Financial Management

Session -2 & 3

Capital Budgeting & Project Valuation

Stages in Capital Budgeting

A firm must continually evaluate possible investments, therefore, capital budgeting is an ongoing process. Long-term decisions; involve large expenditures. Analysis of potential additions to fixed assets.

Stages in Capital Budgeting Investment screening and selection Capital budget proposal Budgeting approval and authorization Project tracking Post-completion audit

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Project Classifications

Independent Projects If the cash flows of one are unaffected by the acceptance of

the other.

Mutually Exclusive Projects If the cash flows of one can be adversely impacted by the

acceptance of the other

Contingent Projects Complementary Projects

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Mutually Exclusive Projects: Example

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BRIDGEvs.BOATtogetproductsacrossariver.

(1) Steps in Capital Budgeting

A firm must continually evaluate possible investments, therefore, capital budgeting is an ongoing process. A project can be viewed in financial terms as inflow and outflows of cash at certain points of time.

1)The first step is to estimate project cost and cash outflows along with the timings. Project cost is the sum of the cost of fixed assets and margin money required for organizing working capital for the business.

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Steps in Capital BudgetingContd 2)An estimation of net cash inflows from the project after its

implementation is called for, along with the timings of such inflows. The sale value of assets created in the project will also have to be estimated at a specified terminal date based on economic life of the assets.

3)The possible variations in project cash flows due to changes in parameters affecting the project are also to be estimated. The risk factor of cash flows also needs to be evaluated.

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Steps in Capital BudgetingContd 4) A decision has to be taken regarding the discount rate to be

used for calculating present values of cash flows. The discount rate should reflect the risk factors of the business.

5) Finally, the project has to be evaluated based on an appropriate capital budgeting decision rule.

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(2) Estimating Project Cash Flows

Incremental Cash FlowsCash flow during a particular period

= Cash flow if the project is implemented Cash flow without the project.

Sunk Costs Sunk cost is a cost that has already been incurred and as

such, exists irrespective of whether the project is undertaken or not. This cost should not to be considered as part of project cash flows

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Estimating Project Cash FlowsContd

Opportunity Costs Opportunity costs should be part of project cash flows. Suppose, a company has some vacant land. It now wants to

set up a factory on that land as part of an investment project.

The project should be charged with the current selling price of the piece of land.

Net Working Capital Increase in NWC is cash outflow and vice versa. At the end

of the project life, remaining NWC is cash inflow.

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Estimating Project Cash FlowsContd Externalities

All side effects should be considered for calculating incremental cash flows for a project.

Post-tax Cash Flows Taxes are positive cash outflows. So, they have to be

accounted as cash outflows whenever payments are made. So, we consider only the post-tax incremental cash flows.

Timing of Cash Flows The cash flows have to be reckoned when they are incurred

and not when they accrue in an accounting sense.

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(3) Evaluation of Project Using Cash Flows

i. Payback Periodii. Discounted Payback Periodiii. Accounting Rate of Return (ARR)iv. Net Present Value (NPV)v. Internal Rate of Return (IRR)vi. Modified Internal Rate of Return (MIRR)vii. Profitability Index

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Evaluation of Project : Example

Year Project A Project B0 (1000) (1000)1 100 5002 200 4003 400 3004 500 2005 600 100

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Consider two projects A and B, whose cash flows are given with timings

(i) Payback Period

The number of years required to recover a projects cost, or how long does it take to get the businesss money back?

The decision rule for accepting an investment is that an investment is acceptable if its calculated payback period is less than the specified time of the project.

While comparing two investment projects using this rule, then the project with shorter payback period would be preferred.

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Payback PeriodContd

Project AInitial cost = 1000Recovery over the first 3 years = 100 + 200

+ 400 = 700Balance amount to be recovered

= 1000 700 = 300Cash flow during the 4th year = 500So, payback period = 3+300/500 = 3.6 years

Similarly for Project B 2.3 years

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Payback PeriodContd

Advantages Provides an indication of a projects risk and liquidity. Because projects with lower payback period get selected.

These projects would free up cash for other uses more quickly than projects with longer payback period.

Disadvantages Does not consider the time value of money. Ignores cash flows beyond the payback period. Negatively biased towards projects like R&D which have

longer payback period.

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(ii) Discounted Payback Period

A discounted payback period is calculated by finding out the payback period based on discounted net cash flows.

