Introduction of Capital Budgeting Dr. Himanshu Joshi FORE School of Management New Delhi

Overview Capital budgeting is process of deciding whether or not to undertake an investment project. There are two standard concepts used in capital budgeting: 1.Net Present Value (NPV) 2.Internal Rate of Return (IRR) We will discuss the application of these concepts in Capital Budgeting Process.

After this session you should be able to answer these questions: Should you undertake a specific project? – “yes”/ “No” Decision. Ranking projects: if you have several alternative investments, only one of which you can choose, which should you undertake? Should you use NPV or IRR? Sunk costs. How should you account for costs incurred in the past? The cost of forgone opportunities? Salvage value and terminal values?

Finance Concepts Discussed Payback Discounted payback ARR IRR NPV Project Ranking using IRR and NPV Terminal Value Cost of foregone opportunities Sunk costs

Excel Function used NPV IRR Data Tables

Investment Criteria / Evaluation Techniques : It is classified into two broad categories – traditional methods and time adjusted methods (or discounted cash flow methods). Investment Criteria Traditional Method or Non-Discounting Criteria Time Adjusted Methods or Discounting Criteria Payback Period Average rate of return Net Present Value Benefit Cost Ratio Net Terminal Value Internal Rate of Return Profitability Index Modified IRR

A. Traditional Method / Non-Discounting Criteria : Payback Period It is the length of time required to recover the initial cash outlay on the project. PB = Investment / Constant annual cash flow (if cash flow is constant) Accept-Reject Criterion: If actual pay back period is less than the predetermined by the management, project will be accepted, otherwise rejected.

Payback period.. For irregular cash flow, cumulative cash flow will be calculated and then pay back period will be calculated. suppose a project require investment of Rs and the stream of cash flow is as follows – Rs 15000,12000,15000,10000,5000 for next 5 years,

Calculation.. YearCash FlowCumulative C. F Thus pay back period will be between 3 rd and 4 th year. The fractional part (after 3 rd year) can be calculated as – 8000/10000 = 0.8, therefore pay back period will be 3.8 years.

Discounted Payback Period A major shortcoming of the conventional payback method is that it does not consider time value of money. To overcome this limitation, discounted payback period is used. Here the project is evaluated on the basis of time value of money of each cash-flow.

Average Rate of Return / Accounting Rate of Return (ARR) It based on the concept of ROI or rate of return. Defined as the annualized net income earned on the average funds invested in a project. ARR = Profit After Tax. Book value of the investment

Accept-Reject Rule The actual ARR will be compared with predetermined or a minimum required rate of return or a cut-off rate. A project would be accepted if actual ARR is higher than the minimum desired ARR.

ARR… Consider the following investment opportunity: a machine is available for purchase at a cost of Rs.80,000. we expect it to have a scrap value of Rs.10,000 at the end of five year period. We have estimated that it will generate additional profits over its life time as follows: YearAmount (Rs.) 120, , , ,000 55,000

B. Time Adjusted Methods / Discounting Criterion : NPV It is defined as the sum of the present values of all the cash inflows less the sum of present values of all the cash outflows.

NPV..

If cash outflow is also expected to occur at some time other than at initial investment and salvage value and working capital is also to be adjusted, then NPV will be calculated as

where C t = cash inflow at different time periods CO t = cash outflow at different time periods r = discount rate t = time periods S n = salvage value W n = working capital adjustment Accept-Reject Rule : NPV > zero, accept; NPV < zero, reject; NPV = zero, indifferent. However it is rare that NPV is equal to zero.

NPV..SpreadsheetModelling.xlsxSpreadsheetModelling.xlsx Calculate the NPV of a Project having cash outlay of Rs. 1,00,000 at present, and homogenous cash inflow of Rs. 28,000 per year for five years after one from the commencement of the project. Appropriate discounting rate for the project is 10%.

Basic NPV

Proper NPV Format in Spreadsheet

NPV for Two Projects.. Lets assume that you are trying to decide whether to undertake one of the two projects. Project A involves buying expensive machinery that produces better product at a lower cost. The machine for project A cost $1,000 and if purchased, you anticipate that the project will produce cash flows of $500 per year for the next five years. Project B’s machines are cheaper, costing $800, but they produce smaller annual cash flows of $420 per year for the next five years. We will assume that the correct discount rate is 12%.

