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Capital Budgeting A Framework for Corporate Investments

Dr. C. Bulent Aybar

Professor of International Finance

Investment Analysis and Capital Budgeting

At the beginning of the course, I emphasized three pillars of value creation:

Investment

Funding

Distribution

It is time to discuss what we mean by value creating investment.

Capital Budgeting is a framework we can use to discipline our analysis to make consistent value creating investment decisions.

This framework requires us to determine project cash flows and use a decision rule to determine if the project adds value to the investor’s wealth.

Three Stages of Project Cash Flows

A typical investment project requires investment today or over a period of time until the project becomes operational.

This is the investment stage where we incur sizable cash outflows to acquire land, build a plant, to purchase equipment and make working capital investments to be prepared for the operations.

Once project is operational, it starts to generate revenues and incur operating costs.

It is also highly plausible that the project may require new working capital and fixed assed investments during the operational period. This phase is referred to as operational stage.

Three Stages of Project Cash Flows

While the companies are ongoing concerns, projects invested by firms are considered to have limited economic life.

This fundamental assumption implicitly suggests that each project is terminated at the end of its economically useful life.

Terminal stage involves liquidation of project fixed assets and working capital, environmental clean up and other expenses and may create tax liabilities or tax benefits.

Project Cash Flows & Decision Rules: Summary

Initial Investment

Operational Cash Flows

Terminal Cash Flows

(+) Land

(+) Plant

(+) Equipment +Installation

(+) Working Capital Investment

=Initial Outlay

+Revenues

-Operating Costs

-Taxes

+Depreciation

-Change in WCR

-CapEx

=FCFP

(+) Proceeds from liquidation

(-) Tax Liability /(+) Tax Credit

(+) CF from Recall of WC

(=)Terminal Cash Flows

Decision Rules

Net Present Value

Internal Rate of Return (IRR)

MIRR

Profitability Index

Payback Period

Discounted Payback Period

Three Stages of Project Cash Flows-Expansion Project

New England Casting Company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by a group led by Nick Jordan.

The production line would be set up in unused space in New England Casting's main plant.

The equipment’s invoice price would be approximately $200,000; another $10,000 in shipping charges would be required; and it would cost an additional $30,000 to install the equipment.

The machinery has an economic life of 4 years, and New England Casting has obtained a special tax ruling which places the equipment in the MACRS 3-year class.

The equipment is expected to have a salvage value of $25,000 after 4 years of use.

The new line would generate incremental sales of 1,250 units per year for four years at an incremental cost of $100 per unit in the first year, excluding depreciation.

MACRS Depreciation Tables

Each unit can be sold for $200 in the first year. The sales price and cost are expected to increase by 3% per year due to inflation.

Initially, NEC invests $25,000 in WCR, but it projects the firm’s net operating working capital to be 12% of sales revenues during the operational period.

The firm’s tax rate is 21 percent, and its overall weighted average cost of capital is 10 percent.

Should New England Casting Company go for the investment to introduce new line of products?

Tasks

For the proposed expansion determine:

Initial investment.

Operating cash inflows

Terminal cash flow

Using the data developed at the stage A, apply decision rules to make a recommendation to the management team.

Project Data and Assumptions

Equipment cost	$200,000
Shipping charge	$10,000
Installation charge	$30,000
WCR Investment at T=0	$25,000
Economic Life	4
Salvage/Liquidation Value	$25,000
Tax Rate	21%
Cost of Capital	10%
Units Sold	1250
Sales Price Per Unit	$200
Incremental Cost Per Unit	$100
Net Working Capital (WCR)	12%
Inflation rate	3%

Initial Investment

The initial Outlay is composed of fallowing:

(+) Land

(+) Plant

(+) Equipment +Installation

(+) Working Capital Investment

=Initial Outlay

In our example, NEC uses an idle space with no alternative use for its expansion project; therefore there are no land & plant acquisition costs, but we need to account for equipment installation and working capital investments.

Initial Investment

The initial Outlay for NEC expansion project is composed of fallowing:

Equipment Cost	200,000
Shipping Charge	10,000
Installation Charge	30,000
Net Working Capital Investment	25,000
Initial Outlay	265,000

3 Year MACRS Scheme

MACRS-3	Percentage
1	0.33
2	0.45
3	0.15
4	0.07

MACRS-3	Percentage	Basis	Depreciation	Book Value
1	0.33	240,000	79,200	160,800
2	0.45	240,000	108,000	52,800
3	0.15	240,000	36,000	16,800
4	0.07	240,000	16,800	-

Note that the depreciable base includes costs that make the asset available for use such as installation and shipping costs.

