Principles
of
Corporate
Finance
Ninth Edition
Chapter 7
Making Investment
Decisions With the Net
Present Value Rule
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved
7- 2
Topics Covered
Applying the Net Present Value Rule
IM&C Project
Equivalent Annual Costs
7- 3
What To Discount
Only Cash Flow is Relevant
7- 4
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
7- 5
Inflation
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
7- 6
Inflation
Example
You own a lease that will cost you $8,000 next
year, increasing 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+inflation rate
7- 7
Inflation
Example - nominal figures
Year Cash Flow
1
2
8000
8000x1.03 = 8240
3
4
8000x1.032 = 8240
8000x1.033 = 8487.20
PV @ 10%
7272.73
6809.92
8000
1.10
8240
1.102
8487 .20
1.103
8741.82
1.104
6376.56
5970.78
$26,429.99
7- 8
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
PV@6.7961%
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
7- 9
IM&C’s Guano Project
Revised projections ($1000s) reflecting inflation
Period
1
2
3
4
5
6
7
8
9
10
11
12
Capital Investment
Accumulated depreciation
Year-end book value
Working capital
Total book value (3+4)
Sales
Cost of goods sold
Other Costs
Depreciation
Pretax profit (6-7-8-9)
Tax at 35%
Profit after tax (10-11)
0
10,000
10,000
10,000
4,000
(4,000)
(1,400)
2,600
1
1,583
8,417
550
8,967
523
837
2,200
1,583
(4,097)
(1,434)
(2,663)
2
3,167
6,833
1,289
8,122
12,887
7,729
1,210
1,583
2,365
828
1,537
3
4,750
5,250
3,261
8,511
32,610
19,552
1,331
1,583
10,144
3,550
6,595
4
6,333
3,667
4,890
8,557
48,901
29,345
1,464
1,583
16,509
5,778
10,731
5
7,917
2,083
3,583
5,666
35,834
21,492
1,611
1,583
11,148
3,902
7,246
6
9,500
500
2,002
2,502
19,717
11,830
1,772
1,583
4,532
1,586
2,946
7
(1,949)
-
1,449
507
942
IM&C’s Guano Project
NPV using nominal cash flows
1,630 2,381 6,205 10,685 10,136
NPV 12,000
2
3
4
1.20 1.20 1.20 1.20 1.205
6,110 3,444
3,520 or $3,520,000
6
7
1.20 1.20
7- 10
7- 11
IM&C’s Guano Project
Cash flow analysis ($1000s)
Period
0
1
2
3
4
5
6
7
8
9
Sales
Cost of goods sold
Other costs
Tax on operations
Cash flow from operations (12-3-4)
Change in working capital
Capital investment and
Net cash flow (5+6+7)
Present value at 20%
4,000
(1,400)
(2,600)
(10,000)
(12,600)
(12,600)
Net Present value= +3520 (sum of 9)
1
523
837
2,200
(1,434)
2
12,887
7,729
1,210
828
3
32,610
19,552
1,331
3,550
4
48,901
29,345
1,464
5,778
5
35,834
21,492
1,611
3,902
6
19,717
11,830
1,772
1,586
(1,080)
(550)
3,120
(739)
8,177
(1,972)
12,314
(1,629)
8,829
1,307
4,529
1,581
(1,630)
(1,358)
2,381
1,654
6,205
3,591
10,685
5,153
10,136
4,074
6,110
2,046
7
2,002
1,442
3,444
961
IM&C’s Guano Project
Details of cash flow forecast in year 3 ($1000s)
7- 12
IM&C’s Guano Project
Tax depreciation allowed under the modified accelerated cost recovery
system (MACRS) (Figures in percent of depreciable investment)
Year(s)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17-20
21
Tax Depreciation Schedules by Recovery-Period Class
3-Year
5-Year
7-Year
10-Year
15-Year
33.33
20
14.29
10
5
44.45
32
24.49
18
9.5
14.81
19.2
17.49
14.4
8.55
7.41
11.52
12.49
11.52
7.7
11.52
8.93
9.22
6.93
5.76
8.92
7.37
6.23
8.93
6.55
5.9
4.45
6.55
5.9
6.56
5.9
6.55
5.9
3.29
5.9
5.9
5.91
5.9
5.91
2.99
20-Year
3.75
7.22
6.68
6.18
5.71
5.28
4.89
4.52
4.46
4.46
4.46
4.46
4.46
4.46
4.46
4.46
4.46
2.23
7- 13
7- 14
IM&C’s Guano Project
Tax Payments ($1000s)
0
1
2
3
4
5
6
Sales
Cost of goods sold
Other Costs
Tax depreciation
Pretax profit (1-2-3-4)
Taxes at 35%
4,000
(4,000)
(1,400)
1
523
837
2,200
2,000
(4,514)
(1,580)
2
12,887
7,729
1,210
3,200
748
262
3
32,610
19,552
1,331
1,920
9,807
3,432
Period
4
48,901
29,345
1,464
1,152
16,940
5,929
5
35,834
21,492
1,611
576
11,579
4,053
6
19,717
11,830
1,772
5,539
1,939
7
1,949
682
7- 15
IM&C’s Guano Project
Revised cash flow analysis ($1000s)
0
1
2
3
4
5
6
7
8
9
Sales
Cost of goods sold
Other costs
Tax
Cash flow from operations
(1-2-3-4)
Change in working capital
Capital investment and
disposal
Net cash flow (5+6+7)
Present Value= +3802
(sum of 9)
4,000
(1,400)
(2,600)
1
523
837
2,200
(1,580)
(934)
(550)
2
12,887
7,729
1,210
262
3,686
(739)
3
32,610
19,552
1,331
3,432
Period
4
48,901
29,345
1,464
5,929
5
35,834
21,492
1,611
4,053
6
19,717
11,830
1,772
1,939
8,295
(1,972)
12,163
(1,629)
8,678
1,307
4,176
1,581
(682)
2,002
7
682
(10,000)
(12,600)
(1,484)
2,947
6,323
10,534
9,985
5,757
1,949
3,269
(12,600)
(1,237)
2,047
3,659
5,080
4,013
1,928
912
Net present value= +3802 (sum of 9)
7- 16
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
7- 17
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
present value of costs
Equivalent annual cost =
annuity factor
7- 18
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost machine
using equivalent annual cost method.
Machine
A
B
Year
0
1
15
5
10
6
2
5
6
3
5
PV@6%
28.37
21.00
EAC
10.61
11.45
7- 19
Equivalent Annuities
Example (with a twist)
Instead of calculating an equivalent annual cost, what if you
were asked to calculate the equivalent annual annuity on a
series of cash flows with a positive NPV. Which project would
you select with the following cash flows and a 9% discount rate?
Project
0
1
2
3
4
NPV
Eq. Ann.
C
-15
4.9
5.2
5.9
6.2
2.82
.87
D
-20
8.1
8.7
10.4
2.78
1.10
7- 20
Web Resources
Click to access web sites
Internet connection required
http://finance.yahoo.com
www.bloomberg.com
http://hoovers.com
www.investor.reuters.com
www.cbs.marketwatch.com
http://money.cnn.com
http://moneycentral.msn.com
www.euroland.com
www.valueline.com
