CHAPTER 6
HOW TO ANALYZE INVESTMENT PROJECTS
MAIN OBJECTIVE
How Discounted Cash Flow analysis is used to make investment decisions?
6.1. The Nature of Project Analysis
Individual Investment Project is the unit of analysis for capital budgeting
6.2. Where do investment ideas come from?
There are three main categories of capital expenditure.
- New Products
- Cost Reduction
- Replacement of existing plants and factories
6.3 The Net Present Value Rule
A project’s NPV is the amount by which it is expected to increase the wealth of
the firm’s current shareholders.
Rule: Invest if the proposed project’s NPV is positive
Convention: A positive sign for each cash flow that is an inflow
A negative sign for each cash flow that is an outflow
We also need to know the discount rate or the capitalization rate to discount the
cash flows. This rate is called the project’s cost of capital
P.1
Here we need to calculate the NPV of each of the 2 projects. We will select the
project with the higher NPV.
The cost of capital for both projects is 10%. This is the rate we will use to
discount the cash flows.
Initial outlay is give to be $ 10 million. In cash flow terms this is – 10,000,000
at time 0 (today).
Calculation of present values of each of the cash flows.
Project A
Year 1: PV = 1,000,000 / (1 + i) = 1,000,000 /(1 .1 ) = 909090.91
Year 2: PV = 2,000, 000 / (1 + i)2 = 2,000,000/ ( 1.1)2 = 2,000,000/1.21=
1,652,892.56
Year 3: PV = 3,000,000 / (1+ i)3 = 3,000,000 / (1.1)3 = 3,000,000/1.331=
2,253,944.40
Year 4: PV = 4,000,000/ (1+ i)4 = 4,000,000/(1.1)4 = 4,000,000/1.4641 =
2,732,053.82
Year 5: PV = 5,000,000/ (1+ i)5 = 5,000,000/(1.1)5 = 5,000,000/1.61051
=3,104,606.61
NPV of Project A = -10000000 + 909091 +1652893 + 2253944 + 2732054 +
3104607
= $652,589
Similarly NPV of Project B = 2,092,132
Year
1
2
3
4
5
Total PV
NPV
Project A
Cash Flows
$ 1 million
2 million
3 million
4 million
5 million
PV of Project
A Cash Flows
909,091
1,652,893
2,253,944
2,732,054
3,104,607
10,652,589
652,589
Project B
Cash Flows
$5 million
4 million
3 million
2 million
1 million
PV of Project
B Cash Flows
4,545,454
3,305,785
2,253,944
1,366,027
620,921
12,092,132
2,092,132
Since project B has a higher NPV than project A, we choose B.
Intuitively: Observe that the higher cash inflows occur earlier in project B, while
the higher inflows occur later in project A. This is the reason for a higher NPV
in project B.
6.4. ESTIMATING A PROJECT’S CASH FLOWS
1.
2.
3.
4.
5.
Regular Cash Flows
Initial Outlay
Future Capital Spending
Future changes in working capital
No financial expenses – such as interest payments or dividends
1. Regular Cash Flows
Regular Cash Flows = Revenue – Cash Expenses – Taxes
= Revenue – Total Expenses - Taxes + Non-cash Expenses
= Net Income* + Non cash expenses
= Net Income* + Depreciation + Amortization
Relationship Between Cash Flow and EBITDA (i.e., Earnings before
Interest, Taxes, Depreciation, and Amortization)
EBITDA = Revenue – Cash Expenses
Regular Cash Flows = EBITDA - Taxes
*Net income is computed without subtracting out any interest expense. As a
general rule, any financial expenses such as interest payments or dividends
should not be subtracted when making capital budgeting decisions.
2. Initial Outlay
Initial Outlay = Initial Capital Spending + Initial increase in Working
Capital
Working Capital = Current Assets – Current Liabilities
Initial Outlay is a negative cash flow
3. Future Capital Spending
Any additional capital spending for the project in the future. These are
negative cash flows
4. Future Changes in Working Capital
Any future increase in working capital is a negative cash flow. Any future
decrease in working capital is a positive cash flow
5. No Financial Expenses – such as Interest Payments or Dividends
Example: See Table 6.2
Regular Cash Flow = Net Income* + Non-Cash Expense = $0.9 + $0.4 = $1.3
Initial Outlay = Initial Capital Spending + Initial increase in Working Capital =
- ($2.8 + $2.2) = - $5
Future Capital Spending = $0
Future changes in Working Capital = A decrease in Working capital of $2.2 at
the end of year seven = $2.2
Year
0 1
2
3
4
5
6
7
_________________________________________________
Cash Flow -5 1.3 1.3 1.3 1.3 1.3 1.3 1.3
2.2
NPV = $1.236 Million (at a discount rate of 15%)
6.5 COST OF CAPITAL
- The risk of a particular project may be different from the risk of the firm’s
existing assets.
