Lecture Notes 3(1)

Capital Budgeting Principles and Techniques Lecture 3

Net Present Value (NPV) • Net present value (NPV) is the sum of the present values of the project’s future cash flows minus the cost of the project. • Projects with positive NPVs add to shareholder wealth; those with negative NPVs reduce shareholder wealth. e n t v a lu lu e i n v e s t m e n t d e c i s i o n • T h e n e t p r e s en r u l e i s i n v e s t i n p o s i t i v e N PV PV p r o j e c t s a n d reject reje ct n egative NPV N PV pr ojects !

• If two projects are mutually exclusive, accept the one with higher net present value.

Net Present Value Decision Rule • The NPV rule is implemented as follows: Calculate the  present value of the expected cash flows generated generated by the investment, using an appropriate discount rate, and subtract from this present value the initial net cash outlay for the project.

• By taking into account all cash flows (and only cash flows), the time value of money, and risk (which is incorporated in the discount rate) NPV evaluates the projects the same way that investors do. Therefore, it is consistent with the objective of shareholder shareholder wealth maximization. • The discou discount nt rate rate used used in calcul calculati ating ng an an inves investme tment’ nt’s s NPV, also called cost of capital or the required rate of return, is the minimum acceptable rate of return on projects of similar risk. It is determined by the required return in the market for investments of comparable risk.

Net Present Value Formula • The formula for NPV is Net present Initial = – outlay value

Present value of + future cash flows

CF 1 CF 2 CF n    NPV   I 0  n 2 1  k  (1  k ) (1  k ) n

CF t   I 0  t   1 k  ( ) t 1



where I 0  is the initial cash outlay, CF t  is the net cash flow in period t , k  is the cost of capital for the project, and n is the economic life of the investment.

Net Present Value Formula

• The initial outlay should include any investment in net w o r k i n g c a p i tal .  Working capital refers to the money that firm must invest in accounts receivable, inventory, and cash to support the sales and production of its products and services. Initial investment in working capital must be recovered  at the termination of the project. • N et c a s h f l o w   is usually calculated as profit after tax, plus depreciation and other non-cash charges, minus (plus) any additions to (recovery of) working capital during the period, and minus (plus) capital expenditures (sales of fixed assets) during the period. This measure includes all project cash inflows and outflows and ignores non-cash items. Depreciation is added back to net income because it is a non-cash item. Net CF= Profit after tax + Depreciation ± Change in net working capital ± Capital Expenditures Net CF = (Revenues – Costs – Depreciation)x(1 – T) + Depreciation ± ΔNWC ± CapEx, where T is the tax rate

 Application of NPV Rule • Example: • Company ABC is considering a five year investment project which requires an initial investment in plant and equipment of $6 million. • The project’s estimated revenue in year 1 is $8 million and $16 million in years 2 through 5. The project’s estimated costs in year 1 are $6.9 million and $12.1 million in years 2 through 5. •  At the end of year five the plant will be scrapped and sold for $1 million. • Depreciation charges will be equal to $1 million each year. • Initial working capital requirement is $1.2 million which will be recovered in year 5. If the tax rate is 40% and ABC’s cost of capital is 10%, what is the NPV of the investment project?

 Application of NPV Rule • •

I 0  (Initial outlay) = $7.2 million

This includes the investment in plant and equipment of $6 million plus $1.2 million invested in working capital. Next estimate net cash flows

CF = (Rev.  – Cost  – Depr.)x(1  – T) + Depr. ± NWC + Sale of plant CF 1 = ( 8  –  6.9  – 1 )x(1 – 0.4) + 1 = 1.06 = 2.74 CF 2-4 = (16  – 12.1 – 1 )x(1 – 0.4) + 1 CF 5  = (16  – 12.1 – 1 )x(1 – 0.4) + 1 + 1.2 + 1 = 4.94

•

Net cash flow in year 5 includes also cash received from the sale of the plant ($1 million) and the recovery of net working capital ($1.2 million). Notice that the book value of the plant at the end of year 5 is exactly $1 million because total depreciation amount for five years was $5 million and initial investment was $6 million. Since the plant is sold for its book value there are no taxes associated with taxable gains or losses. 1.06 2.74 2.74 2.74 4.94      3.03 NPV   7.2  2 3 4 5 1  0.1 (1  0.1) (1  0.1) (1  0.1) (1  0.1) The project should be accepted since it has a positive NPV of $3.03 million

