The Basics of Capital Budgeting
Capital Budgeting •
•
•
The process of planning expenditures on assets whose cash flows are expected to extend beyond one year Involves making long-term decisions, and involves large expenditures Extremely important to a firm’s future
Some Projects that can be decided through Capital Budgeting •
Replacement Decisions –
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•
•
•
•
•
Maintenance (replace damaged equipment) Cost Reduction Decisions (replace serviceable but obsolete obsolete equipment to lower costs)
Expansion of existing projects or markets (Jollibee Cebu Branch 1,2,3) Expansion into new products or markets (Jollibee expand for the first time to US, Singapore) Safety (DNV/mining companies) and/or environmental projects (Nestle Vietnam’s water purification system *ISO+) = (mandatory investments) Expansion of existing projects or markets (Jollibee Cebu Branch 1,2,3) Mergers Others (Office buildings, parking lots, executive aircrafts)
Projects can be: •
Independent –
–
•
Projects with cash flows that are not affected by the acceptance or non-acceptance of other projects. You can pick as many projects as you wish.
Mutually Exclusive –
A set of projects where only one can be accepted.
Steps in Capital Budgeting: 1. Estimate the project’ project ’s cash flows 2. Assess riskiness of the project’s cash flows 3. Determ Determine ine r (W (WACC) ACC) for the the p pro rojec jectt 4. Find Find payba payback ck period period,, disc discoun ounte ted d payba payback ck period, NPV, IRR, and MIRR 5. Deci Decide de whe wheth ther er to to acce accept pt or or rej rejec ectt the the project
Payback Payback Period • •
• •
• •
A breakeven analysis Refers to the number of years or length of time required to recover a project’ project ’s cost. How long does it take to get your money back? You must add the project’s cash inflows to its cost until the cumulative cash flows of the project turns positive Uses Nominal Cash Flows Two possible scenarios: – –
When annual cash inflows are equal When annual cash inflows are unequal
Computing Payback Period, when Annual Cash Inflows are Equal
•
•
Example: A project costs P200,000. P200,000. The expected returns of the project amount to P40,000 annually annuall y. What is the payback period? Answer: P200,000/P40,000 = 5 years years
Computing Payback Period, when Annual Cash Inflows are Unequal Project L CFt Cumulative PaybackL Project S CFt Cumulative PaybackS
0 -100 -100
== 2
2
3
10 -90
60 -30
80
30 / 80
+
0 -100 -100
== 1
1
+
2
70 -30
50 20
30 / 50
50
= 2.375 years
1
0
0
3 20 40
= 1.6 years
PBP – PBP – Accept or Reject? •
•
•
Depends if the project is independent independent or mutually exclusive (if you accept one, you have to reject the other) Independent: If you have two projects which fits your firm’s “acceptable” criteria, then you ACCEPT BOTH PROJECTS. Mutually Exclusive: Exclusive: If you have two projects which fits your firm’s “acceptable” criteria, ACCEPT THE PROJECT WITH THE SHORTER PAYBACK PERIOD, PERIOD, because in mutually exclusive projects, you cannot undertake both projects at the same time.
Advantages/Strengths of Payback Period Indicates a project’s project’s risk and liquidity
•
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–
Risk: Cash flows expected in the th e distant future are generally riskier than near-term cash flows Liquidity: The shorter the payback period, ceteris paribus, the th e greater the project’ project ’s liquidity
Serves as a screening tool Identifies investments that recoup cash investments quickly. Identifies products that recoup initial inves i nvestment tment quickly. quickly. Easy to calculate and understand
• • • •
Disadvantages/Weaknesses Disadvantages/Weaknesses of Payback Period • •
Ignores the time value of money Ignores cash flows flows occurring after after payback period. Therefore, Therefore, in mutually exclusive exclusive projects, it is possible that you might choose the project with the faster payback period but with lower total returns.
