1. Alternate Measures of Capital Investment Desirability
Chapter 6
Alternate Measures of Capital Investment
Desirability
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2. Profitability index (PI) Modified profitability index (MPI)
Internal rate of return (IRR)
Modified internal rate of return (MIRR)
Payback period (PB)
Present payback period (PBP)
Accounting rate of return (ARR)
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3. Profitability Index (PI)
The value increase per dollar invested
= Present value of future cash flows
initial investment
PI = [ ∑CFt /(1+k)t]/I0
NPV = PV – I0 , NPV/ I0 = PV/ I0 – 1
PI = NPV/ I0 + 1
An initial outlay o f $500,000 t hat is expected to
generate cash flows of $100,000 at the end of each
year for the next 10 years. Find PI at 10% RRR?
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4. Modified Profitability Index (MPI)
MPI is based on the assumption that the initial
commitment to a project should be in the
denominator
Initial commitment (IC) = the initial
investment Plus any amount that would be
needed to set aside today to provide funds for
future outflows
MPI = 1 + NPV/Initial commitment
FIN421-CH6. N. ALSALEH
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5. Example 1. To find PI Find the project NPV ( PVFB – PVCost)
Year
Cash flow , , , ,000
Assuming a 10 percent required return
1. To find PI
Find the project NPV ( PVFB – PVCost)
PI = 1+ NPV/i0
2. To find MPI
a. Find Initial commitment
MPI = 1 + NPV/ Initial commitment
PI = 1.67, MPI = 1.30
FIN421-CH6. N. ALSALEH
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6. Another method for calculating the PI index is:
a. Find the present value of net yearly cash
inflows (PVinf)
b. Find the present value of the net yearly
cash outflows (PVouf)
c. PI = (PVinf)/ (PVouf)
(500/ ,000/ ,000/1.104)
(1, ,000/1.102)
= 1.25
FIN421-CH6. N. ALSALEH
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7. Methods for Calculating PI
PI = 1 + NPV/Initial outlay
2. MPI = 1 + NPV/initial commitment.
3. MPI = present value of cash inflows (PVi)
Present value of cash out flows (PVo
FIN421-CH6. N. ALSALEH
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8. Profitability index (PI) rule is an arbitrary rule
It shows no clear relationship between PI and wealth creation
PI ignores the project size, and therefore
ignores the amount of net present value
generated.
compare a $1 investment with a PI of 1.31 and
a $1 million investment with a PI of 1.30
PI is used sometimes as an indicator of risk
PI is often used when the company is operating under capital rationing.
FIN421-CH6. N. ALSALEH
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9. Internal rate of Return (IRR)
IRR is the discount rate that results in a net
present value (NPV) of zero.
a. Conventional Capital Investment (CCI)
An initial outflow followed by only a series of
inflows
Example:
Find IRR for A $300 million investment that
Produces cash flows of $35,237,700 at the end of
each year over a 20 year life.
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10. Initial outflow that is followed by a mixed
b. Uneven Cash Flows:
Initial outflow that is followed by a mixed
Stream of cash inflows or outflows
Example: (P.169. Berkeley Dev. Partnership)
an investment of $264,050 generates cash
flows of $100,000 at the end of year 1 and
$200,000 at the end of year 2. What is the
investment IRR.?
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11. For conventional capital investments, the
IRR gives the same accept-reject signals
as the NPV and PI
Business people prefer to use IRR since it
expresses the rate of return on invested
capital.
They find NPV more difficult to use because it does not measure benefits relative to amount Invested.
FIN421-CH6. N. ALSALEH
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12. Reinvestment Rate Assumptions
IRR assumes that intermediate cash inflows are reinvested at the IRR.
NPV assume that intermediate cash inflows are reinvested at the cost of capital.