Operational Cash Flows

We estimate the free cash flows to the project using the following structure:

(+) Revenues

(-) Operating Costs

(-) Taxes

(+) Depreciation

(-) Change in WCR

(-) CapEx

(=) Free Cash Flows to Project

Operational Cash Flows

	Year 0	Year 1	Year 2	Year 3	Year 4
Units		1,250	1,250	1,250	1,250
Unit price		200.00	206.00	212.18	218.55
Unit cost		100.00	103.00	106.09	109.27
Sales		250,000	257,500	265,225	273,188
Costs		(125,000)	(128,750)	(132,613)	(136,591)
Depreciation		(79,200)	(108,000)	(36,000)	(16,800)
EBIT		45,800	20,750	96,613	119,797
Taxes (21%)		(9,618)	(4,358)	(20,289)	(25,157)
NOPAT		36,182	16,393	76,324	94,639
Depreciation		79,200	108,000	36,000	16,800
WCR	25,000	30,000	30,900	31,827	32,783
Change in WCR	(25,000)	-5000	-900	-927	-955.5
Cap-Ex
FCFP		110,382	123,493	111,397	110,484

Terminal Cash Flows at Liquidation

The terminal cash flows of the project are composed of:

(+) Proceeds from liquidation

(-) Tax liablity /(+) Tax Credit

(+) CF from Recall of WC

(=)Terminal Cash Flows

Terminal Cash Flows at Liquidation

The terminal cash flows of the project are composed of:

(+) Liquidation/Salvage Value	$25,000
(-) Book Value of Equipment	0
(=) Capital Gains	$25,000
(-) Tax Liability	$5,250
(+) Recall NWC	$32,783
(=) Terminal Cash Flows	$52,533

Relevant Cash Flow for the Project

Year 4 cash flows include terminal cash flows  110,484 +52,533

Year	Project Cash Flow
0	(265,000)
1	110,382
2	123,493
3	111,397
4	163,016

Decision Rules

Net Present Value

Internal Rate of Return (IRR)

MIRR

Profitability Index

Payback Period

Discounted Payback Period

Decision Rule #1: Net Present Value

0	1	2	3	4
(265,000)	110,382	123,493	111,397	163,016

Decision Rule #1: Net Present Value

The NPV of the project is positive or NPV>0  Project should be executed.

We can also use =NPV function to calculate the PV of project cash flows and then subtract the initial outlay from the PV of cash flows.

Decision Rule #2: IRR

0	1	2	3	4
(265,000)	110,382	123,493	111,397	163,016

Decision Rule #2: IRR

There is no closed form solution for this equation; we need an algorithm to solve it. We can use =IRR function in Excel to solve the equation.

IRR of the project is 30.16% > Cost of Capital  Project Should be executed!

Decision Rule #3: Modified IRR

IRR assumes that investment cash flows can be reinvested at the IRR (similar to YTM of a bond); however this may be an optimistic assumption; therefore IRR may overstate the project performance.

A realistic, and relatively conservative approach is to assume reinvesting the project cash flows at the cost of capital.

This approach is referred to as Modified IRR or MIRR.

Manual MIRR Calculation

Step-1: Calculate future value of all the cash flows at the end of project life assuming that they will be reinvested at cost of capital

Step-2:

Aggregate the future value of all cash flows

Step-3:

Calculate CAGR or Geometric Mean Return of the investment

MIRR Calculation

We can also calculate the MIRR in Excel using MIRR function; it requires

MIRR Calculation in Excel: =MIRR

The function requires a finance rate and reinvestment rate; finance rate is the cost of capital, reinvestment rate can be set any rate, but the general assumption is the cost of capital

Profitability Index

Profitability index reflects the benefit cost ratio of a project. It is the ratio of PV of project cash flows to the project cost.

NEC expansion project, generates $1.50 PV per $1 invested; this suggests significant benefits for every dollar invested. It points to execution of the project

Profitability Index

Profitability index reflects the benefit cost ratio of a project. It is the ratio of PV of project cash flows to the project cost.

NEC expansion project, generates $1.50 PV per $1 invested; this suggests significant benefits for every dollar invested. It points to execution of the project

Payback Period

Note that the cost for the investment, 265,000 can be recovered sometime between 2nd and 3rd year. The portion recovered in the 3 year is (265,000-233,874.50)/111,396.88=0.28. Therefore the payback period for the investment is 2 years + 0.28 years or ~2.28 years

Year	FCFP	Cumulative FCFP
1	110,382.00	110,382.00
2	123,492.50	233,874.50
3	111,396.88	345,271.38
4	163,016.33	508,287.71

Discounted Payback Period

The cost for the investment, 265,000 can be recovered sometime between 2nd and 3rd year. The portion recovered in the 3 year is (265,000-202,407)/83,694.12=0.75. The discounted payback period for the investment is 2 years + 0.75 or ~2.75 years.

Year	FCFP	PV of Cash Flows	Cumulative PV
1	110,382.00	100,347.27	100,347.27
2	123,492.50	102,059.92	202,407.19
3	111,396.88	83,694.12	286,101.31
4	163,016.33	111,342.35	397,443.66

Conclusion

Given the information, NEC Expansion project is a value creating project and it should be executed.

It has significantly positive NPV and MIRR well above cost of capital.

Other decisions rules such as PI also points to a favorable conclusion. The payback period is relatively short, and the investment is recovered in early or mid second year.

Note that the project cash flows are expected cash flows; they are the mean of a distribution and the realized cash flows may be materially different from these.

