Proj. Appr. Investment Criteria Mba

Investment Criteria The key steps involved in determining whether a project is worthwhile or not are:  Estimate the costs and benefits of the project  Assess the riskiness of the project  Calculate the cost of capital  Compute the criterion of merit and judge whether the project is good or bad It is proposed to discuss the criteria of merit, referred to as investment criteria or capital budgeting techniques. A familiarity with these criteria facilitates an easier understanding of costs and benefits, risk analysis, and cost of capital. The important investment criteria, classified into two broad categories- discounting and non-discounting

Investment Criteria 1. Discounting Criteria :  Net Present Value  Benefit Ratio  Internal Rate of Return 2. Non-discounting Criteria:  Pay Back Period  Accounting Rate of Return Net Present Value The NPV of a project is the sum of the present values of all the cash flows that are expected to occur over the the life of the project. The general formula for NPV is: n

t

NPV = Σ C t / (1 + r ) – Initial Investment t =1

Where C t = cash flow at the end of year t n = life of the project r = discount rate The NPV represents the net benefit over and above the compensation for time and risk. Hence the decision rule associated with the NPV criterion is: Accept the project if the NPV is positive Reject the project if the NPV is negative ( If the NPV = 0 it is the matter of indifference) Properties of NPV Rule a) The value of a firm can be expressed as the sum of the present value of projects in place and the NPV of future projects. Value of a firm = Σ Present value of projects + Σ NPV of expected future projects The first term on RHS captures the value of assets in place and the second term the value of growth opportunities.

(b) When a firm terminates an existing project which has a negative NPV based on its expected future cash flows, the value increases by that amount. Likewise, when a firm undertakes a new project that has a negative NPV, value of the firm decreases by that amount. (c) When a firm divests itself of an existing project, the price at which the project is divested affects the value of the firm. If the price is greater/lesser than the present value of the anticipated cash flows of the project the value of the firm will increase/decrease with the divestiture. (d) When a firm takes on a new project with a positive NPV, its effect on the value of the firm depends on whether its NPV is in line with expectation. (e) When a firm makes an acquisition and pays a price in excess of the present value of the expected cash flows from the acquisition it is like taking on a negative NPV

project and hence will diminish the value of the firm. NPV calculation Permits Time-varying Discount Rates The formula used is as under: n

t

t

NPV = Σ C t / Π(1 + r j )– Initial Investment t =1

j=1

Where C t = cash flow at the end of year t n = life of the project r j = one period discount rate To illustrate for a 5-year project, the following date is available. Discount rate(%) 14 15 16 18 20 Investment -12,000 Cash flow 4,000 5,000 7,000 6,000 5,000 Calculate the Net Present Value.

The PV of each of the cash flows can be calculated as under: PV of C1 = 4,000/ 1.14 = 3509 PV of C2 = 5,000/(1.14*1.15) = 3814 PV of C3 =7,000/(1.14*1.15*1.16) = 4603 PV of C4 = 6,000/(1.14*1.15*1.16*1.18) = 3344 PV of C5 = 5,000/(1.14*1.15*1.16*1.18*1.20) = 2322 PV of project =17592 NPV of project = 17592 – 12,000 = Rs. 5592

Modified NPV The standard NPV method is based on the assumption that the intermediate cash flows are reinvested at a return equal to the cost of capital. However, when this assumption is not valid, the reinvestment rates are applicable to intermediate cash flows need to be defined for calculating the modified NPV as under: Step : Calculate Terminal value of the project’s cash inflows using the explicitly defined reinvestment rate(s). n

n-1

TV = Σ CF t ( 1 + r’) t=1

Where TV = terminal value of the project’s cash inflows CF t = cash inflow at the end of year t r’ = reinvestment rate applicable to the cash inflows of the project

Step 2 : Determine the modified NPV n

NPV* = TV / (1 +r ) – I Where NPV* = Modified NPV TV = terminal value r = cost of capital I = investment outlay Calculate modified NPV: Investment outlay Rs. 1,10,000 Year Cash inflows 1 31,000 2 40,000 3 50,000 4 70,000 Cost of capital 10 % and reinvestment rate is 14%

3

TV

2

= 31000( 1.14)+40,000(1.14) +50,000(1.14) +70,000 = Rs. 2,24,911 4

NPV* = TV/(1.10) – 1,10,000 4

= 2,24,911/(1.10) – 1,10,000 = Rs. 43,614 Benefit Cost Ratio Benefit Cost Ratio BCR = PVB I Net Benefit Cost Ratio NBCR = PVB – I = BCR - 1 I Where PVB = present value of benefits I = initial investment

Year Cash flow 1 Rs. (1,00,000) 2 25,000 3 40,000 4 50,000 5 40,000 6 60,000 If the cost of the capital is 12%, calculate BCR and NBCR BCR = 25,000+ 40,000+50,000+40,000 +60,000 = 1.273 (1.12) (1.12)² (1.12)³ (1.12)4 (1.12)5 1,00,000 NBCR = BCR – 1 = 0.273 Rule is as under: When BCR or NBCR Rule is >1 >0 Accept =1 =0 Indifferent <1 <0 Reject