The rate of discount used is the projects overall cost of capital.

Suppose the overall cost of capital of the projects A and B are 10 % p.a. What will be the discounted payback period for project A and B

Discounted payback period for project A = 4.27 yearProject B 2.95 years

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(iii) Accounting Rate of Return (ARR)

Accounting rate of return (ARR)= Average net accounting income / Average book value

of investment

The decision rule : A project is acceptable if its accounting rate of return is

more than the target rate of return.

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ARRExample Suppose a project needs investment of Rs.1000, has a life of 5

years and PAT in each of the 5 years are as follows.

Year Net Accounting Income (PAT)1 1122 1673 2334 1505 58

Then, the average net accounting income = Rs.144 The book values of investment at the start of the project and at

the end are Rs.1000 and zero respectively. So, average book value of investment = Rs.500 So, accounting rate of return (ARR) = 144/500 = 28.8 %

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Accounting Rate of Return (ARR)Contd Advantages:

Required simple calculation and easy availability of desired information

Disadvantages: Does not consider time value of money, Uses book value of investment and accounting income

instead of market value of investment and cash flows. An arbitrary cut-off rate of return is used to approve a

project.

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(iv) Net Present Value (NPV) Net present value is the difference between the

present values of cash inflows and cash outflows.

NPV =

where CFt = cash flow during the period tn = number of periodsr = discount rate of return

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Net Present Value (NPV)Contd Steps Involved in estimating NPV

Estimate CFs (inflows & outflows).

Assess riskiness of CFs.

Determine k = WACC for project.

Find NPV

Accept if NPV > 0

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Net Present Value (NPV)Example With 10% discount rate, NPV of Project A = -1000 +100/1.1 + 200/1.1^2 +

400/1.1^3 + 500/1.1^4 + 600/1.1^5 = Rs. 270.79

NPV of Project B = -1000 +500/1.1 + 400/1.1^2 + 300/1.1^3 + 200/1.1^4 + 100/1.1^5 = Rs. 209.21

The decision rule using NPV method is that an acceptable project should have positive NPV because in that case the investment earns more than it costs. The value of the firm rises by the positive NPV of the

project. It also has value additivity property.

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(v) Internal Rate of Return (IRR) Internal rate of return (IRR) is defined as that discount

rate at which the net present value of cash flows is equal to zero.

This means that the present value of cash inflows is equal to the present value of cash outflows.

The decision rule using IRR is that an investment is acceptable if IRR exceeds the required rate of return.

IRR summarizes the information about a project in a single rate of return.

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Internal Rate of Return (IRR) NPV = CFt/(1+IRR)^t = 0 over the life period.

IRR for Project A = 17.73%

IRR for Project B = 20.27%

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NPV Profile

The Net present value profile is a graphical representation of the relationship between an investments NPVs and various discount rates.

Discount Rate NPV Project A NPV Project B

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NPVProfile NPVA NPVB0% 800.00 500.006% 452.59 312.7310% 270.78 209.2114% 119.26 119.2316% 52.92 78.57

17.73% (0.08) 45.4620.27% (71.26) 0.03

NPV ProfileContd

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Crossoverrate

(200.00)

(100.00)

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

900.00

0% 6% 10% 14% 16% 17.73% 20.27%

NPVProfile

NPVA NPVB

CrossOverRate

Cross Over Rate

Specific return required for the projects to have the same net present value

Helps to determine out of two projects which will be more profitable in the short and long terms

Steps Involved in Calculating CoR: Find cash flow differences between the projects. Calculate IRR on cash flow differential. Crossover rate =

14% for project A and B. Can subtract cash flows of A from B or vice versa, but

better to have first CF negative. If profiles dont cross, one project dominates the other.

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Two Reasons NPV Profiles Cross

Size (scale) differences. Smaller project frees up funds early.

The higher the opportunity cost, the more valuable these funds, so high k favours small projects.

Timing differences. Project with faster payback provides more CF in early years for reinvestment.

If k is high, early CF especially is good, NPVShort > NPVLong.

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NPV ProfileContd

NPVs of the projects A and B are same at the discount rate of 14 %. This rate is called the crossover rate.

The NPV of project A is higher than the NPV of project B at discount rates lower than the crossover rate but the NPV of project B is higher than the NPV of project A at

discount rates higher than the crossover rate.

