chapter 6 principles of corporate finance tenth edition making investment decisions with the net...
TRANSCRIPT
Chapter 6Principles of
Corporate FinanceTenth Edition
Making Investment Decisions With the Net Present Value
RuleSlides by
Matthew Will
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
6-2
Topics Covered
Applying the Net Present Value RuleIM&C ProjectInvestment TimingEquivalent Annual Cash Flows
6-4
What To Discount
Rule 2: Estimate Cash Flows on an Incremental Basis Do not confuse average with incremental payoffs Include all incidental effects Forecast Sales Today and Recognize After-Sales Cash Flows
to come Later Do not forget working capital requirements Include opportunity costs Forget sunk costs Beware of allocated overhead costs Remember salvage value
Points to “Watch Out For”
6-5
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
Rule 3 - Treat Inflation Consistently
6-6
Inflation
Example
You invest in a project that will produce real cash flows of -$100 in year zero and then $35, $50, and $30 in the three respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?
1rate inflation+1ratediscount nominal+1=ratediscount real
6-7
Inflation
Example
You invest in a project that will produce real cash flows of -$100 in year zero and then $35, $50, and $30 in the three respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?
045.110.1
15.1
1rateinflation +1ratediscount nominal+1=ratediscount real
6-8
Inflation
Example - nominal figures
55
23263
75452
4833
100
3
2
151939
151560
151538
.$
.39.9=1.1030
.60.5=1.1050
.38.5=1.10351
100-0
15% @PV Flow CashYear
..3
..2
..
6-9
Inflation
Example - real figures
55
3
2
100
.
26.29=30
45.79=50
-33.49=351
100-0
[email protected]%Flow CashYear
3
2
1.04530
1.04550
1.04535
= $
6-10
IM&C’s Guano Project
Revised projections ($1000s) reflecting inflation
0 1 2 3 4 5 6 7
1 Capital Investment 10 000 (1 949) 2 Accumulated depreciation 1 583 3 167 4 750 6 333 7 917 9 500 - 3 Year-end book value 10 000 8 417 6 833 5 250 3 667 2 083 500 - 4 Working capital 550 1 289 3 261 4 890 3 583 2 002 - 5 Total book value (3+4) 10 000 8 967 8 122 8 511 8 557 5 666 2 502 - 6 Sales 523 12 887 32 610 48 901 35 834 19 717 7 Cost of goods sold 837 7 729 19 552 29 345 21 492 11 830 8 Other Costs 4 000 2 200 1 210 1 331 1 464 1 611 1 772 9 Depreciation 1 583 1 583 1 583 1 583 1 583 1 583 10 Pretax profit (6-7-8-9) (4 000) (4 097) 2 365 10 144 16 509 11 148 4 532 1 449 11 Tax at 35% (1 400) (1 434) 828 3 550 5 778 3 902 1 586 507 12 Profit after tax (10-11) (2 600) (2 663) 1 537 6 595 10 731 7 246 2 946 942
Period
6-11
IM&C’s Guano Project
NPV using nominal cash flows
$3,520,000or 520,320.1
444,3
20.1
110,6
20.1
136,10
20.1
685,10
20.1
205,6
20.1
381,2
20.1
630,1600,12
76
5432
NPV
6-12
IM&C’s Guano Project
Cash flow analysis ($1000s)
0 1 2 3 4 5 6 71 Sales 523 12,887 32,610 48,901 35,834 19,717 2 Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 3 Other costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 4 Tax on operations (1,400) (1,434) 828 3,550 5,778 3,902 1,586
5Cash flow from operations (1-2-3-4) (2,600) (1,080) 3,120 8,177 12,314 8,829 4,529
6 Change in working capital (550) (739) (1,972) (1,629) 1,307 1,581 2,002 7 Capital investment and (10,000) 1,442 8 Net cash flow (5+6+7) (12,600) (1,630) 2,381 6,205 10,685 10,136 6,110 3,444 9 Present value at 20% (12,600) (1,358) 1,654 3,591 5,153 4,074 2,046 961
Period
Net Present value= +3520 (sum of 9)
6-14
IM&C’s Guano Project
Tax depreciation allowed under the modified accelerated cost recovery system (MACRS) (Figures in percent of depreciable investment)
Year(s) 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year
1 33.33 20 14.29 10 5 3.752 44.45 32 24.49 18 9.5 7.223 14.81 19.2 17.49 14.4 8.55 6.684 7.41 11.52 12.49 11.52 7.7 6.185 11.52 8.93 9.22 6.93 5.716 5.76 8.92 7.37 6.23 5.287 8.93 6.55 5.9 4.898 4.45 6.55 5.9 4.529 6.56 5.9 4.46
10 6.55 5.9 4.4611 3.29 5.9 4.4612 5.9 4.4613 5.91 4.4614 5.9 4.4615 5.91 4.4616 2.99 4.46
17-20 4.4621 2.23
Tax Depreciation Schedules by Recovery-Period Class
6-15
IM&C’s Guano Project
Tax Payments ($1000s)
0 1 2 3 4 5 6 71 Sales 523 12,887 32,610 48,901 35,834 19,717 2 Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 3 Other Costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 4 Tax depreciation 2,000 3,200 1,920 1,152 576 5 Pretax profit (1-2-3-4) (4,000) (4,514) 748 9,807 16,940 11,579 5,539 1,949 6 Taxes at 35% (1,400) (1,580) 262 3,432 5,929 4,053 1,939 682
Period
6-17
Investment Timing
Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision. A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow.
6-18
Investment Timing
Example
You own a large tract of inaccessible timber. To harvest it, you have to invest a substantial amount in access roads and other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices will rise as you wait, and the trees will keep growing, although at a gradually decreasing rate. Given the following data and a 10% discount rate, when should you harvest?
6-19
Investment Timing
Example
You own a large tract of inaccessible timber. To harvest it, you have to invest a substantial amount in access roads and other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices will rise as you wait, and the trees will keep growing, although at a gradually decreasing rate. Given the following data and a 10% discount rate, when should you harvest?
Answer: Year 4
6-20
Investment Timing
Another Example
You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?
6-21
Investment TimingAnother Example
You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?
Year Cost PV Savings NPV at Purchase NPV Today
0 50 70 20 20.01 45 70 25 22.72 40 70 30 24.83 36 70 34 Date to purchase 25.54 33 70 37 25.35 31 70 39 24.2
6-22
Equivalent Annual Cash Flows
Equivalent Annual Cash Flow - The cash flow per period with the same present value as the actual cash flow as the project.
factorannuity
flowscash of luepresent va=annuity annual Equivalent
6-23
Example
Given the following cash flows from operating two machines and a 6% cost of capital, which machine has the higher value using equivalent annual annuity method.
Year
Mach. 0 1 2 3 PV@6% E.A.A.
A +15 +5 +5 +5
B +10 +6 +610.61
11.45
Equivalent Annual Cash Flows
28.37
21.00