Strengths and Weakness of NPV Rule • NPV rule is consistent with shareholder wealth maximization. • NPV obeys the v a l u e ad d i t i v i ty p r i n c i p l e . This means that the NPV of a set of independent projects is just the sum of the NPVs of the individual projects • Value additivity principle implies that the value of a firm equals the sum of the values of its component parts. Consequently, when a firm undertakes a series of projects, its value increases by an amount equal to the sum of the NPVs of the accepted projects. • This means that when confronted with mutually exclusive projects, a firm should accept the one with the highest NPV as it will make the largest contribution to shareholder wealth. • The weakness of NPV is that many managers and nontechnical people have hard time understanding the concept. Time value of money and cost of capital are not intuitively obvious to most people. • Finally, NPV requires computation of a proper discount rate, which is not trivial as we will see later.

 Alternative Investment Evaluation Criteria •  Although NPV is the theoretically correct technique for evaluating investments, there are other capital budgeting methods • These methods can be divided into two broad categories: non-discounted cash flow (non-DCF) methods and discounted cash flow (DCF) methods • Non-DCF methods:  – Payback  –  Accounting Rate of Return

• DCF methods:  –  –  –  –

Discounted Payback Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR) Profitability Index (PI)

Payback • T h e p a y b a c k p er i o d i s t h e le n g t h o f t i m e n e c e s s a r y t o r ec o u p t h e in i t i al o u t l a y f r o m n e t c as h f l o w s .

• From the earlier example of ABC company the initial outlay is $7.2 million (including investment in plant and equipment and working capital). • By the end of third year the cumulative net cash flow will be $1.06 + $2.74 + $2.74 = $6.54 million. This leaves another $7.2 - $6.54 = $0.66 million until payback. Assuming that cash flows are spread evenly throughout the year, payback will occur in another 0.66/2.74 = 0.24 years. • So payback period is 3.24 years.

Payback: Decision Rule • Decision rule is simple: Projects with a payback less than a specified cutoff period are accepted, whereas those with a  payback beyond this figure are rejected.

• In our example, if ABC company has a threeyear payback requirement then the investment project would be rejected, otherwise with a four year cutoff period the project would be accepted. • Usually the riskier is the project the shorter is the required payback period.

Payback: Strength and Weakness • Payback is easy to understand and simple to apply. • However it has two major weaknesses:  – It ignores the time value of money. The timing of cash flows is of critical importance because of time value of money. Payback assigns the same value to a dollar received at the end of the payback period as it does to one received in the beginning.  – It ignores the cash flows beyond the payback period.  In our example the project is expected to generate $7.68 million in years 4 and 5; with a cutoff period of three years these cash flows are ignored in evaluating the project.

• The payback method is biased against long-term projects; if a quick payoff is not forthcoming, the project will be rejected.

Discounted Payback Period • This is a modification of payback method which corrects one of its weaknesses, the time value of money. • Discou nted payback metho d is the length of tim e required for the present value of cash inflow s to equal the cost of initial ou tlay.

•  Again, from the example of ABC company the present values of net cash flows are as follows: Year 1 2 3 4 5

CF x 1.06 2.74 2.74 2.74 4.94

PV Factor 0.9091 0.8264 0.7513 0.6830 0.6209

=

PV 0.96 2.26 2.06 1.87 3.07

Cumulative PV 0.96 3.22 5.28 7.15 10.22

• The cumulative present value of the project at the end of year four is $7.15 million. So the discounted cash back period is slightly over 4 years. •  Again, this method ignores the cash flow in year five. If the required cutoff period was 4 years this project would be rejected, although the project would increase the value of ABC company by $3.03 million (its NPV).

 Accounting Rate of Return • Accounting rate of return (also known as average rate of return or average return on book value or return on investment) is the ratio of average after-tax profit to average book investment. •  Average book value is calculated as the average of initial outlay (including any investment in working capital) and the ending book value, which is initial investment less accumulated depreciation (again including any recovery of net working capital). • The formula is n

 After  - tax  profit in year  t  n t 1  Accounting rate of  return  Initial  outlay   Ending book value 2 



 Accounting Rate of Return •  After-tax profit can be calculated as (Revenues – Costs – Depreciation)x(1 – T) • In our example of ABC company:  –  After-tax profit in year 1 = = (8 – 6.9 – 1)x(1 – 0.4) = $0.06 million  –  After-tax profits in years 2 through 5 = = (16 – 12.1 – 1)x(1 – 0.4) = $1.74 million  – Initial outlay (including working capital) = $7.2 million  – Ending book value = $2.2 million (book value of the plant of $1 million plus recovery of working capital of $1.2 million) (0.06  4  1.74)  Accounting rate of  return 

5

(7.2  2.2) 2

 0.299 or  29.9%

 Accounting Rate of Return: Strengths and Weakness • To apply this method a firm must specify a target rate of return. Investments yielding a return greater than this standard are accepted, whereas those falling below it would be rejected.