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NPV Vs IRR

NPV is calculated using a discount rate (k) and assumes reinvest at k (opportunity cost of capital).

IRR is the discount rate at which NPV is equal to zero and IRR assumes reinvest at IRR.

Reinvest at opportunity cost, k, is more realistic, so NPV method is better. NPV should be used to choose between mutually exclusive projects.

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NPV Vs IRRContd For any independent project, if the project has a

positive NPV at a discount rate equal to the cost of capital, Then its IRR will automatically be higher than the cost of

capital.

This implies that both the NPV and the IRR decision rules will lead to the same conclusion for independent projects.

So, the IRR and the NPV rules have no conflict for such projects.

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NPV Vs IRRContd

NPV and IRR always lead to the same accept/reject decision for independent projects

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k > IRRand NPV < 0.

Reject.

k (%)IRR

IRR > kand NPV > 0

Accept.NPV

NPV Vs IRRContd

However, for mutually exclusive projects the situation is different. Suppose, the projects A and B are mutually exclusive

meaning that if the project A is taken up then the project B need not be taken up.

Then, which project is financially superior?

If we apply the IRR rule then the project B with IRR of 20.27 % will be accepted instead of project A, whose IRR is 17.73 %.

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NPV Vs IRRContd If we apply the NPV rule and the cost of capital is

more than the crossover rate of 14 % then the NPV of project B is higher than the NPV of project A. So, the project B should be accepted.

If the cost of capital is less than the crossover rate of 14 % then the NPV of project A is higher than the NPV of project B and the project A should be accepted.

The conflict arises because of differences in scale and timings of the cash flows.

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NPV Vs IRRContd

The critical issue is the reinvestment rate at which the intermediate cash inflows can be reinvested.

The implicit assumption in the IRR method is that the intermediate cash inflows are reinvested at the IRR rate.

However, in case of NPV method, it is assumed implicitly that the intermediate cash inflows are reinvested at the cost of capital that is generally used as the discount rate for estimating NPV.

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NPV Vs IRRContd So, we need to decide which is the better reinvestment

rate IRR or cost of capital.

IRR is usually higher than the cost of capital and if it is possible to raise money from capital markets at the cost of capital. So, reinvestment of the intermediate cash inflows at the rate of

cost of capital is certainly a more logical assumption.

In view of the above argument, NPV method would be preferred for mutually exclusive projects whenever conflict arises.

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Disadvantages of IRR Lending/Investing or Borrowing/Financing Multiple IRRs

The equation used to calculate IRR, is a polynomial equation of degree n. So, there will be n solutions of IRR.

This is usually not a problem when initial negative cash flow is followed by a series of positive cash flows. In this case, all except one solution will be imaginary.

However, when project cash flows are such that initial negative cash flows are followed by positive cash flows and again followed by negative cash flows in some of the future periods, then mathematically multiple real solutions of IRR are available.

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Disadvantages of IRRContd

Multiple IRRsExample Suppose a company takes a machine on rent from a

supplier for a period of 2 years with the understanding that the company will pay the rent of the machine of Rs.20 million at the end of 2 years when the machine will be returned.

The company spends Rs.2 million to install the machine and earns Rs.10.5 million and Rs.10 million in the 1st and 2nd year respectively before returning the machine. What is the IRR of this investment?

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Disadvantages of IRRContd

Multiple IRRs..Example The cash flows are as follows:

Time (Yrs) Amount0 - Rs.2 million1 + Rs.10.5 million2 Rs.10 million [ -20+10 ]

So, the IRR of the investment can be calculated by solving the equation,

- 2 + 10.5/(1+k) -10/(1+k)^2 = 0 Solving we get,

K = 25% and also 300%

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Disadvantages of IRRContd

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-2000

-1000

0

1000

0 25 90.5 300

Discount rate (%)

NPV

(Rs.

thou

sand

)

Disadvantages of IRRContd

Multiple IRRsExample Now, we are in a dilemma - which IRR is correct?

In some cases there may be more than two solutions

In all such cases, the NPV rule should be applied.

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(vi)Modified Internal Rate of Return (MIRR) Returns the modified internal rate of return for a series of

periodic cash flows by considering both the cost of the investment and the interest received on reinvestment of cash.

The PV of all cash outflows are calculated using cost of capital as the discount rate.

Then the terminal values of all cash inflows are calculated using the cost of reinvestment.

