher NPV of % 42,460.52, as compared to Machine B having a lower NPV of %17971.86. Thus it is obvious that Machine A is a more profitable choice for X Ltd.Discounted Payback Period B fe Cum Dis CE 1 1,00,000|86956.52| 8656.52! 173913] 173913.04) 2 1,50,000| 113421.6| _ 200378.07| _2,10,000_158790.2| _332703.21 3 1,80,000| 118352.9| _318730.99|__1,80,000| 1183529) _451056.14| 4 200,000] 114350.6 _433081.64| _1,70,000| 97198.05|__548254.19 3 1,70,000) 84520.05) 517601.69| 40,000, 19887.07|__568141.26) 5(Salvage)| 0.4972) 50,000) 24858.84) 542460.52, 60,000, 29830. 597971.86, Machine A Machine B Initial Cash Outflow = %5,00,000 Disc. PBP = 4+ 500000 ~433082 542461 433082 = 4.62 Years Initial Cash Outflow = %5,80,000 Disc. 580000 -548254 PBP = 4+ = 4.64 Years 597972 548254 Both the machines have more or less the same Discounted Payback PeriodDesirability Factor / Profitability Index Sum of discounted cash in flows Profitability Index (PI) = [-itaTcash outlay Or Total discounted cash outilow Medline A Machine B _ 597972 Profitability Index (PI) = $4246 Profitability Index (PI) = Seo909 = 108 = 1.03 The desirability factor (Profitability Index) is higher in the case of Machine A, it is therefore better to choose Machine A.Problem: B Ltd. has a machine having an additional life of 5 years which cost 710,00,000 and has a book value of %4,00,000. A new machine costing %20,00,000 is available. Its capacity is same as the old machine but will result in a savings of variable cost of %7,00,000 p.a. The life of this machine will be 5 years, at the end of which it will have a scrap value of % 2,00,000. Tax rate is 40% and the cost of capital is 12%. The old machine if sold today will realise %1,00,000 and it will have no salvage value at the end of the fifth year. i, Ignoring income tax on additional depreciation and capital gain tax, decide whether the machine will be purchased or not. ii. What will be the difference if additional depreciation and capital gains, both are subject to 40% tax and the scrap value of the new machine is %3,00,000.Solution: tatement showing computation of Incremental Cash Inflow: BN Buss AMOL @ Savings in cost / Incremental revenue 7,00,000 Less: Incremental Depreciation [(20lakh — 2 lakhy/S - (4Laklv/5)] __(2,80,000) Eamings Before Tax 4,20,000 Less: Tax @ 40% (7 Lac @ 40%) (2,80,000) ees acca Profit after Tax 1,40,000 depreciation and ‘Add back: Depreciation 280,000 “ital gain tax Cash Inflow 4,20,000 Statement showing computation of Cash Outflow: Las U RS Cost Less: Redeemable Value of Old Machinery Cash Outflow/Initial Investment