• The project in our example would be accepted if ABC’s target rate of return was less than 29.9%. • This method is simple to apply, but  – It ignores the time value if money.  It treats income derived in year 1 the same as it treats income in year 5, though earlier income is more valuable than later one.  – It is based on accounting income instead of cash flow.  Investors value only cash provided by companies; accounting income not associated with cash flows cannot be spent (consumed) and therefore is of no value to investors.

Internal Rate of Return (IRR) • Internal rate of return (IRR) is the discount rate that sets the present value of the project cash flows equal to the initial investment outlay. In other words IRR is the discount rate that sets NPV equal to zero. • IRR is the rate of return earned on money committed to a capital investment and measures the  profitability  of the investment. • It is calculated as the rate of return k  for which n

CF t  0 NPV   I 0  t  t 1 (1  k )



• In our example of ABC company IRR is calculated as NPV   7.2 

1.06 2.74 2.74 2.74 4.94      0  k   22.4% 2 3 4 5 1  k  (1  k ) (1  k ) (1  k ) (1  k )

NPV Profile for ABC’s Project • Net present value profile is the relationship between the NPV of a project and the discount rate used to calculate the NPV. 8 7

   )   s 6   n   o    i    l    l    i 5   m    $    ( 4   e   u    l   a 3   v    t   n 2   e   s   e   r 1   p    t   e 0    N

0%

2%

4%

6%

8%

10% 1 2% 1 4% 16% 1 8% 2 0% 2 2% 2 4% 26% 2 8% 3 0%

-1 -2

Discount rate

Decision Rule for Using IRR and its Strength • If the IRR exceeds the cost of capital for the project, the firm should undertake the project; otherwise the project should be rejected.

• The rationale for this rule is that any project yielding more than its cost of capital will have a positive net present value. • In our example ABC company should invest in its project if the cost of capital is less than 22.4%. • The strength of IRR method is that many firms prefer IRR because managers visualize and understand more easily the concept of a rate of return than they do the concept of a sum of discounted dollars.

IRR: Weaknesses 1. Lending or Borrowing?

 –  –

 –

IRR does not differentiate between lending- and borrowing-type transactions. With some borrowing-type transactions (where initial outlay is positive while future cash flows are negative) the NPV of the project is increasing as the discount rate increasing. This is contrary to the normal relationship between NPV and discount rate. Project CF0 CF1  A (lending) -100 +150 B (borrowing) +100 -150

IRR 50% 50%

NPV (k  = 10%) $36.36 -$36.36

IRR: Weaknesses 2.

Multiple rates of return.  –

 –  –

When an investment has an initial cash outflow, a series of positive cash inflows, and then at least one additional cash outflow (negative cash flow), then there may be more than one IRR! The number of solutions may be as great as the number of sign reversals in the stream of cash flows. Example: The following project has three IRRs Year 0 1 2 3 . Cash flow -$200 +$1,200 -$2,200 +$1,200

1,200 2,200 1,200 NPV 1  200     0  IRR 1  0% 2 3 1  0 (1  0) (1  0)

1,200 2,200 1,200    0  IRR 2  100% 2 3 1  1 (1  1) (1  1) 1,200 2,200 1,200 NPV 3  200     0  IRR 3  200% 2 3 1  2 (1  2) (1  2)

NPV 2  200 

IRR: Multiple Rates of Return NPV Profile of Previous Example: Multiple IRRs 10 5 0    )    $    ( -5 0%   e   u    l   a -10   v    t   n -15   e   s   e   r -20   p    t   e -25    N -30

40%

80%

120%

160%

-35 -40

Discount Rate

200%

240%

280%

IRR: Weaknesses

3.

Mutually exclusive projects. • •

•

•

In the case of mutually exclusive projects when the firm has to choose either one project or another, NPV and IRR can favor conflicting projects. Example: Consider the following two projects: Cash Flow for Project Year A B . 0 -1,000 -1,000 1 800 100 2 300 400 3 200 500 4 100 800 NPV (k = 17%) $81.2 $116.8 IRR 22.99% 21.46% NPV and IRR give conflicting results when discount rate is less than the crossover rate  - rate at which NPVs of mutually exclusive projects are equal. Crossover rate in this example is 19.78%. NPV and IRR are most likely to give conflicting results when the mutually exclusive projects are substantially different (i) in the timing of cash flows  or (ii) in scale.