Finally the sum of the PV of cash outflows and the sum of the terminal values of cash inflows are equated to calculate the MIRR.

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(vii) Profitability Index (PI) PI is the ratio of payoff to investment of a proposed

project

PI is defined as:PI = PV (cash inflows subsequent to initial

investment) / Initial investment

An investment is acceptable only if the PI is greater than 1.0.

The PI decision rule is a variant of the NPV.

PI method is very useful for capital rationing.

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Mutually Exclusive Projects

In case of mutually exclusive projects, one of the projects needs to be selected.

Such projects differ in three ways: Size of investment Cash flow pattern Life of the project

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Mutually Exclusive Projects with Unequal Lives

If size of investment is the only difference, then NPV method may be preferred. Use incremental cash flows if uses PI.

If cash flow pattern is the only difference, then NPV/PI method should be used.

If lives are different, then one of the following methods should be used. Equivalent annual annuity method (EAA) Replacement chain method

In both methods we assume that the firms reinvestment opportunities in future will be similar to the current ones.

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Evaluating Mutually Exclusive Projects with Unequal Lives Equivalent annuity method

Calculates the constant annual cash flow generated by a project over its lifespan if it was an annuity.

The annuity value that provides the same NPV over the economic life is calculated for each project using the cost of capital as the discount rate.

Then, the annuities of the mutually exclusive projects are compared and the project with the higher annuity is accepted.

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Evaluation of Project : Example EAA

Year Project A Project B0 (400) (1000)1 100 5002 200 4003 400 3004 2005 100

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Consider two projects A and B, whose cash flows are given with timings, Project A & B has economic life of 3 years and 5 years respectively.

Evaluating Mutually Exclusive Projects with Unequal Lives Equivalent annuity method

NPV(A.) is Rs.156.72, NPV(B) is 209.21 Then, the equivalent annuity, A can be determined by

using the equation:156.72 = A/1.1+A/1.1^2+A/1.1^3A = 63.02

Similiarly 209.21 = B/1.1+B/1.1^2+B/1.1^3+B/1.1^4+B/1.1^5

B = 55.19 Therefore, Project A is better

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Mutually Exclusive Projects with Unequal Lives

Replacement chain method Each of the individual projects is replicated until the lowest

common life span is reached.

Each replication is treated as if the initial NPV is received at the replication dates of each project, and this stream of NPVs is discounted to the present day to give a common life NPV.

The decision is then made on the current NPVs.

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Mutually Exclusive Projects with Unequal Lives

Replacement chain method

NPV(A) = 477.13 NPV(B) = 419.35 Therefore project A is better

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t 0 1 2 3 4 5 6 7 8 9 10

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12 13

14

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A 156 156 156 156 156

B 209 209

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Capital Rationing Capital rationing is undertaken when a company has

many positive NPV projects but not enough funds to take up all of them.

This can be solved by linear programming but if the number of projects is small, then all possible sets of projects can be checked and the set which provides the highest NPV can be selected.

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Capital RationingContdSuppose, a company has five projects with investment, NPV and PI as follows: -Project Investment NPV PI

1 Rs.100, 000 Rs.10, 000 1.12 Rs.100, 000 Rs.25, 000 1.253 Rs.200, 000 Rs.30, 000 1.154 Rs.200, 000 Rs.10, 000 0.955 Rs.300, 000 Rs.15, 000 1.05

Suppose, the company has Rs.400, 000 for investment.Then, which projects are to be selected?

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Capital RationingContd The project 4 need not be considered because PI < 1.0

and has negative NPV. In terms of ranking, the project 2 is most profitable (highest PI) and the projects 3, 1 and 5 are attractive in that order.

Now, since investible fund is Rs.400, 000, the possible selection could be (2 and 5), (1 and 5) and (1, 2 and 3). All these would require Rs.400, 000 of investment.

The net NPVs of these sets are Rs.40,000, Rs.35,000 and Rs.65,000 respectively.

The final selection is the projects 1, 2 and 3 since this set of projects would maximize the NPV.

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Exercise: 1 Identify which of the following items would be part

of net cash flow of an investment proposal.