It is always prudent to conduct a sensitivity analysis to understand the project risks and the conditions under which the project lead to sub optimal results.

Question

Do you prefer a $1 project with 100% IRR or $100 project with 10% IRR? Why?

Projects with unequal economic lives

So far we conveniently assumed that mutually exclusive projects we evaluated had equal economic lives.

What if the economic lives of the projects are not equal? Should we still go ahead and use NPV of each project and compare them?

Would this be an apples to apples comparison?

What assumptions are necessary to make sound decisions?

Sorting out Unequal lives

Two approaches:

Annualized NPV or ANPV Approach

Common Economic Life Approach

In both cases we implicitly assume that projects can be repeated.

Capital Budgeting: Projects with Unequal Lives

Shao Airlines is considering two alternative planes.

Plane A has an expected life of 5 years, will cost $100 million, and will produce net cash flows of $30 million per year.

Plane B has an expected life of 10 years, will cost $132 million, and will produce net cash flows of $25 million per year.

Shao plans to serve the route for 10 years. Inflation in operating costs, airplane costs, and fares is expected to be zero, and the company’s cost of capital is 12 percent.

By how much would the value of the company increase if it accepted the better project (plane)?

Approach-1: Annualized NPV (ANPV)

This approach requires calculation of annualized contribution of the project to NPV, and implicitly assumes that project can be repeated indefinitely generating the perpetual ANPV.

Three steps:

Step-1: Calculate NPV for each project

Step-2: Calculate annualized contributions to NPV or ANPV

Step-3: Assume that annualized NPV will be created perpetually and calculate the perpetual value of each project; select the project with higher value

Annualized NPV (ANPV) Approach

Project-A

Project-B

Hint: You can use PMT function in Excel to calculate ANPV; NPV is the PV

Common Economic Life Approach

This approach requires finding a common economic life for both projects.

For instance by assuming that 5 year project can be repeated once to create a 10 year project , we can calculate NPV of both project under the assumption that 5 year project repeated once by investing the original $100m at the end of the year five.

The assumption is that the project will generate same cash flows as in years 1 through 5 during years 6 through 10.

If one of the projects had a 3 year economic life and the second one had 5 year economic life, the common economic life would be 15 years. In this case first project will be assumed to be repeated 5 times while the second project will be assumed to be repeated 3 times.

Common Economic Life Approach

Common Economic Life Approach
Required Rate of Return=	12%
	A	B
0	-100,000,000.00	-132,000,000.00
1	30,000,000.00	25,000,000.00
2	30,000,000.00	25,000,000.00
3	30,000,000.00	25,000,000.00
4	30,000,000.00	25,000,000.00
5	-70,000,000.00	25,000,000.00
6	30,000,000.00	25,000,000.00
7	30,000,000.00	25,000,000.00
8	30,000,000.00	25,000,000.00
9	30,000,000.00	25,000,000.00
10	30,000,000.00	25,000,000.00
NPV	12,764,005.28	$9,255,575.71

In this case, project A is expected to be repeated twice; the investment is made at the end of year 5 and cash flows are expected to be repeated from years 6 through year 10

How should firms pursue investment opportunities?

When there are no limits to capital budget, and the firm faces mutually exclusive projects, decision rules like NPV and IRR should guide the investment decisions. The ultimate criteria is the value created by the project!

When there are no limits to capital budget, and the firm faces a number independent projects, firm should pursue all the positive NPV projects.

When there are limits to capital (capital rationing), firm should adopt all the positive NPV projects until it consumes its budget. This may require optimization with capital constraints.

Simple Example-1: Mutually Exclusive Projects

If the company can raise large amounts of money at an annual cost of 15%, and if the investments are mutually exclusive, which project should the company undertake?

Answer:

Undertake investment A because it has the highest NPV, and NPV is a direct measure of the increase in wealth from undertaking the investment

Investment	A	B	C
Initial Cost	$ 5,500,000	$ 3,000,000	$ 2,000,000
Expected Life (yrs.)	10	10	10
NPV @15%	$ 340,000	$ 300,000	$ 200,000
PI @ 15%	1.06	1.10	1.10
IRR	20%	30%	40%

Example-2: Independent Projects with Capital Constraints

Considering only these three independent investments, if the company has a fixed capital budget of $5.5 million, which projects should the company undertake?

Investment	A	B	C
Initial Cost	$ 5,500,000	$ 3,000,000	$ 2,000,000
Expected Life (yrs.)	10	10	10
NPV @15%	$ 340,000	$ 300,000	$ 200,000
PI @ 15%	1.06	1.10	1.10
IRR	20%	30%	40%

If the capital budget is fixed at $5.5 million, invest in C and B, and put the remaining $500,000 in A if possible.

This is the bundle of investments with the highest total NPV.

One can select this bundle by ranking investments by their IRR, or occasionally more accurately by their PI (or Benefit Cost Ratio or BCR)

Appendix-I: More on IRR

Important Characteristics of IRR

IRR is highly sensitive to the timing of the cash flows

IRR is blind to the size of the investment;

When cash flows are unconventional (i.e. project cash flows change sign more than once) IRR produces multiple solutions. It is difficult to economically interpret multiple IRRs.