- The Cost of Capital should reflect only the market related risk of the
project
- Risk that is relevant in computing a project’s cost of capital is the risk of
the project’s cash flows and not the risk of the financing instruments.
6.6 SENSITIVITY ANALYSIS USING SPREADSHEETS
6.6.1 Break Even Point
The sales volume at which the NPV of the project would be zero is the project’s
break even point. At this level we are indifferent between accepting and
rejecting the project.
See Table 6.4
6.7 ANALYZING COST REDUCING PROJECTS
P.2
This problem illustrates the method of deciding whether to invest in cost
reducing equipment. Essentially, you want to determine if investing in this
equipment justifies the reduction in costs.
Information provided:
Cost of the equipment : $ 10,000,000
Useful life: 4 years ( This implies that we will look at a 4 year horizon of cash
flows and also depreciate the equipment over 4 years)
Expected reduction in labour costs by investing in this equipment : $ 4,000,000/
year
Tax rate on profits: 40 %
Depreciation method: Straight line (This implies that you will expense
$2,500,000 each year on account of depreciation)
Incremental Regular Cash Flow = Incremental net income + Incremental
non-cash expense.
Pre-tax income increases by:
Cost savings – Annual Depreciation = $ 4MM - $2.5 MM= $1.5 MM
Incremental Net income = 1.5*( 1 – Tax rate) = 1.5*0.6 = 0.9 MM
Depreciation is a non-cash expense, so we need to add it back to determine the
incremental cash flow.
Incremental Regular Cash Flow = 0.9 + 2.5 = $ 3.4MM
Initial outlay = - $ 10MM
Now all we need to do is find the NPV of this project.
The hurdle rate is give to be 15 %( discount rate)
We first find the PV of each of the cash flows for year 1-4.
Year 1:
Year 2:
Year 3:
Year 4:
$3.4MM/ ( 1+ i ) = 3,400,000/1.15000000= 2,956,521
$3.4MM/ ( 1+ i )2 = 3,400,000 /1.3225000= 2,570,888
$3.4MM/ ( 1+ i )3 = 3,400,000/ 1.5208750 = 2,235,555
$3.4MM/ ( 1+ i )4 = 3,400,000/1.74900625=1,943,961
NPV = -10,000,000 + 2,956,521 + 2,570,888 + 2,235,555 + 1,943,961
NPV = - 293,073
Since the NPV is negative we don’t take the project.
To find IRR, we need to calculate the discount rate at which NPV=0
The IRR is found to be 13.54%.
Since the IRR is lower than the hurdle rate of 15%, we don’t take the project.
P.5 Replacement Decision
Here we are evaluating a replacement decision. The principle is again the same.
We need to find the incremental regular cash flows that result from investing in
the project and find the NPV/IRR.
The discount rate or the cost of capital is given to be 12%
a. The After-Tax Net Cash Flows are given as follows:
Initial Outlay
The old equipment has a current market value of $ 2000. However if it is sold
there is a capital gains tax of 50%. We also spend $25,000 on the new machine.
So the after tax cash flow at time 0 = -25,000 + 2000 (1 –0.5) = -24,000
Hence, Initial Outlay = -24,000
Incremental Regular Cash Flows
Cash flow from increase in revenue:
Cash flow from increase in expense:
Increase in Depreciation:
(straight line for ten years)
10,000
-3,000
-2,500
Increase in Pre-tax Income =
$4,500
Incremental Net Income = 4,500 * 0.5 = $2,250
Incremental non-cash expense = Increase in Depreciation = $2,500
Incremental Regular Cash Flow = Incremental net income + Incremental
non-cash expense.
Incremental Regular Cash Flow = $2,250 + $2,500 = $4,750
Year
0
1
2
…
10
_________________________________________________
Cash Flow -24,000 $4,750
$4,750 …
$4,750
b. IRR
IRR= 14.82%
IRR is that discount rate at which NPV=0
c. NPV
Discount Rate = 12%
NPV= -24000 + 4,750/(1.12) + 4,750/(1.12)2 ……. + 4,750/(1.12)10
NPV= -24,000 + 4241.07 + 3786.67 +3380.95 + 3018.71 + 2695.27 + 2406.49 +
2148.65 +1918.44 + 1712.89 + 1529.37
NPV = $2,838.56
d. Since NPV is positive the project is worthwhile. Also the IRR is greater than
the cost of capital.