1. Savings due to reduction of wastage of raw materials because of the implementation of the project.

2. Depreciation of new machinery purchased for the project.3. Fees of a consultant engaged for evaluating the investment

proposal.4. Loss of sale of some existing products resulting from sale of

some products, available from the new investment project.Optionsa) 1, 2 and 3b) 1 and 4c) 1 and 2d) all of them

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Exercise: 2

The implicit assumption in the IRR rule is that the reinvestment of the intermediate cash flows takes place at the rate equivalent to :

a) cost of capitalb) appropriate market rates prevailing when the cash

inflows are receivedc) internal rate of returnd) none of the above rules

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Exercise: 3 A company is planning an overseas expansion

project. The estimated cash flows are as follows:-Year Cash flow0 -Rs.2,000,0001 Rs.200,0002 Rs.300,0003-10 Rs.500,000

The payback period for the project is a) 10 yearsb) 8 yearsc) 5 yearsd) None of the above

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Exercise: 4 A company is planning an overseas expansion

project. The estimated cash flows are as follows:-Year Cash flow0 -Rs.2,000,0001 Rs.200,0002 Rs.300,0003-10 Rs.500,000

The cost of capital is 10 %. The NPV of the project is:a) Rs.634,268b) Rs.441,496c) Rs.2,634,268d) None of the above

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Exercise: 5

A machine has an NPV of Rs.15 million for one 4-year replacement cycle. The cost of capital for this machine is 10 percent. The equivalent annuity for the NPV of this machine is

a) Rs.3.75 millionb) Rs.1.50 millionc) Rs.4.73 milliond) None of the above

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Exercise: 6 A company is considering a capital investment project

that has the following expected cash flows. abandonment values that the company expects to receive if the project is Abandoned at the end of the particular years are also given. Year 0 1 2 3 4 5 6Cash flow - 80 30 30 40 30 20 10Abandonment value 60 50 35 25 10

Cost of capital of the project is 12 %. For maximizing shareholders wealth, At the end of which year it will be optimal to abandon the project. The figures are in Rupees million.

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Exercise: 6ContdSolution:NPV of the project if not abandoned

= - 80 + 30/1.12 + 30/1.12^2 + 40/1.12^3 + 30/1.12^4 + 20/1.12^5 + 10/1.12^6 = 32.88

NPV if abandoned after one year= - 80 + 90/1.12 = -5

NPV if abandoned after two years = - 80 + 30/1.12 + 80/1.12^2 = 8.78

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Exercise: 6ContdNPV if abandoned after three years

= - 80 + 30/1.12 + 30/1.12^2 + 40/1.12^3 = 22.30

NPV if abandoned after four years= - 80 + 30/1.12 + 30/1.12^2 + 40/1.12^3 + 30/1.12^4 = 32.34

NPV if abandoned after five years= - 80 + 30/1.12 + 30/1.12^2 + 40/1.12^3 + 30/1.12^4 + 20/1.12^5 = 33.48

So, NPV is maximized if the project is abandonedafter 5 years.

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Exercise: 7 For a project the projected initial investment is Rs.1m

The net cash flow after tax is expected to be Rs.0.5m per year for each of five years of plant life. The market- based marginal cost of capital is 15 %. The new project will reduce the after-tax cash flow from the existing lines by Rs.0.1m per year. Should the project be taken?

a) Yesb) Noc) Yes, if the cost of capital could be reduced to 12

percentd) Do not know

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Exercise: 7Contd The cash flows are as follows considering the reduced

cash flows from the existing lines.

Year Net Cash flow PV of cash flow0 - Rs.1, 000, 000 -1, 000, 0001 400, 000 347, 8262 400, 000 302, 4573 400, 000 263, 0064 400, 000 228, 7015 400, 000 198, 871

__________ NPV 340, 861

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Exercise: 8 A company takes a machine on rent from a supplier

for a period of 2 years with rent of Rs.2 million payable at the time of return of the machine after 2 years. The company spends Rs.100, 000 for installation of the machine and earns net cash revenue (after deducting all cash expenses) of Rs.700,000 and Rs.1,000,000 respectively in the first and second years. What is the IRR of the investment? What is your recommendation regarding the method to be used for the appraisal of the project?

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Exercise: 8Solution:

The project cash flows are: -Year Cash flow

0 - 100,0001 + 700,0002 1,000,000 (- 2,000,000 + 1,000,000)

If the IRR is K, then,-100,000+700,000/(1+k)-1,000,000/(1+K)^2 = 0 Solving, we get,K = 4 or 1or, IRR = 400% or 100%This is a case of multiple IRR.It is better to use NPV method.

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Thank You!

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