Under some circumstances, there is no IRR!

would you rather have a small project with a higher rate of return or a large project with a lower rate of return? Sometimes, the larger, low rate of return projects have the higher NPVs.

Project Scale and IRR-NPV Conflict

As the NPV profile

Shows, project B has higher NPV for discount rates between 0 and 21.83%

Multiple IRR Problem

Unconventional cash flows where the sign of cash flows change more

than once, produce multiple IRRs. For instance the following cash flow

pattern leads and IRR of 100% and 200%.

In this case NPV profile of the project intersects the horizontal line twice:

at discount rate 100% and discount rate 200%.

Multiple IRR Problem

200%

100%

No IRR Problem

In some cases, NPV profile may never cross the horizontal axis.

Appendix-II: Replacement Projects

Replacement Projects

The example we considered is an “Expansion Project”. In this case the company expanded its existing capacity and we evaluated if the expansion was economical in the sense that if it added value for investors.

Our conclusion was affirmative as project had positive NPV and its IRR exceeded its cost of capital.

Companies also frequently engage in “Replacement” projects. Replacement analysis is a little more complicated and it requires us to focus on incremental cash flows.

Now we will frame the investment project as a Replacement and conduct the analysis.

Lasting Impressions LLC: Replacement Project

Lasting Impressions (LI) Company is a medium- sized commercial printer of promotional advertising brochures, booklets, and other direct-mail pieces.

The typical job is characterized by high quality and production runs of more than 50,000 units.

LI has not been able to compete effectively with larger printers because of its existing older, inefficient presses.

Lasting Impressions LLC

The firm is currently having problems in meeting demand cost effectively and quality requirements of the industry.

The general manager has proposed the purchase of one of two large, six-color presses designed for long, high- quality runs.

The purchase of a new press would enable LI to reduce its cost of labor and therefore the price to the client, putting the firm in a more competitive position.

LI Investment Proposals

Keep the Old Equipment

Replace it with highly automated press that can be purchased for $830,000 and will require $40,000 in installation cost

Replace it with a less sophisticated press that can be purchased for $640,000 and requires $20,000 in installation costs.

Existing Equipment (Old Equipment)

Old press Originally purchased 3 years ago at an installed cost of $ 400,000, it is being depreciated under MACRS using a 5- year recovery period.

The old press has a remaining economic life of 5 years. It can be sold today to net $ 420,000 before taxes; if it is retained, it can be sold to net $ 150,000 before taxes at the end of 5 years.

5 Year MACRS – 20% 32% 19% 12% 12% 5%

Alternative-1: Press-A

This highly automated press can be purchased for $ 830,000 and will require $ 40,000 in installation costs.

It will be depreciated under MACRS using a 5- year recovery period. At the end of the 5 years, the machine could be sold to net $ 400,000 before taxes.

If this machine is acquired, it is anticipated that the current asset changes on the left would result:

Cash	$25,400
A/R	$120,000
Inventories	($20,000)
A/P	$35,000

5 Year Modified Accelerated Cost Recovery System (MACRS)

Depreciation	MACR-5Yr
1	20%
2	32%
3	19%
4	12%
5	12%
6	5%

Alternative-2: Press-B

This press is not as sophisticated as press A. It costs $640,000 and requires $20,000 in installation costs.

It will also be depreciated under MACRS using a 5- year recovery period.

At the end of 5 years, it can be sold to net $ 330,000 before taxes.

Acquisition of this press will have no effect on the firm’s net working capital investment.

Earning Projections Before Depreciation Interest and Taxes

		EBITDA
Year	Old Press	Press A	Press B
1	$120,000	$250,000	$210,000
2	$120,000	$270,000	$210,000
3	$120,000	$300,000	$210,000
4	$120,000	$330,000	$210,000
5	$120,000	$370,000	$210,000

The firm is subject to a 40% tax rate. The firm’s cost of capital, r, applicable to the proposed replacement is 14%.

Tasks

A. For each of the two proposed replacement presses, determine:

Initial investment.

Operating cash inflows

Terminal cash flow

B. Using the data developed at the stage A, apply decision rules to make a recommendation to the management team.

Initial Investment Outlay

Item	Press A	Press B
Cost of Old Machine	$400,000	$400,000
Cost of New Machine	$870,000	$660,000
Proceeds from Old Machine	$420,000	$420,000
Book Value of Old Machine	$116,000	$116,000
Gains from Sale	$304,000	$304,000
Tax Liability	$121,600	$121,600
NWC Investment	$90,400	$0
Net Initial Outlay	$662,000	$361,600