Discounted Payback Period •
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•
The length of time (number of years) required for the present value of an investment’s cash flows (discounted at the investment’s investment’s cost of capital) to recover a project’s cost. Discounts the cash inflows and outflows, and compute the same way as you compute payback period. Uses Discounted Cash Flows
Discounted Payback Period •
Uses discounted cash flows rather than raw CFs. 0
10%
1
2
3
CFt
-100
10
60
80
PV of CFt
-100
9.09
49.59
60.11
Cumulative
-100
-90.91
-41.32
18.79
Disc PaybackL ==
2
+
41.32 / 60.11
= 2.7 years
DPBP – DPBP – Accept or Reject? •
•
•
Depends if the project is independent independent or mutually exclusive (if you accept one, you have to reject the other) Independent: If you have two projects which fits your firm’s “acceptable” criteria, then you ACCEPT BOTH PROJECTS. Mutually Exclusive: Exclusive: If you have two projects which fits your firm’s “acceptable” criteria, ACCEPT THE PROJECT WITH THE SHORTER DISCOUNTED PAYBACK PERIOD, PERIOD, because in mutually exclusive projects, you cannot undertake both projects at the same time.
Advantages/Strengths of Discounted Payback Period Indicates a project’s risk and liquidity Risk: Cash flows expected in the distant future are generally riskier than near-term cash flows (riskiness of cash flows through the cost of capital) Liquidity: The shorter the payback period, ceteris paribus, the greater the project’s liquidity
•
–
–
Serves as a screening tool Identifies investments that recoup cash investments quickly. Identifies products that recoup initial investment investment quickly. Easy to calculate and understand Considers the time value of money mo ney
• • • • •
Disadvantages/Weaknesses of Discounted Payback Period •
Ignores cash flows flows occurring after payback payback period. Therefore, Therefore, in mutually exclusive exclusive projects, it is possible that you might choose the project with the faster payback period but with lower total returns.
Net Present Value Method •
•
A method of ranking investment proposals using the NPV, which is equal to the PV of future net cash flows, discounted at the cost of capital. NPV depends on: –
–
–
–
Risk WACC Timing of Cash Flows Amount of Cash Flows
To determine NPV… •
Calculate the present value of cash inflows
•
Calculate the present value of cash outflows
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Subtract the present value of the outflows from the present value of the inflows
NPV emphasizes cash flows and not accounting net income. The reason is that accounting net income is based on accruals that ignore the timing of cash flows into and out of an organization.
Net Present Value Method •
Sum of the PVs PVs of all cash inflows and outflows of a project n
NPV
CFt
(1 r )
t
t 0
0
10%
1
2
3
CFt
-100
10
60
80
PV of CFt
-100
9.09
49.59
60.11
NPV(L) = -100 + 9.09 + 49.59 + 60.11 = 18.79 NPV (S) = 19.98
NPV – NPV – Accept or Reject? •
•
•
•
Depends if the project is independent independent or mutually exclusive (if you accept one, you have to reject the other) Independent: Accept Projects with Positive (+) NPV Mutually Exclusive: Exclusive: Accept the Project with the highest Positive (+) NPV Therefore, in the previous example, if the project is independent, we should accept both L and S. But if the project is ME, we should reject L and accept S.
Advantages/Strengths of NPV •
Gives a direct measure of dollar benefit of o f the project to the shareholders (Tells (Tells whether the investment will increase the firm’s value or not) = NPV will add value to the firm
•
Considers all cash flows and the time value of money
•
Considers the risk of future cash flows (through the cost of capital)
•
Does not suffer from Multiple IRR problems
Disadvantages/Weaknesses of NPV
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•
Expressed in terms of dollars, not as a percentage
•
Very complex analysis, too many variables to forecast
There is a direct relationship between NPV and EVA. EVA. NPV is the PV of the project’s future EVAs.