initial inv Y Y2 IRR NPV
@10%
A $10, $10, $14, % $1,901
B $10, $10, , % $1,074
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13. IRR Complications B. Projects with Multiple IRRs: Year Cash Flow
0 -$2,000
,000
,000
NPV = 0 = -$2,000 + $7000/(1+IRR) - $6,000/(1+IRR)2
Multiplying both sides by (1+IRR)2 we get
0 = -2,000 (1+IRR)2 +7,000(1+IRR) – 6,000
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14. ax2 + bx + c X = - b + b2 – 4ac (6-1) 2a
a= -2,000, b = 7,000, c =-6,000
Let (1+ IRR) = x
(1+ IRR) = -7, , (-2,000)(-6,000)
2(-2,000)
(1+ IRR) = 1.50, 2.00, IRR = 50%, and 100%
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15. IRRs for this project can be found by
Projects with No IRR
Year Cash Flow
0 - $1,000
1 +$1,500
2 -$ 1,000
IRRs for this project can be found by
Using equation a= -1,000, b =1,500,
and c =-1000
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16. -1, (1,500)2 - 4x (-1,000) x (-1,000)
1+IRR =
2 ( -1,000)
(1 +IRR) =
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17. Modified Internal Rate of Return (MIRR)
Used to develop a single internal rate of
return measure when a project has
Multiple IRR
Compute the terminal value of all cash flows at the cost of capital except the initial outlay (IRR)
Find the discount rate that equates the PV of terminal cash flows with the initial outlay
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18. San Jose development is considering the
Example: (P.175)
San Jose development is considering the
purchase of three lots as follows:
Year Cash Flow
0 ($264,050)
,00,000
,00,000
,00,000
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19. Advantages of MIRR
MIRR gives an unambiguous accept-reject signal when a project has multiple rate of return.
MRR assumes that intermediate cash inflows are reinvested at the cost of capital which is a conservative estimates.
FIN421-CH6. N. ALSALEH
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20. The payback period is the number of years
it takes to recover the initial investment
Example:
Investment = $100,000
Cash benefits = $ 20,000 a year
Payback period = $100,000/$20,000 = 5 years
For an annuity project , the payback period is
calculated by dividing the initial investment
by the size of the annuity.
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21. Payback period for a mixed stream cash flow project.
Year CF Cum. CF.
0 ($100,000)
$40,000 $40,000
, ,000
, ,000
20, ,000
Payback period = 3 + ($5,000/20,000) = 3.25
years = 3 years and 3 months
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22. Advantages of the payback period Very easy to understand
Very easy to compute
PB is used as a risk measure
PB gives an indication of the project’s liquidity
Any PB gives an indication of the productivity of the project.
A 5-year payback period is equivalent to
annual cash flow of $20 per $100 of initial
Outlay. $100 =$20xPVA110yr,k , k=15.1%
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23. Disadvantages of the payback period
Ignores the time value of money.
Ignores the cash flows after the payback
Period.
The payback period is used today primarily
As supplementary information.
Mostly used by managers who are not
familiar with discounted cash flow techniques
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24. Present Value Payback Period
The present value payback period is the
number of years it takes for the cumulative
present value of cash flows to equal zero
Consider the following investment
10% cost
of capital
-2, ,000 1,000 1,000
x x x
-2,
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25. Accounting Rate of Return (ARR) or: Average rate of return or ROI
ARR is defined as the ratio of average
accounting income to average investment.
Accounting income
Income after tax
Income before interest and taxes (EBIT)
after tax income if debt had not existed
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26. Accounting Rate of Return ARR = EBIT x (1 – tax rate)
(Beginning value + Ending value)/2
Example:
Investment requires $1M ($1,000,000)
Useful life is 10 years
Yearly EBIT are $185,545, tax rate = 36%
Salvage value at the end of year 10 = $0
What is ARR?
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27. Acceptance criterion : accept the project
ARR = $185,545 (1-.36)
($1,000,000 +$0)/2
Acceptance criterion : accept the project
If the accounting rate of return is higher
than The minimum acceptable rate of
return.
the existing average accounting return on
the company’s assets or:
b. the company’s target accounting return on
investment
= 23.6%
FIN421-CH6. N. ALSALEH
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28. Consistency with management reward
Advantages of ARR
Simplicity
Consistency with management reward
systems that focus on accounting return on
investment
ARR reflects the importance of accounting
income for mangers who are concerned
about the income they report to their
stockholders.
FIN421-CH6. N. ALSALEH
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29. ARR ignores the time value of money ARR ignores asset life
Disadvantages of ARR
ARR ignores the time value of money
ARR ignores asset life
A $100,000 investment that generates income of $20,000 a year will have the same ARR whether it has a life of 2 years or 20 years
ARR focuses on accounting income rather
than on cash flows
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30. sheet accounts will move Except N/p , LTD & Com Stock
Financial Planning
Pro-Forma*
Income statement
Sales
Forecast
Sales
projection
Addition
to R/E
Review of
past sales
*All income and balance
sheet accounts will move
by same percentage
Except N/p , LTD & Com Stock
Additional Funds
Needed
AFN=$42.7m
Pro-Forma
Balance Sheet
Short-term
Borrowing
(15%)
Long-term
borrowing
(20%)
Selling new
stock
(65%)
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