Crossover rate for Projects A and B NPV Profiles of Projects A and B, and Crossover Rate 1000

800

Project A Project B

   ) 600    $    (   e   u    l   a 400   v    t   n   e   s 200   e   r   p    t   e    N 0

0%

2%

4%

6%

.

Crossover rate

8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30%

-200

-400

Discount rate

IRR: Weaknesses 3(i). Timing of Cash Flows

• The conflict in the IRR and NPV rankings of projects A and B arises because of differences in the timing of their cash flows, with most of A’s cash flows arriving in the early years and most of B’s cash flows arriving in the later years. • The reason for conflicting rankings is that IRR implicitly assumes that intermediate cash flows occurring during the life of the project can be reinvested at a rate equal to IRR, whereas NPV implicitly assumes a reinvestment rate equal to the project’s cost of capital. • In such cases always trust NPV as it more realistically represents the opportunity cost of funds.

IRR: Weaknesses 3 (ii). Scale Differences

• Difference in the scale of projects (or difference in the amount of initial investment) can lead to conflicting ranking of projects. • Example: Consider the following two projects: Year 0 1 NPV (k = 15%) IRR

Cash Flow for Project X Y . -100 -1,000 140 1,250 $21.8 $87.0 40% 25%

• NPV and IRR rules yield conflicting results. This is because NPV takes into account the size differences in initial investment while IRR does not. • NPV rule in this case is correct, assuming there is no capital rationing.

Modified IRR (MIRR) • Modified IRR solves some of the weaknesses associated with IRR. • MIRR is a discount rate at which the present value of a project’s annual cash outflows is equal the present value of its terminal value, where the terminal value is found as the sum of the future values of the cash inflows, compounded at the firm’s opportunity cost of capital.  PV  out flows



Terminal Value ( FV  of  inflows at the end of  the project' s life)

1   MIRR 

t 

n

n

COF t 

 1  r  t  0

 t 



n t 

CIF t 1  r 

t  0 n

1  MIRR 

where COF  refers to cash outflows (negative numbers), or the cost of the project. And CIF  refers to cash inflows (positive numbers).

Modified IRR: Calculation • Let’s go back to our old example of multiple IRRs and assume that the cost of capital is 10%. Example: The following project has three IRRs. Year Cash flow

0 -$200

1 +$1,200

2 -$2,200

3 . +$1,200

• Present value at time 0 of all cash out flows is:  – 200 – 2,200/(1.10)2 = –2,018.18 • Future value (at the end of project’s life at time 3) of all cash inflows is: +1,200(1.10)2 + 1,200 = +2,652 • We have separated all negative cash flows at time 0, and all positive cash flows at time 3. Year Cash flow

0 -$2,018.18

1

2

3 . +$2,652

• The MIRR for this project is found as: 2,652 0  2,018.18  1  MIRR 3 MIRR = 0.0953 or 9.53% (we have only one IRR here).

Modified IRR: Strengths and Weaknesses •  Advantages of MIRR over IRR are that it:  – Solves the problem with borrowing-type projects (by switching the places of negative and positive cash flows).  – Solves the problem of multiple IRRs (by guaranteeing only one cash flow sign reversal).  – Solves the problem with mutually exclusive projects with differences in the timing of cash flows (by assuming intermediate cash flows are reinvested at the opportunity cost of capital).  – B u t , it still gives conflicting results with mutually exclusive projects with scale differences.

Incremental IRR • Since MIRR does not work with mutually exclusive projects with scale differences, we can use incremental  IRR to make a decision with such projects. • Incremental IRR is the IRR of incremental cash flows. • If the incremental IRR exceeds the cost of capital, the firm should undertake the larger project; otherwise the firm should undertake the smaller project. • Example. Assume k  = 15%.

Year 0 1 NPV IRR

Cash Flow for Project X Y -100 -1,000 140 1,250 $21.8 $87.0 40% 25%

Incremental (Y – X) . -1000 - (-100) = -900 1,250 - 140 = 1,110 $65.2 23.3%

• Since Incremental IRR of 23.3% > 15%, accept larger project.