Accepting Accepting +NPV projects will result to +EVA +EVA and +MVA +MVA
•
EVA = NOPAT – Capital Charges (Invested Capital x Cost of Capital)
•
MVA = Market Value of the Firm – Capital Invested in the Firm [MV – Invested Capital]
Internal Rate of Return Method •
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A method of ranking investment proposals using the rate of return on an investment This is calculated by finding the discount rate that equates the PV of future cash inflows to the project’s cost PV(Inflows) = PV(Outflows) IRR is the rate that forces the PV of cash flows =0
Internal Rate of Return •
IRR is the rate that forces the PV of cash flows = 0. Therefore, this is equivalent to to forcing forcing the NPV to equal zero n
0 t 0
•
CFt ( 1 IRR)
t
Two possible scenarios: –
When annual cash inflows i nflows are equal
–
When annual cash inflows are unequal
Internal Rate of Return •
•
IRR and a bond’s YTM are the same thing. Therefore, when annual cash inflows are equal, the computation of IRR is similar to the computation of YTM. You can also use the CALC function or the trial and error method. Illustration: Suppose an initial investment worth 1,134.20 good for 10 years earn a 9% interest per year. year. Its future value is 1,000. Solve for IRR:
Internal Rate of Return •
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When Future Value Value is not given, g iven, and/or cash flows are not equal, you have to use the TRIAL AND ERROR approach. Assume the following information, information, with initial investment investment of P45,000 and k (WACC) of 20%, compute IRR: Choices: a) 17% b) 18% c) 19% d) 21% e) 22% Start with the middle choice. If answer is +, try the higher answer. answer. If answer is – is –,, try the lower answer. Year (t)
Cash inflows
PVIF (19%, t)
Present Value at 19%
1
28,000
0.840
23,520
2
12,000
0.706
8,472
3
10,000
0.593
5,930
4
10,000
0.499
4,990
5
10,000
0.419
4,190
Present Value of Cash inflows
47,102
Less: Initial Investment Investment
45,000
Net Present Value (NPV)
2,102
Internal Rate of Return •
Since using 19% reveals a positive NPV, when NPV computed has to be 0 (ZERO), we try the higher answer, 21%. Year (t)
Cash inflows
PVIF (21%, t)
Present Value at 21%
1
28,000
0.826
23,128
2
12,000
0.683
8,196
3
10,000
0.564
5,640
4
10,000
0.467
4,670
5
10,000
0.386
3,860
Present Value of Cash inflows
45,494
Less: Initial Investment Investment
45,000
Net Present Value (NPV) •
Using 21% still reveals a positive NPV. NPV. However, However, it is significantly smaller than the + NPV of k = 19%. Now, Now, let us try to compute using the last choice, 22%.
494
Internal Rate of Return •
Now we try using r = 22%. We still still try 22% because we are not sure if the answer is nearer to 21% or 22%. Year (t)
Cash inflows
PVIF (22%, t)
Present Value at 22%
1
28,000
0.820
22,960
2
12,000
0.672
8,064
3
10,000
0.551
5,510
4
10,000
0.451
4,510
5
10,000
0.370
3,700
Present Value of Cash inflows
44,744
Less: Initial Investment Investment
45,000
Net Present Value (NPV)
•
•
– 256
Now your answer is a negative negative NPV of 256. This is nearer to zero than than is the positive NPV of 494 if k = 21%. Therefore, the approximate approximate answer is D) 22%. Take note however, that the answer has to be in between 21% and 22%, but it is nearer to 22%. If we want to be more mo re accurate and find the exact answer, answer, we have to interpolate.
Internal Rate of Return •
How to interpolate: K (WACC)
NPV
21%
+ 494
22%
– 256
X
0
•
(22% – (22% – x) / ( – – 256 – 256 – 0) = (22% – (22% – 21%) / ( – 256 – 256 – 494)
•
X = 21.66%
IRR – IRR – Accept or Reject? •
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Depends if the project project is independent independent or mutually exclusive (if you accept one, you have to reject the other) Independent: Accept Projects if IRR > WACC, because projects whose IRR > WACC means that NPV is positive. Mutually Exclusive: Exclusive: Accept the Project with the higher IRR, provided that the IRR must be greater than WACC. Therefore, in the previous example, if the project is independent, independent, we should accept accept both L and S. But if the project is ME, we should reject L and accept a ccept S.
Advantages/Strengths of IRR •
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•
IRR measures a project’ project ’s profitability in the rate of return sense (IRR = WACC WACC implies that there are just sufficient returns on the project to provide investors with their required rate of return. IRR > WACC WACC implies that the project’s rate of return return is more than sufficient to meet investors’ rate of return. It contains information regarding a project’s safety margin It is more appealing because it provides a basis (rate of return) for decision making, rather than a dollar amount like the NPV method.
Disadvantages/Weaknesses of IRR •
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•
Reinvestment rate rate assumption (assume that cash flows f lows are reinvested at the same IRR) is unrealistic. Using WACC is more more realistic because it is what what projects earn on average.
