Department of Economics
An Introduction to Capital
Budgeting Methods
Econ 466
Spring, 2010
Chapters 9 and 10
Consider the following choice
You have an opportunity to invest $20,000 in one
of the following capital assets. You have
estimated the annual cash flows for each option
(in $1000)
Year
A
B
C
0
-20
-20
-20
1
2
5.8
10
2
4
5.8
8
3
6
5.8
6
4
8
5.8
3
5
10
5.8
1
Which option would you select?
Department of Economics
Simple rate of return
Calculate the average return to each investment and
then compare.
Select the investment with the highest simple rate of
return
SRR = Y/I
Where
SRR = simple rate of return
Y = annual profit (less depreciation)
I = original investment
Department of Economics
SRR calculations
Total Gross
Returns
Total
Depreciation
Average
Annual
Profits
A
30,000
20,000
B
29,000
C
28,000
Project
Simple rate of return
Original
Investment
Average
Investment
2,000
10%
20%
20,000
1,800
9%
18%
20,000
1,600
8%
16%
Department of Economics
SRR analysis
How would you rank the investments?
A>B>C
Good points
• Simple because you are working with an
average (annualized) budget
Weak points
• Timing of returns is not considered
Department of Economics
Payback period
Key question:
• How long before I get my investment back?
• Simple, intuitive
• Widely used
If the cash flows are uniform, the calculation is easy
P = I/E
Where
P= payback period
I = investment
E= income per period
•
Otherwise you need to add up the cash flows until the
investment is recaptured
Department of Economics
Calculate the payback period for
these investments
Year
A
B
C
0
-20
-20
-20
1
2
5.8
10
2
4
5.8
8
3
6
5.8
6
4
8
5.8
3
5
10
5.8
1
Project Payback Period
A
4 years
B
~ 3.4 years
C
~ 2.3 years
Department of Economics
Payback period analysis
How would you rank the investments?
C>B>A
In terms of payback period
Good points
•
•
•
Very simple
Reflects liquidity needs
Assumes future returns are too risky to trust
Weak points
•
•
•
Does not consider earnings beyond payback date
Does not consider differences in timing of cash flows
Does not measure profitability
Department of Economics
Signal check – on compounding and
discounting
Suppose you had $1,000 to invest in an
investment that earned 10% per year
• After one year, how much would you have?
• FV = (1+.10)x$1,000 = $1,100
And after two years, at 10%?
• FV = (1.10)x$1,100) = $1,210 = 1,000x(1.10)2
Department of Economics
Buying the rights to an income stream
How much would you pay me for a “bond” that
would pay you $1,100 in a year?
• If the opportunity cost of your money was 10%?
• PV = $1,100/(1.10) = $1,000
What if the payout was in two years?
• PV = $1,210/(1.10)2 = $1,000
OK??
Department of Economics
Net present value
Determine the value of the cash flows in a way
that reflects timing and the time value of money
NPV = -INV + P1/(1+i) + P2/(1=i)2 + P3/(1+i)3 + …..
(PN + VN)/(1+i)N
Where
NPV = net present value
INV = initial investment
P t = cash flow in period t
VN = salvage value of the investment
i = discount rate, required rate of return, opportunity
cost of capital
Department of Economics
Calculate the NVP for the three
investments
•
Assuming a discount rate of 8%
Year
Discount Project A
Factor
Cashflow
PV
0
1
-20,000
-20,000
1
.9259
2,000
1,851.80
2
.8573
4,000
3,429.20
3
.7938
6,000
4,762.80
4
.7350
8,000
5,880.00
5
.6806
10,000
6,806.00
Net Present Value for A
2,730.27
Department of Economics
Calculate the NVP for the three
investments
•
Assuming a discount rate of 8%
Year
Discount Project B
Factor
Cashflow
PV
0
1
-20,000
1
.9259
5,800
5370.22
2
.8573
5,800
4972.34
3
.7938
5,800
4604.04
4
.7350
5,800
4263.00
5
.6806
5,800
3947.48
3,157.72
Net Present Value for B
-20,000
Department of Economics
Calculate the NVP for the three
investments
•
Assuming a discount rate of 8%
Year
Discount Project C
Factor
Cashflow
PV
0
1
-20,000
-20,000
1
.9259
10,000
9259.00
2
.8573
8,000
6858.40
3
.7938
6.000
4762.80
4
.7350
3,000
2205.00
5
.6806
1,000
680.60
Net Present Value for C
$3,766.64
Department of Economics
NVP analysis summary
Project
NPV
A
2,730
B
3,158
C
3,766
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NPV summary
Decision rule for income earning investments
• Specify required rate of return (discount rate)
• Select or rank projects based on their NPV (if
positive)
Ranking by NPV
• C>B>A
What about cost reducing investments such as
machinery?
Department of Economics
Internal rate of return
Consider the following problem. You have an
opportunity to invest $1,000 in a one year
project that returns $1,100 at the end. What is
the minimum opportunity cost of capital that
would be acceptable to invest in this project?
• NPV = 0 = $1,000 - $1,100/(1+ r)
• Solve for r = IRR
• r = ($1100 – $1000)/$1000 = 0.10
Decision rule: invest in this project if there are no
other investments that earn more than 10%
Department of Economics
Internal rate of return
Good points
• Popular approach with lenders and investors
• Simple – seems like a “breakeven” rate
Weak points
• Assumes investors can always reinvest at the
IRR
• Multiple rates of return if cash flows change
from + to – more than once over the
investment’s time horizon
Department of Economics
Internal rate of return analysis
A more complete model
•
NPV = 0 = -INV + P1/(1+i) + P2/(1=i)2 + P3/(1+i)3 +
….. (PN + VN)/(1+i)N
•
Solve for i = IRR (using a financial calculator or
a spreadsheet)
Department of Economics
Internal rate of return analysis
Solving for the IRR for investments A, B and C we
obtain the following results:
• IRR-A 12.01%
• IRR-B 13.82%
• IRR-C 17.57%
Ranking by IRR: C>B>A
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Comparing NPV and IRR
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Bob’s rule
Stick with NPV as an analytical method
• Requires you to specify a discount rate (or
rates) – that is a good thing.
• Relatively unambiguous
• You can always calculate the IRR anyway,
since the underlying model is the same
Department of Economics
Plans for Tuesday, March 9
Meet in the computer lab in Heady Hall
• Learn to use Excel to model capital budgeting or
investment problems
• Hands on session
• More to come after break!
I’ll send an email on Monday to remind you!
Department of Economics