Profitability Index (PI) • Profitability Index (PI), also known as the benefit-cost ratio, is the present value of future cash flows divided by the initial cash investment n

CF t  t  ( k  ) 1  (NPV   I 0 ) t 1 PI    I 0 I 0



• The profitability index for ABC company’s project is $10.23/$7.2 = 1.42. In other words, this project returns a present value of $1.42 for every $1 of the initial investment. • Decision rule: As long as profitability index exceeds 1, the project should be accepted . •  Although for a given project NPV and PI give the same accept-reject signal, they sometimes disagree in the rank ordering of acceptable projects when there are mutually exclusive projects  and when there is capital rationing.

Profitability Index: Mutually Exclusive Projects • We already saw that when scale differences exist, NPV and IRR may give conflicting signals. The same is true for PI. • Example: Consider again our old example with following two projects: Cash Flow for Project Year X Y . 0 -100 -1,000 1 140 1,250 NPV (k = 15%) $21.8 $87. PI 1.22 1.09 Though both NPV and PI give accept decision for both projects, they disagree about the ranking of these projects. • When there is a conflict of ranking the firm should select the project with the higher NPV (unless there is capital rationing)!

Profitability Index: Capital Rationing • Capital rationing is a situation when firms constrain the size of their capital budgets. Capital rationing may be self-imposed or externally imposed. • When constraints prevent the firm from undertaking all acceptable projects, it must select among them the subset of projects that gives the highest net present value. • When all the initial outlays occur in the first period, a simple approach using PI is as follows:  – Calculate PI for each project,  – Rank all projects in terms of their PIs, from the highest to the lowest,  – Starting with the project having the highest PI, go down the list and select all projects having PI>1 until the capital budget is exhausted.

Profitability Index: Capital Rationing • Example: A firm has a capital budget of $5,000 and the following projects Project  A B C D E F

Initial Outlay 500 500 2,000 3,000 1,000 500

NPV 100 70 300 480 170 125

Rank 5 6 2 1 3 4

PI 1.20 1.14 1.15 1.16 1.17 1.25

Rank 2 6 5 4 3 1

• The projects selected under NPV rule are C and D with a combined NPV of $780. Alternatively, PI selects projects F, A, E, and D with a total NPV of $875. • NPV method does not necessarily select the best combination of projects under capital rationing. • PI method will select the optimal combination of projects if the entire budget can be consumed by accepting projects in descending order of PI. Projects are usually indivisible and applying the PI approach may lead to an underutilized budget because the next available project might be too large. In this case PI method cannot be used.

Mutually Exclusive Projects with Different Economic Lives

• Example: Finance Department has to choose between two copying machines. Xerox costs $1,200, will last 5 years, and will require $300 of annual maintenance costs. Alternatively, Canon costs $750, will last only 4 years, and annual maintenance costs are $400. Which one should Finance Department choose? • One way to choose between these two machines is to compare the present values (NPVs) of their costs. Assuming 8% discount rate we have: Year Xerox 0  –$1,200 1  –300 2  –300 3  –300 4  –300 5  –300 NPV at 8%  –$2,398

Canon  –$750  –400  –400  –400  –400  –$2,074

• It looks like Canon is more preferable since it has higher NPV. But these two investments are not directly comparable because they have different economic lives.

Mutually Exclusive Projects with Different Economic Lives

• One way to handle mutually exclusive investments with unequal lives is to assume that at the expiration of the economic life of each asset, the firm will invest in new asset with identical characteristics. E.g., if we buy Xerox today, we will replace it by Xerox again in 5 years. Thus department will buy chains of Xeroxes or Canons. • Then we need to calculate equivalent annual cash flow of using mutually exclusive assets. • Equivalent annual cash flow (EACF) of an asset is an annuity that has the same life as the asset with present value equal to the NPV of the asset. • It is calculated as: EACF = NPV/Present value annuity factor

EACF 

NPV 1 1  1  n k  1  k  

Mutually Exclusive Projects with Different Economic Lives •

EACFXerox 

EACFCanon 

 2,398  1  1 1   0.08  1  0.085   2,074  1  1 1  4 0.08  1  0.08 

 $600

 $626

• Buying a chain of Xeroxes is equivalent to paying $600 a year, whereas a chain of Canons costs $626 a year. • Xerox is the preferred asset as its EACF is higher by $26. • The rule for comparing mutually exclusive assets with unequal economic lives is: Compute the equivalent annual cash flow of each asset. Select the asset with the highest equivalent annual cash flow.