NPV TWO Projects Discount Rate12% YearProject AProject B NPV

NPV Both projects are worthwhile, since each has a positive NPV, if we have to choose between the projects, then project A is preferred over project B because it has higher NPV.

Properties of NPV Rule :  NPVs are additive – the NPVs of different projects can be added to arrive at a cumulative NPV for a business  Intermediate cash flows are reinvested at cost of capital – i.e., the cash flows that occur between the initiation and termination of the project are reinvested at a rate of return equal to the cost of capital.  NPV calculation permits time varying discount rate – same discount rate throughout the entire life of the project may not always the case. Thus for different discount rates, the formula will be as follows -

NPV Profile: NPV Profile shows a project’s NPV graphed as a function of various Discount Rates. Typically NPV is graphed vertically on Y-Axis and Discount Rates are graphed horizontally on X-Axis.

Internal Rate of Return (IRR) : It is defined as the IRR of a project is the discount rate which makes its NPV equal to zero. Thus IRR is the discount rate which will equates the present value of cash inflows with the present value of cash outflows. Therefore for a project, the IRR will be – where CO o = initial cash outflow or investment C t = cash inflow at different time periods S n & W n = salvage value and working capital at the end of n years r = rate of discount / IRR (to be calculated) n = life of the project

If the project requires investment at different time periods, then Accept-Reject Rule : If IRR > cost of capital, accept. If IRR < cost of capital, reject. If IRR = cost of capital, indifferent.

NPV and IRR : The IRR approach solves for a rate unique to each project, while the NPV approach solves for trade-off cash inflows and outflows using a general required rate of return. IRR gives percentage return while NPV gives absolute return. NPV shows expected increase in the wealth of the share holders while IRR does not. NPV of different projects are additive while the IRRs can not be added.

TWO Projects Discount Rate12% YearProject AProject B NPV IRR41%44% NPV vs. IRR

NPV vs IRR

NPV vs. IRR As per NPV both the projects are worthwhile as they both have positive NPV, but project A is having higher NPV, should be selected. As per IRR criterion both the projects having IRR greater than hurdle rate (41% > 12% for A) and (44% >12% for B), thus as per IRR project B should be selected.

NPV or IRR, which to USE? In case of conflict between NPV and IRR results, you should always use the NPV to decide between projects. Why? The answer exists in the Wealth Maximization Theory. The logic is that if individuals are interested in maximizing their wealth, they should use NPV, which measures the incremental wealth from undertaking a project.

A General Principle For conventional projects, projects with an initial negative cash flows and subsequent non negative cash flows (CF 0 0), the IRR and NPV criteria lead to the same “Yes-No” decision: if the NPV criterion indicates “yes” decision, then so will the IRR criterion (and vice versa).

IRR Manual Calculationa A company has to select one of the following two projects: (Rs.) using the IRR method suggest which project is better? Project AProject B Cost11,00010,000 Cash in Flows Year Year Year Year

Calculation..IRRsx.xlsxIRRsx.xlsx Key Factor F = I/C I = Original Investment C = Average Cash inflows per year Key factor should then be located into table for value of Re 1 received annually for n years.

DO NPV and IRR produce the same Project Rankings? RANKING PROJECTS WITH NPV AND IRR Discount Rate15% YearProject AProject B NPV IRR20%27% RANKING PROJECTS WITH NPV AND IRR Discount Rate0.08 YearProject AProject B NPV$216.64$ IRR20%27%

DO NPV and IRR produce the same Project Rankings? Case 1. at 15% discount rate, there is no conflict between NPV and IRR. Case 2. at 8% discount rate, Project A is preferred by NPV over project B, while project B is preferred by IRR over project A. Why?

Why Do NPV and IRR give Different Rankings? Discount RateNPV Project ANPV Project B 0% % % % % % % % % % % % % % % %

Why Do NPV and IRR give Different Rankings? From the Graph on the previous slide: Project B has higher IRR (27.38%) than Project A (19.77%). When discount rate is low, project A has higher NPV than project B, but when the discount rate is high, project B has higher NPV. There is a crossover point (8.51%) that marks the disagreement/agreement range. Project A’s NPV is more sensitive to changes in the discount rate than project B’s NPV. The reason for this is that project A’s cash flows are more spread out over time than those of project B.