Internal Rate of Return The IRR of a project is the discount rate which makes its NPV equal to zero. Alternatively, it is the discount rate which equates the present value of future cash flows with the initial investment. n

t

Investment = Σ C t / (1 + r ) t =1

Where C t = cash flow at the end of year t n = life of the project r = internal rate of return (IRR) In the NPV calculation we assume that the discount rate (cost of capital) is known and determine the NPV. In IRR calculation, we set the NPV to zero and determine the discount rate that satisfies this condition. The calculation of r involves a process of trial and error. (iterative process). Suppose for some project of an initial investment of Rs. 1,00,000 we get at r=15%,

we get RHS= 1,00,802 and at r= 16%, RHS = 98,641, we find that the value of r lies between 15 % and 16 %. For a refined estimate of r we use the following procedure. 1. NPV (for15%) = 802 and NPV (for16%) = -1,359. 2. Sum of the absolute value of both = 802 + 1,359 = 2,162 3. Calculate the ratio of the smaller discount rate, 802 / 2161 = 0.37 4. Add the number to the smaller discount rate 15 +0.37 = 15.37% The rule is: if the IRR is greater than the cost of capital, then accept the project and if less than the cost of capital reject the project. NPV and IRR Both rules lead to identical decision subject to: 1. The cash flows of the project must be conventional i.e. the initial investment is negative and the subsequent cash flows are positive. 2. The project must be independent.

Modified IRR Despite NPV’s conceptual superiority, managers seem to prefer IRR over NPV because IRR is intuitively more appealing as it is a percentage measure.There is a percentage measure that overcomes the shortcomings of regular IRR which is called the modified IRR or MIRR. How to calculate MIRR? Step 1: Calculate the present value of costs (PVC) of the project, using the cost of capital (r) as the discount rate. n

t

PVC = Σ Cash outflow t / ( 1 + r ) t =0

Step 2: Calculate the terminal value(TV) of the cash inflows n

n–t

TV = Σ Cash inflow t ( 1 + r ) t =0

Step 3: Obtain MIRR by solving the following equation: n

PVC = TV / I + MIRR ) Consider the case where the expected cash flows of a project is as follows: Year Cash flows 0 Rs. (1,000) 1 (1,200) 2 (600) 3 (250) 4 2,000 5 4,000 If the cost of the capital is 12 %, calculate the project’s MIRR. Solution: PV = 1,000 + 1200/1.12 +600/(1.12)²+ 250(1.12)³ = 1,000 +1071 +478 +223 =2772 TV = 2,000 (1.12) + 4,000 = 6240

To obtain IMRR, 2772 = 6240 / ( 1+MIIR)ª where a = 5 MIRR = (2.251)1/5 – 1 = Evaluation MIRR is superior to the regular IRR in two ways: 1. It assumes that project cash flows are reinvested at the cost of capital whereas the regular IRR assumes that project cash flows are reinvested at the project’s own IRR. Since reinvestment at cost of capital is more realistic than reinvestment at IRR, MIRR reflects better the true profitability of a project. 2. The problem of multiple rates does not exist with MIRR. Conclusion: 1. If the mutually exclusively projects are of the same size, NPV and MIRR lead to the same decision irrespective of variations in life.

2. If the mutually exclusive projects differ in size, there is a possibility of conflict. Pay Back Period  PBP is the length of time required to recover the initial cash outlay on the project.  According to PBP criterion, the shorter the PBP, the more desirable the project. Firms using this criterion generally specify the maximum acceptable PBP.  PBP is widely used as it is simple, both in concept and application, and it is a rough and ready method for dealing with risk. However, it has serious limitations: it does not consider the time value of money; it ignores cash flows beyond the PBP; it is a measure of capital recovery, not profitability.  To overcome the limitation of not considering time value of money, the discounted payback period has been suggested, as discussed below.

Discounted Pay Back Period Example: Year Cash Flow Discounting Present Value Factor @ 10% Rs. 0 –10,000 1.000 Rs. –10,000 1 3,000 0.909 2,727 2 3,000 0.836 2,478 3 4,000 0.751 3,004 4 4,000 0.683 2,732 5 5,000 0.621 3,105 6 2,000 0.565 1,130 7 3,000 0.513 1,539

Cumulative Net Cash Flow after Discounting –10,000 - 7,273 - 4,795 - 1,791 941

It can be observed that the PBP is 3 years, while discounted PBP lies between 3 and 4 years Accounting Rate of Return The accounting rate of return, also called the average rate of return, is defined as Profit after tax Book Value of the investment

The accounting rate of return has certain virtues: 1. It is simple to calculate. 2. It is based on accounting information which is readily available and familiar to businessmen. 3. It considers benefits over the entire life of the projects. However, there are serious shortcomings; 1. It is based upon accounting profit, not cash flow. 2. It does not take into account the time value of money. 3. It is internally inconsistent. Assessment of Various Methods All the five basic methods of evaluation have been discussed at length. We shall now do a summary assessment of these methods on the basis of certain theoretical and practical considerations.

NPV Theoretical /Practical considerations 1. Does the method consider Yes all cash flows? 2. Does the method discount Yes cash flows at the opportunity cost of funds 3. Does the method satisfy Yes the principle value of additivity? 4. From a set of mutually Yes exclusively projects, does the method choose the project which maximizes shareholder wealth? 5. Is the method simple? Yes 6. Can the method be used No with limited information? 7. Does the method give a No relative measure?

BCR

IRR

PBP

ARR

Yes

Yes

No

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Yes

No

No

No

No

No

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No

No

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Yes No

Yes No

Yes

Yes

Yes Yes Perhaps Yes No

Yes

Project Appraisal International Practice  In the U.S. , the internal rate of return, net present value, accounting rate of return, and pay back period are the most popular methods of project appraisal.  Japanese firms appear to rely mainly on two kinds of analysis (i) One year return on investment analysis, and (ii) residual investment analysis. Residual investment analysis is similar to the discounted payback analysis. This analysis shows how long it will take for the residual investment in the project to become zero after taking into account the time vale of money. This period is conceptually equal to the discounted pay back period.