Multiple IRR problems IRR can only rank rank independent projects properly, properly, if signs do not change. They cannot properly rank mutually exclusive exclusive projects all the time. Sometimes decision rule for IRR can conflict with NPV, NPV, in which case, IRR is erroneous.
Why NPV and IRR conflict? 1. Assumpt Assumption ion of cash cash flo flow w rein reinves vestme tment nt 2. Diff
lives, live s, si
risk fact
timing timing of cash flow
NPV Profiles •
A graphical representation of project NPVs at various different costs of capital. k 0 5 10 15 20
NPVL $50 33.0526 18.7829 6.6656 (3.7037)
NPVS $40 29.2949 19.9850 11.8271 4.6296
Finding the Crossover Crossover Point – Mathematical Way •
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•
Crossover Rate is the cost of capital at which the NPV profiles of 2 projects cross, and thus, at which the projects’ NPVs are equal. Step 1: Find the difference between the cash flows of Project L and Project S (Can be disregarded if NPV Profile is already given. Project S
Difference
0
-100
-100
0
1
10
70
-60
2
60
50
+10
3
80
20
+60
IRR
18.126%
23.56%
Step 2: Find the NPVs of both Projects using various r’s, and find the r closest to where the projects will equalize. (The NPV Profile is usually given, but if not, you have to solve it by yourselves.) r 0 5 10 15 20
•
Project L
NPVL $50 33.0526 18.7829 6.6656 (3.7037)
NPVS $40 29.2949 19.9850 11.8271 4.6296
Notice it is in between k = 5% and k = 10%. So you know for for certain that the crossover point is between k = 5% and k = 10%.
Finding the Crossover Crossover Point – Mathematical Way Step 3: Find the NPV of the difference given k = 5% and k = 10% (because you have already ascertained that the crossover point is between 5% and 10%).
•
k
NPV (Difference)
5%
3.7577
10%
- 1.2021
X
0
Step 4: Do interpolation to solve for r when NPV (Difference) is ZERO.
•
•
(10% – (10% – x) / ( – – 1.2021 – 1.2021 – 0) = (10% – (10% – 5%) / ( – 1.2021 – 1.2021 – 3.7577)
•
X = 8.788%
Finding the Crossover Point Point – Graphical Way •
•
Step 1: Find the IRRs of the individual projects. (You (You have already computed this before) before) Project L
Project S
0
-100
-100
1
10
70
2
60
50
3
80
20
IRR
18.126%
23.56%
r’s, and find the r closest to where Step 2: Find the NPVs of both Projects using various r’s, the projects will equalize. (The NPV Profile is usually given, but if not, you have to solve it by yourselves.) k 0 5 10 15 20
NPVL $50 33.0526 18.7829 6.6656 (3.7037)
NPVS $40 29.2949 19.9850 11.8271 4.6296
Finding the Crossover Point Point – Graphical Way •
Step 3: Draw a graph, with r or WACC in the X-axis and NPV in the Y-axis
NPV 60 ($) 50 40 30 20 10 0 5 -10
10
15
20
23.6
Discount Rate (%)
Finding the Crossover Point Point – Graphical Way •
Step 4: Plot the graph. At r = 0, NPV of Project L is 50 and at r = 0, NPV of Project Project S is 40. At NPV = 0, r of Project L is 18.126% and at NPV = 0, r of Project S is 23.56%
IRR
NPV 60 ($)
. 40 . 50
30
. .
20
Crossover Point = 8.7%
.
10
..
0 -10
10
Project S
18.126%
23.56%
NPVL $50 33.0526 18.7829 6.6656 (3.7037)
NPVS $40 29.2949 19.9850 11.8271 4.6296
IRRL = 18.1%
L 5
k 0 5 10 15 20
Project L
15
S
. .
20
. 23.6
IRRS = 23.6% Discount Rate (%)
Interpreting the NPV Profile If r is less than 8.7%, NPV of Project L is greater than NPV NPV of Project S. So, if it is a mutually exclusive project, we should choose Project L. If r is greater than 8.7%, 8.7%, NPV of Project S is greater greater than NPV of Project Project L. So, if it is a mutually exclusive project, we should choose Project S.