Why Do NPV and IRR give Different Rankings? CriterionDiscount Rate <8.51%Discount Rate = 8.51%Discount Rate > 8.51% NPVProject A is preferred NPV (A) > NPV B Indifferent between A and B NPV (A) > NPV(B) Project B is preferred over B NPV(A)<NPV(B) IRRProject B is always preferred to Project A IRR (B) > IRR (A)

Calculating Crossover Point The crossover point- is the discount rate at which the NPVs of the two projects are equal. The crossover point is the IRR of the differential cash flows. NPV (A) = NPV (B) CF 0 A –CF 0 B + (CF 1 A –CF 1 B )/(1+r) + (CF 2 A –CF 2 B )/(1+r) (CF N A –CF N B )/(1+r) N = 0

Calculating the Crossover Point RANKING PROJECTS WITH NPV AND IRR Discount Rate0.08 YearProject AProject BDifferential Cash Flows NPV$216.64$ IRR19.77%27.38%8.51%

Profitability Index Method..

where CI = cash inflow CO = cash outflow r = discount rate n = project life Accept-Reject Rule : PI >1, accept; PI < 1, reject; PI = 0, indifferent. Profitability Index..

The Multiple IRR Problem and the NO IRR Problem IRRsx.xlsxIRRsx.xlsx A Problem that can arise with the IRR criterion is the “multiple IRR problem”. This is possible when we have non-conventional cash flows: Time012 Cash Flow

No IRR Problem Time012 Cash Flow

Problems with IRR For non-conventional cash flows projects, the multiple IRR problem and no IRR problem can occur. The IRR Equation is essentially an n th degree polynomial. An nth degree polynomial can have up to n solutions, although it will have no real solutions than the number of cash flow sign changes. For example: a project with two sign changes could have zero, one or two IRRs. Analyst should be aware of the unusual cash flow pattern that can generate the multiple IRR problem.

NPV and the Share Price XYZ Inc. is investing $600 million in distribution facilities. The present value of the future after tax cash flows is estimated to be $ 850 million. XYZ has 200 million shares outstanding with a current market price of $32.00 per share. This investment is a new information, and it is independent of other expectations about the company. What should be effect of the project on the value of company and stock?

Capital Budgeting Principle: Ignore Sunk Costs and Consider only Marginal Cash flows You recently bought a plot and built a house on it, your intention was to sell the house immediately, but it turns out that house is really badly built an cannot be sold in its current state. The house and the land cost you $1,00,000, and a friendly local contractor has offered to make the necessary repairs, which will cost $20,000. your real estate broker estimates that even with these repairs you will never sell the house for more than $90,000, what should you do? There are two approaches to answering this question: 1.“Don’t throw good money after bad.” 2.“Don’t cry over spilt milk.”

Sunk Costs? IGNORE SUNK COSts House Cost Fix up cost20000 Option 1Option 2 YearCash flowCash Flow IRR-25%350%

Terminal Value An asset’s value at the end of the investment horizon is called the asset’s terminal value. If the asset has a finite life then the value of asset at the end of that life period is known as salvage value. One need to estimate the expected salvage value of an asset. For assets having infinite life, terminal value is not salvage value, and can be calculated as follows: For no growth in cash flows asset = Cash flows/Hurdle rate For an asset with growing cash flows = Terminal Cash flow/hurdle rate – constant growth

An Example of Capital Budgeting Apartment Cash flows Cost of Apartment Tax Rate30% Annual Reportable Income Rent24000 Expenses property taxes-1500 miscellaneous expenses-1000 depreciation reportable income11500 tax3450 Net Income8050 Expected life of the apartment is 10 years and appropriate hurdle rate is 12%. The expected terminal value (salvage value) at the end of 12 years is 80,000.

Book Value vs. Terminal Value Book value of an asset is its initial purchase price minus the accumulated depreciation. The terminal value of an asset is assumed market value at the time you stop writing down the asset’s cash flows.