6.9 RANKING MUTUALLY EXCLUSIVE PROJECTS
- When we say 2 or more projects are mutually exclusive, we mean that the
firm will take at most only one of them
- The firm should choose the project with the highest NPV
- Ranking projects on the basis of IRR may be inconsistent with the
objective of maximizing shareholder value. This is because a project’s
IRR is independent of scale.
6.10 INFLATION AND CAPITAL BUDGETING
Rule: The 2 correct ways of computing NPV are
1. Use nominal cost of capital to discount nominal cash flows
2. Use a real cost of capital to discount real cash flows
P.6
Initial Outlay: $ 1,000,000
This is made up of 2 components: Equipment of $800,000 and Working Capital
of $200,000
The life of the equipment is 4 years. This implies that we are looking at a 4 year
horizon for cash flows as well as depreciation.
Selling price of each PC: $1800
No of additional units : 1000
Increase in annual fixed costs ( excluding depreciation): 100,000
Variable cost per unit: $1400
Depreciation: Straight line, 4 years, no salvage value
Hurdle Rate: 12%
Income tax rate: 40%
a.
Accounting Break Even Point for the project
Accounting Break even equals the additional number of units sold at which
increase in Net Income equals zero.
Net Income = (Revenues – Fixed costs – variable costs) (1 – tax rate)
(note that fixed cost includes non-cash expense like depreciation)
Let Q be the number of additional units sold
Net Income = (P *Q – Fixed costs – V.Q) *(1 – Tax Rate)
where:
P = Selling Price/Unit
V = Variable Cost/unit
At accounting breakeven, Net Income = 0.
0 = (P *Q – Fixed costs – V.Q) *(1 – Tax Rate)
0 = (P *Q – Fixed costs – V.Q)
Fixed Costs = Q * (P – V)
Fixed Costs = Q * Contribution Margin,
where Contribution Margin = P - V
Hence, breakeven point equals:
Q = Fixed Costs/Contribution Margin
Fixed Costs = Increase in Fixed Costs excluding depreciation + Increase in
depreciation
= 100,000 + 200,000
$300,000
Contribution Margin = Selling Price/Unit – Variable Cost/unit
= 1800 –1400
= $400
Break Even Point = 300,000/400 = 750 additional units per year
b.
Net Present Value
Increase in Sales Revenue (1000 units @ $1800/unit): $1,800,000 per year
Increase in total variable costs (@ $1400 per unit) : $1,400,000 per year
Increase in fixed costs excluding depreciation
Depreciation
: $ 100,000 per year
: $ 200,000 per year
Increase in operating Income = 1800000-1400000-100000-200000 = 100000
Taxes @ 40% p.a: 40,000
Increase in net income: 100,000-40,000=60,000
Add back depreciation to this to get the incremental cash flow
Incremental Regular Cash Flow: 60,000 + 200,000 = $260,000
Cash flows:
Year 0 : - 1,000,000 ( Equipment of $800,000 plus increase in working capital
of $200,000)
Year 1 : 260,000
Year 2 : 260,000
Year 3 : 260,000
Year 4 : 260,000 + 200,000 ( The last cash flow includes a positive cash flow of
$200,000, which represents the decrease in the working capital)
The discount rate to be used is 12%
The disounted cash flows and NPV are as follows:
Year 0
Year 1
Year 2
Year 3
NPV = -1,000,000 + 232142.85 + 207270.40 + 185062.86
Year 4
+ 165234.70
+127103.61
NPV = -1,000,000 + 916814.42
NPV = -83,186
The NPV is negative. The project is not worth taking.
c.
Volume of sales at which NPV will be zero
First we need to find the incremental regular cash flow that will result in a
zero NPV. Lets call that cash flow CF
0 = -1,000,000 + CF/1.12 + CF/1.122 + CF/1.123 + CF/1.124 + 200,000/1.124
1,000,000 = CF ( 0.892857 + 0.79719 +0.71178 + 0.635518 ) + 127103.61
872896.3843 = 3.037345 * CF
CF = 287,387.96
We now need to find the incremental number of units that corresponds to this
cash flow.
Incremental regular cash flow = Incremental net income + Incremental
depreciation
= (1 - 0.4) (1800 Q - 1400 Q - 300,000) + 200,000
287,387.96 = 240Q –180,000 +200,000
240 Q = 267,387.96
Q = 1114.1
The expansion must result in an additional 1115 units per year at a minimum to
justify the outlay.