Book value of the old machine: 400,000-(80,000+128,000+76,000)=116,000

400,000x0.2=80,000

400,000 x0.32=128,000

400,000x0.19=76,000

Cumulative Depreciation=284,000

Depreciation of The New and Old Equipment

Depreciation	MACR-5Yr	Press A	Press B	Existing
1	20%	$174,000	$132,000	$48,000
2	32%	$278,400	$211,200	$48,000
3	19%	$165,300	$125,400	$20,000
4	12%	$104,400	$79,200	$0
5	12%	$104,400	$79,200	$0
6	5%	$43,500	$33,000	$0

Net Operating Cash Flows: Old Machine

Existing Machine	1	2	3	4	5
(+) EBITDA	120000	120000	120000	120000	120000
(-) Depreciation	$48,000	$48,000	$20,000	$0	$0
(=) EBIT	$72,000	$72,000	$100,000	$120,000	$120,000
(-) Taxes	$28,800	$28,800	$40,000	$48,000	$48,000
(=) NOPAT	$43,200	$43,200	$60,000	$72,000	$72,000
(+) Depreciation	$48,000	$48,000	$20,000	$0	$0
(=) NOCF	$91,200	$91,200	$80,000	$72,000	$72,000

Net Operating Cash Flows: Press-A

PRESS-A:	1	2	3	4	5
EBITDA	$250,000	$270,000	$300,000	$330,000	$370,000
Depreciation	174000	278400	165300	104400	104400
EBIT	$76,000	-$8,400	$134,700	$225,600	$265,600
Taxes	30400	-3360	53880	90240	106240
NOPAT	$45,600	-$5,040	$80,820	$135,360	$159,360
Depreciation	174000	278400	165300	104400	104400
NOCF	$219,600	$273,360	$246,120	$239,760	$263,760

Net Operating Cash Flows: Press-B

PRESS-B:	1	2	3	4	5
EBITDA	$210,000	$210,000	$210,000	$210,000	$210,000
Depreciation	132000	211200	125400	79200	79200
EBIT	$78,000	-$1,200	$84,600	$130,800	$130,800
Taxes	31200	-480	33840	52320	52320
NOPAT	$46,800	-$720	$50,760	$78,480	$78,480
Depreciation	132000	211200	125400	79200	79200
NOCF	$178,800	$210,480	$176,160	$157,680	$157,680

Incremental Operating Cash Flows for Press A & B

Column1	1	2	3	4	5
Existing Machine	$91,200	$91,200	$80,000	$72,000	$72,000
Press-A	$219,600	$273,360	$246,120	$239,760	$263,760
Press-B	$178,800	$210,480	$176,160	$157,680	$157,680
Press A IOCF	$128,400	$182,160	$166,120	$167,760	$191,760
Press B IOCF	$87,600	$119,280	$96,160	$85,680	$85,680

IOCF=Incremental Operating Cash Flows

Terminal Cash Flows

Terminal Cash Flows	Press A	Press B	Old Mach.
Proceeds from Liquidation	$400,000	$330,000	$150,000
BV at Liquidation	$43,500	$33,000	$0
Profit from Sale	$356,500	$297,000	$150,000
Tax Liability	$142,600	$118,800	$60,000
Net Proceeds from Sale	$257,400	$211,200	$90,000
Recall NWC Investment	$90,400	$0	$0
Net Terminal Cash Flows	$347,800	$211,200	$90,000
Net Incremental TCF	$257,800	$121,200

347,800-90,000=257,800

211,200-90,000=121,200

Relevant Cash Flow for the Projects

Year	Press A	Press B
0	-$662,000	-$361,600
1	$128,400	$87,600
2	$182,160	$119,280
3	$166,120	$96,160
4	$167,760	$85,680
5	$449,560	$206,880

Year 5 cash flows include terminal cash flows

Cash Flows on a Time Line

Pay Back Period Analysis

Payback Period	Press A	Press B
1	$128,400	$87,600
2	$310,560	$206,880
3	$476,680	$303,040
4	$644,440	$388,720
5	$1,094,000	$595,600

Cumulative Cash Flows

Note that the cost for Press A (662,000) can be recovered only sometime

between 4th and 5th year. The portion recovered in the 5th year is

(662,000-644,440)/449,560=0.0391. Therefore payback period for the

Press A is 4 years + 0.039 years or ~4.04 years. The recovery for press B is faster as initial investment of 361,600 can be recovered in 3.68 years.

In calculation of the payback period, we consider only the operating cash flows for a given year. For instance, in this particular case we did not include terminal cash flows of the project in year 5 cash flows.

Discounted Payback Period

Year	Press A	Press B	Cumulative Cash Flows A	Cumulative Cash Flows B
0	(662,000)	(361,600)	(662,000)	(361,600)
1	112,632	76,842	112,632	76,842
2	140,166	91,782	252,798	168,624
3	112,126	64,905	364,924	233,529
4	99,327	50,729	464,251	284,259
5	233,487	107,447	697,739	391,706
Discounted Payback Period			4.85	4.72

Discounted Payback period requires discounted value of each cash flow. Each cash flow is discounted to time 0 at the cost of capital, and payback period is calculated by using these discounted cash flows. In this particular case, method favors project “B” as in the standard Payback Period method.

