Transcript Principles of Corporate Finance

Making investment
decisions with the Net
Present Value rule
This town's full of money grabbers Go ahead-Bite the Big Apple,
don't mind the maggots, huh Shadoobie, My brain's been battered
My friends they come around they Flatter, flatter, flatter, flatter, flatter
Pile it up, pile it high on the platter- Jagger, Richards
What to discount
1. Only cash flow is relevant.
2. Estimate incremental cash flows.
3. Be consistent in treatment of inflation.
4. Recognize project interactions.
Only cash flow is relevant
1. Depreciation is not a cash flow.
2. Remember investment in working capital.
Dec
Jun
Sales
500
0
Less investment in receivables
-500
+500
0
500
Cash flow
Receivables
paid off
in June
What To Discount
Points to “Watch Out For”
Estimate Cash Flows on an Incremental Basis
Do not confuse average with incremental payoffs
Include all incidental effects
Do not forget working capital requirements
Include opportunity costs
Forget sunk costs
Beware of allocated overhead costs
Treat inflation consistently
INFLATION RULE
Be consistent in how you handle inflation!!
Use nominal interest rates to discount
nominal cash flows.
Use real interest rates to discount real cash
flows.
You will get the same results, whether you
use nominal or real figures
Inflation
Example
You own a lease that had cost you $7,7666.99 last
year, but your lease cost will grow to $8,000 next
year, and the cost will increase at 3% a year (the
forecasted inflation rate) for 3 additional years (4
years total). If discount rates are 10% what is the
present value cost of the lease?
(1+nominal interest rate)
(1  real interest rate) =
(1+inflationrate)
Inflation
Example - nominal figures
Year Cash Flow
1
8000
P V @ 10%
8000
1.10  7272.73
2
3
8000x1.03= 8240
8000x1.032 = 8487.20
4
8000x1.033 = 8741.82
8240
1.10 2
8487 .20
1.10 3
8741 .82
1.10 4
 6809.92
 6376.56
 5970.78
$26,429.99
Inflation
Example - real figures
Year
1
2
3
4
Cash Flow
8000
1.03
8240
1.032
8487.20
1.033
8741.82
1.034
= 7766.99
= 7766.99
= 7766.99
= 7766.99
[email protected]%
7766.99
1.068
7766.99
1.0682
7766.99
1.0683
7766.99
1.0684
 7272.73
 6809.92
 6376.56
 5970.78
= $26,429.99
Be consistent in handling inflation
Another example (for you to check at home):
1. Discount nominal flows (growing at 10%) at nominal 20% rate
55
NPV = -100
+
60.5
+
+
1.202
1.20
2.
66.7
= 26.5
1.203
Discount real flows at real rate
Without 10% inflation:
50
NPV = -100 +
50
+
1.09
50
+
1.092
Note: Real rate = 1.20/1.10 - 1 = .09
= 26.5
1.093
Do not assume all cash flows
rise in line with inflation
• Differential price changes, e.g. wages and prices
• Some cash flows are fixed
Cost of capital is likely to be
more stable in real terms
But even if you work in real terms:
You need to estimate inflation
• to calculate taxes
• to calculate working capital
• to calculate real discount rate
Should you measure returns
before or after tax
1.
The cost of capital is the return required by investors
after tax.
2.
Discount cash flows after corporate tax.
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
Project interactions - 1
investment timing
The cost of computers is steadily falling. The
savings from a new computer are constant. When
should the firm buy the computer?
Year
of
purchase
0
1
2
3
4
5
Cost of
computer
$50
45
40
36
33
31
PV
savings
$70
70
70
70
70
70
NPV in
year of
purchase
(r = 10%)
$20
25
30
34
37
39
NPV
today
$20.0
22.7
24.8
25.5
25.3
24.2
MORAL: NPV is maximized by investing in Year 3
Project interactions - 2
long- versus short-lived equipment
Year:
A
B
COSTS
0
1
15
4
10
6
2
4
6
3
4
PV @ 10%
25
20
Equivalent annual cost of A =
25/(3-year annuity factor) = 25/2.5 = 10.05
Equivalent annual cost of B =
20/(2-year annuity factor) = 20/1.7 = 11.52
MORAL: Annual cost of A is LESS than that of B
Project interactions - 3
machine replacement
Annual operating cost of old machine = 8
Cost of new machine
Year:
0
1
2
3
15
5
5
5
PV @ 10%
27.4
Equivalent annual cost of new machine =
27.4/(3-year annuity factor) = 27.4/2.5 = 11.0179
MORAL: Do not replace until operating cost
of old machine exceeds 11.018