NPV 60 ($)
. 40 . 50
30
. .
20
Crossover Point = 8.7%
.
10
IRRL = 18.1%
L
..
0 5 -10
10
15
S
. .
20
. 23.6
IRRS = 23.6% Discount Rate (%)
Comparing the NPV and IRR methods NPV 60 ($)
. 40 . 50
30
. .
20
Crossover Point = 8.7%
.
10
IRRL = 18.1%
L
..
0 5
10
15
S
. .
20
.
IRRS = 23.6%
23.6
-10 •
•
If projects are independent, the two methods always lead to the same accept/reject decisions. If projects are mutually exclusive … If r > crossover point, the two methods lead to the same decision and there is no conflict. If r < crossover point, the two methods lead to different accept/reject decisions. –
–
Reinvestment Reinvestment rate assumpti assumptions ons •
• •
NPV method assumes CFs are reinvested reinvested at k, the opportunity cost of capital. IRR method assumes CFs are reinvested at IRR. Assuming CFs are reinvested at the opportunity cost of capital is more realistic, because: –
–
–
•
•
If a firm has a reasonably good access to capital markets, markets, it can raise all the capital it needs at the going rate (WACC). Since the firm can obtain capital at the going rate (WACC), (WACC), if it has investment investment opportunities with positive NPVs, it should take them on and finance them at the going rate (WACC). If the firm uses internally generated generated cash flows from past projects rather than external capital, it will save the going rate (WACC).
Thus, NPV method is the best. NPV method should be used to choose between mutually exclusive exclusive projects. Perhaps a hybrid of the IRR that assumes cost of capital reinvestment reinvestment is needed. In case of conflict between NPV NPV and IRR, ALW ALWA AYS choose choos e NPV!!! NPV!! !
Another Problem for using IRR •
Multiple IRR – IRR – the situation where a project has 2 or more IRRs –
A non-normal cash flow occurs when a project calls for a large cash outflow sometime during or at the end of its life. Project P has cash flows (in 000s): CF0 = -$800, CF1 = $5,000, and CF2 = -$5,000. Find Project P’s P’s NPV and IRR. 0 -800
r = 10%
1
2
5,000
-5,000
Project P has cash flows (in 000s): CF0 = -$800, CF1 = $5,000, and CF2 = -$5,000. -$5,000. Find Project P’s P’s NPV NPV and IRR. 0
•
5,000
-5,000
NPV = -$386.78 IRR = ? n
0 t 0 •
2
k = 10%
-800
•
1
CFt (1 IRR)
t
Try using 25% and try using 400%
Multiple IRRs NPV Profile A situation where a project has two o r more IRRs or NPV IRR2 = 400% 450 0 -800
100
400
k
IRR1 = 25%
You typically encounter Multiple IRR problems when any of your cash flows change signs more than once. (Non-normal Cash Flows)
I don’t care about what you
said! I still still prefer prefer to use IRR than NPV!!!! I don’t care if there’s a conflict, and I don’t
care about Multiple IRR Problems!!!
Some managers prefer the IRR to the NPV method, even though NPV method method is is more reliable. Is there there a better IRR measure?
YES!!! •
• •
• •
MIRR (Modified Internal Rate of Return) is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. MIRR assumes cash flows are reinvested at the WACC. MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR.
Calculating MIRR (Normal CFs) 0 -100.0
10%
1
2
3
10.0
60.0
80.0 66.0 12.1
10%
10% MIRR = 16.5%
-100.0 PV outflows
$100 =
$158.1 (1 + MIRRL)3
MIRRL = 16.5%
158.1 TV inflows
Calculating MIRR (Non-Normal CFs) 0
1
r = 10%
-1,000
5,000
2 -1,000
-826.446 PV outflows
TV inflows
5,500 -1,826.446
1,826.446
5,500 = (1 + MIRRA)2
MIRR = 73.53%
MIRR – MIRR – Accept or Reject? •
•
•
Depends if the project is independent or mutually exclusive (if you accept one, you have to reject the other) Independent: Accept Projects if MIRR MIRR > WACC Mutually Exclusive: Accept the Project with the higher MIRR, provided that the MIRR must be greater than WACC.