NPV Rule

Investment outlay may take place at time 0, or it may spread over time. If that is the case then IO can be expressed as:

NPV Analysis

Year	Press A	Press B
0	-$662,000	-$361,600
1	$128,400	$87,600
2	$182,160	$119,280
3	$166,120	$96,160
4	$167,760	$85,680
5	$449,560	$206,880

NPVPress-A=35,738.82>NPVPress-B=30,105.88

Since both projects have 5 year life spans there is no need to consider

Annualized NPV, but have we had done it, ANPV-A would have been higher than ANPV-B.

IRR and MIRR

IRR is the rate of return that equates the present value of the project cash inflows to initial outlay; alternatively it can be described as the rate of return that satisfies NPV=0

IRR implicitly assumes that project cash flows are reinvested at the IRR

If we revise that assumption and assume that cash flows are reinvested at cost of capital we get MIRR

IRR

Project A’s IRR is 15.8,

Project B’s IRR is 17.06.

Both projects have IRR above cost of Capital. If we used IRR to choose the projects, Press B would be favored by the IRR method. Note that IRR assumes that cash flows can be reinvested at the IRR.

A consideration of reinvestment at cost of capital (MIRR) suggest that ranking does not change. MIRR-A=15% MIRR-B=16%

Profitability Index

Profitability index reflects the benefit cost ratio of a project. It is the ratio of PV of project cash flows to the project cost.

LI’s two projects have PIA=1.05 and PIB=1.08 . While profitability index suggests that project B generates more value per dollar invested, the total value created by project A is higher.

Summary

	Project A	Project B
0	-$662,000	-$361,600
1	$128,400	$87,600
2	$182,160	$119,280
3	$166,120	$96,160
4	$167,760	$85,680
5	$449,560	$206,880
NPV	$35,738.82	$30,105.88
IRR	15.85%	17.06%
MIRR	15.21%	15.84%
PI	1.05	1.08
Payback	4.04	3.68

Conflict between NPV and IRR

Two questions arise:

Why do these two methods disagree?

What do we do?

The “Why?” question

NPV and IRR decision rules usually agree; but under some circumstances conflicts may emerge simply because of:

Size of projects;

Differing cash flow patterns

When the cost of capital of the project is below the point where NPV curves of the mutually exclusive projects cross-over, the NPV and IRR contradict each other.

Cost of Capital (14%)<Cross-over Point (14.59%)

14%< Cross-over point=14.59%

Project A

Project B

NPV_A Cost of Capital 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0. 14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 259269.49651832771 229550.3994204925 201222.3696731271 174204.73043695919 148422.27985137681 123804.8692650153 100287.01764169781 77807.558734363061 56309.31796841661 35738.816286218971 16045.9984808144 -2816.0162066004768 -20891.16323104826 -38220.643439061212 -54843.116948258212 -70794.881687242771 -86110.037930901162 -100820.6400397197 -114956.8364982255 -128546.9992456288 -141617.8432 -154194.53679468151 -166300.80427122701 -177959.02040600771 -189190.29828704981 -200014.57070292209 NPV_B Cost of Capital 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 145670.71245299769 130397.4309240104 11581 5.5768085709 101885.8034831503 88571.402798039198 75838.103457910765 63653.886595667602 51988.816927099098 40814.888038390061 30105.88050491759 19837.23167022027 9985.9160303501831 530.33527269388935 -8549.7828888313707 -17273.47785724566 -25658.64197530851 -33722.099661655462 -41479.68043445173 -48946.286343020161 -56135.954279608341 -63061.9136 -69736.639442548505 -76171.902099925908 -82378.812766075134 -88367.865952089429 -94148.978838814641

Cost of Capital and NPV

Cost of Capital	NPV Press A	NPV Press B
0.11	$100,287	$63,653.89
0.12	$77,808	$51,988.82
0.13	$56,309	$40,814.89
0.14	$35,739	$30,105.88
0.15	$16,046	$19,837.23
0.16	-$2,816	$9,985.92
0.17	-$20,891	$530.34
0.18	-$38,221	-$8,549.78
0.19	-$54,843	-$17,273.48

As the above table shows, when cost of capital is approximately

Below 15%, press A has higher NPV than Press B.

But this changes when the cost of capital Increases to 15% and

Beyond. This suggest a cross-over point between 14 and 15% (14.59)

cost of capital.

The “What to do?” question

The answer is straightforward: when there is a conflict choose NPV

Caveat: When the conflict arise because of size and if the small project has high IRR, we need to ask the following question:

Can we mobilize the excess capital to generate a net present value in access of the differential NPV between the small and the large project?

If the answer is yes, small project can be given priority. In practice this is a difficult question to answer.

Example

In our illustrative case LI, project A has roughly 5K higher NPV than project B:

NPV=$35,738.82- $30,105.88=$5,633

If Excess Capital =662,000-361,600=$300,400 can be mobilized to a new project with NPV in excess of 5,633, project B may be preferable.

Otherwise, project A should be selected!

Incremental Cash Flows Approach

	Project A	Project B	Incremental Cash Flows
0	($662,000)	($361,600)	($300,400)
1	$128,400	$87,600	$40,800
2	$182,160	$119,280	$62,880
3	$166,120	$96,160	$69,960
4	$167,760	$85,680	$82,080
5	$449,560	$206,880	$242,680
NPV	$35,738.82	$30,105.88
IRR	15.85%	17.06%	15%

Another way to rest the conflict is to measure the IRR of the incremental cash flows. If the IRR of the incremental cash flows of the larger project exceed the required return, the larger project should be chosen. In our example IRR of the incremental cash flows exceed cost of capital of 14%; we can conclude that project A should be chosen.

>14%

Note that when we use the IRR method:

We choose project B because it has higher IRR

We also choose the hypothetical incremental project (A-B) as it has IRR> Cost of Capital

This amounts to selecting: B +(A-B)=A

An important point to emphasize is the IRR’s blindness to optimal scale of investment; NPV, therefore is a superior decision rule as compared to IRR.

NPV can be construed as an absolute dollar return measure whereas IRR is a percentage return method.

Example: Project Size, IRR & NPV Conflict

Consider the two projects above with different initial outlays and cash flow structures. The company in question should choose one of these two service station projects. Which one should company adopt? Since these are mutually exclusive projects, it does not make sense to adopt both.

	NPV at 10%	PI at 10%	IRR
Inexpensive Project	92,500	1.18	14%
Expensive Project	98,200	1.09	12%

Mutually Exclusive Projects and NPV

	NPV at 10%	PI at 10%	IRR
Inexpensive Project	92,500	1.18	14%
Expensive Project	98,200	1.09	12%

While the expensive project’s direct contribution to shareholder wealth is larger, inexpensive project earns higher return on each dollar invested, and has a higher return.

The impressive performance of inexpensive project documented in PI and IRR obviously in conflict with the value maximization objective.

What should company do? If company invests $1.1m it creates $7,700 more value! However, investing $522,000 makes $578,000 available.

If the company had an opportunity to deploy this amount to create NPV in excess of $7,700 by taking same level of risk, inexpensive project would be viable.

Otherwise, the firm should go for the expensive project. Scale insensitivity of PI and IRR confirms the use of NPV as an appropriate figure of merit.

234

110,382123,493111,397163,016

265,000

(10.1)(10.1)(10.1)(10.1)

397,443.66265,000132,443.66

NPV

=+++-

++++

=-=

NPV =

FCFPt (1+ k )t

− t=1

∑ IO > 0

NPV=

FCFP

(1+k)

t=1

IO>0

.........

(1)(1)(1)

AAA

FCFP

FCFPFCFP

IRRIRRIRR

=+++

+++

234

110,382123,493111,397163,016

265,000

(1)(1)(1)(1)

IRRIRRIRRIRR

=+++

++++

MIRR =N

FCFt × (1+ k ) N −t

t=1

∑ IO

−1

MIRR=

FCF

´(1+k)

N-t

t=1

-1

1/4

(1)

581,897

1121.73%

265,000

FCFk

MIRR

´+

æö

=-=-=

ç÷

èø

397,443.66

(1)

1.50

265,000

FCFP

===

(

)

(

)

(

)

(

)

=´®=

+´+-

+´

111

NPV

NPVANPVANPV

iii

ANPV

PerpValue

Perpetual Value =

1,638,090 0.12

=13,650,733

Perpetual Value=

1,638,090

0.12

=13,650,733

unequal economic lives

EXAMPLE: PROJECTS WITH UNEQUAL ECONOMIC LIVES
Annualized NPV Approach			Common Economic Life Approach
Required Rate of Return	12%		Required Rate of Return	12%
	A	B		A	B
- 0	- 100,000,000.00	- 132,000,000	0	- 100,000,000.00	- 132,000,000.00
1	30,000,000.00	25,000,000	1	30,000,000.00	25,000,000.00
2	30,000,000.00	25,000,000	2	30,000,000.00	25,000,000.00
3	30,000,000.00	25,000,000	3	30,000,000.00	25,000,000.00
4	30,000,000.00	25,000,000	4	30,000,000.00	25,000,000.00
5	30,000,000.00	25,000,000	5	- 70,000,000.00	25,000,000.00
6		25,000,000	6	30,000,000.00	25,000,000.00
7		25,000,000	7	30,000,000.00	25,000,000.00
8		25,000,000	8	30,000,000.00	25,000,000.00
9		25,000,000	9	30,000,000.00	25,000,000.00
10		25,000,000	10	30,000,000.00	25,000,000.00
NPV	$8,143,286.07	$9,255,575.71	NPV	12,764,005.28	$9,255,575.71
ANPV	$2,259,026.81	$1,638,090.33
Perpetual Value	18,825,223.38	13,650,752.76		- 0	- 0

Shao Airlines is considering two alternative planes. Plane A has an expected life of 5 years, will cost $100 million, and will produce net cash flows of $30 million per year. Plane B has a life of 10 years, will cost $132 million, and will produce net cash flows of $25 million per year. Shao plans to serve the route for 10 years. Inflation in operating costs, airplane costs, and fares is expected to be zero, and the company’s cost of capital is 12 percent. By how much would the value of the com- pany increase if it accepted the better project (plane)?