Can NPV and MIRR conflict? (Page (Page 410) Size
Life
Verdict
Equal
Same
NPV and MIRR same conclusion
Equal
Different
NPV and MIRR same conclusion
Different
Same/Different
NPV and MIRR may conflict
Which should be followed if NPV and MIRR conflict?
OO LALA!!!! NPV JUD!!!!
Conclusions: NPV is important in the capital budgeting process as it gives a DIRECT MEASURE of the dollar/peso benefit of the project to the shareholders. NPV is absolutely the best single measure of profitability profitability.. Hence, in case of conflicts between PBP, DPBP, NPV,, IRR and NPV an d MIRR, we must choose NPV!
IRR is also important as it also measures profitability as a percentage rate of return and gives information concerning a project’s safety margin. These information are not revealed by the NPV. NPV. That That’’s why manag managers ers prefer to use IRR. However However,, problems such as assuming cash flows to be reinvested at the IRR are unrealistic, and we also encounter Multiple IRR Problems if cash flows are non-normal.
Conclusions: To counter with problems with IRR, we can use MIRR as it has all the virtues of the IRR but incorporates a better reinvestment rate assumption (reinvest at WACC), and it avoids multiple rate of return problems as well!
Still, even when MIRR looks infallible, we must still use NPV in case of conflicts!
Decision Criteria Used in Practice Practice 1960 (Primary Criterion)
1970 (Primary Criterion)
1980 (Primary Criterion)
1999 (USES)
Payback
35%
15%
5%
57%
Discounted Payback
NA
NA
NA
29%
NPV
0%
0%
15%
75%
IRR
20%
60%
65%
76%
Others
45%
25%
15%
NA
TOTAL TOTAL
100%
100%
100%
Post-Audit •
•
A comparison of actual versus expected results for a given capital project. Purposes: –
–
To Improve Cash Flow Forecasts To Improve Operations and bring results in line with forecasts
Problems 12-1 to 12-5 •
•
Project K costs $52,125, its expected net cash inflows are $12,000 per year for 8 years, and its WACC is 12% Requirements: –
Problem 12-1: 12-1: What is the project’s NPV?
–
Problem 12-2: 12-2: What is the project’s IRR?
–
Problem 12-3: 12-3: What is the project’s project’s MIRR?
–
Problem 12-4: 12-4: What is the project’s payback?
–
Problem 12-5: 12-5: What is the project’s discounted payback?
Problem 12-11 •
Project S costs $15,000, and its expected cash flows would be $4,500 per year for 5 years. Mutually exclusive Project L costs $37,500, and its expected cash flows would be $11,100 per year for 5 years. years. If both projects projects have a WACC of 14%, which project would you recommend? Explain.
Problem 12-13 •
A firm is considering two mutually exclusive projects, X and Y, Y, with the following cash flows:
•
Project X = -1000, 100, 300, 400, 700
•
Project Y = -1000, 1000, 100, 50, 50
•
The projects are equally risky and their WACC is 12%. What is the MIRR of the project project that maximizes shareholder value?
Problem 12-14 •
K. Kim Inc. must install a new air conditioning unit in its main plant. Kim must install one or the other of the units; otherwise, the highly profitable plant would would have to shut down. down. Two units are available, available, HCC and LCC (for (for high and low capital costs, respectively). respectively). HCC has a high capital cost but relatively low operating o perating costs, while LCC has a low capital cost but higher operating costs because it uses more electricity. electr icity. The costs of the units are shown here. Kim’s WACC is 7%.
•
HCC = -600k, -50k, -50k, -50k, -50k, -50k
•
LCC = -100k, -175k, -175k, -175k, -175k, -175k
•
Requirements: –
–
–
Which unit would you you recommend? recommend? Explain. If Kim’s controller controller wanted to know the IRRs of the two projects, what would you tell him? If the WACC WACC rose to to 15%, would this affect affect your recommendation? recommendation? Explain your answer and the reason this result occurred.
Problem 12-20 •
A project has annual cash flows of $7,500 for the next 10 years and then $10,000 each year for the following following 10 years. years. The IRR of this 20year project project is 10.98%. If the firm’s firm’s WACC WACC is 9%, what is the project’s NPV?