This approach requires annualized contribution of the project to NPV, and implicitly assumes that project can be repeated indefinetly generating the perpetual ANPV. Perpetual Value is calculated with this assumption where Perpetual Value=ANPV/k

This approach requires finding a common economic life for both projects. For instance by assuming that 5 year project can be repeated once to create a 10 year project , we can calculate NPV of both project under the assumption that 5 year project repeated once by investing the original 100 m at the end of year five. The assumption is that the project will generate same cash flows as in years 1 throgh 5 during years 6 through 10. If one of the projects had a 3 year economic life and the second one had 5 year economic life, the common economic life would be 15 years. In this case first project will be assumed to be repeated 5 times while the second project will be assumed to be repeated 3 times.

Sheet5

			3,900,000.00
			0.0800
			48,750,000.00
			42,750,000.00
			0.14
			52006986.2226666
EBIT	6,000,000.00
Tax Rate	35%	8.75
EBIT x (1-T)	3,900,000
Unlevered Beta	1.1
Risk Free Rate	2.50%
EMRP	5.00%
Unlevered CoE	8.00%
Unlevered Firm Value	48,750,000.00
Outsanding Shares	400,000
Pre Recap Share Price	121.88
Cost of Debt	2.75%
Levered Beta	1.2676675
Cost of Levered Equity	8.84%
E/V	0.8100445525
D/V	0.1899554475
D/E	0.2345
WACC	7.50%
Value	52,006,986.22
Theoretical ITS	3,500,000.00
Actual ITS	3,256,986.22
Debt	10,000,000.00
Equity	42,006,986.22
D/E	0.2381
Post Reap Share Price	130.02
Post Recap Outsanding Shares	323,087

Phoenix Inc. is an all-equity firm with 400,000 shares outstanding. It has $6,000,000 of EBIT, which is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per share (DPS). Company's CapEx is equal to its annual depreciation allocation and change in WCR is expected to be zero in the foreseeble future. Company's tax rate is 35%. Phoenix is considering issuing $10,000,000 of 2.75 % bonds at par value and using the proceeds to repurchase stock. The risk-free rate is 2.5%, the market risk premium is 5.0%, and firm's asset beta is 1.10. The CFO estimates that recapitalization initially will increase firms's D/V ratio to about 19%. Based on the information provided what is the best estimate of post recapitalization WACC of Zelnick Inc.?

ANPV = NPV

(1+i)N −1 (1+i)N ×i

= 8,143,286 (1+0.12)5 −1 (1+0.12)5 ×0.12

⎛ ⎝⎜

⎞ ⎠⎟

=2,259,027

ANPV=

NPV

(1+i)

-1

(1+i)

´i

8,143,286

(1+0.12)

-1

(1+0.12)

´0.12

=2,259,027

Perpetual Value =

2,259,027 0.12

=18,825,223

Perpetual Value=

2,259,027

0.12

=18,825,223

ANPV = NPV

(1+i)N −1 (1+i)N ×i

= 9,255,575

(1+0.12)10 −1 (1+0.12)10 ×0.12

⎛ ⎝⎜

⎞ ⎠⎟

=1,638,090

ANPV=

NPV

(1+i)

-1

(1+i)

´i

9,255,575

(1+0.12)

-1

(1+0.12)

´0.12

=1,638,090

IO =

IOt (1+ k )tt=1

∑

IO=

(1+k)

t=1

NPVA = 128, 400

(1+ 0.14)1 +

182,160 (1+ 0.14)2

+ 166,120

(1+ 0.14)3 +

167,760 (1+ 0.14)4

+ 449,560

(1+ 0.14)5 − 662,000 = 35,738.82

NPV

128,400

(1+0.14)

182,160

(1+0.14)

166,120

(1+0.14)

167,760

(1+0.14)

449,560

(1+0.14)

-662,000=35,738.82

123

87,600119,28096,160

(10.14)(10.14)(10.14)

85,860206,880

361,60030,105.88

(10.14)(10.14)

NPV

=+++

+++

+-=

IO =

FCF1 (1+ IRRA )

1 + FCF2

(1+ IRRA ) 2 + .........+

FCFN (1+ IRRA )

IO=

FCF

(1+IRR

)

FCF

(1+IRR

)

+.........+

FCF

(1+IRR

)

IO =

FCFt × (1+ k ) N −t

t=1

∑ (1+ MIRR) N

IO=

FCF

´(1+k)

N-t

t=1

(1+MIRR)

12345

128,400182,160166,120167,760449,560

662,000

(1)(1)(1)(1)(1)

AAAAA

IRRIRRIRRIRRIRR

=++++

+++++

12345

87,600119,28096,16085,860206,880

361,600

(1)(1)(1)(1)(1)

BBBBB

IRRIRRIRRIRRIRR

=++++

+++++

(1)

FCFP

697,739

1.05

662,000

391,705

1.08

361,600