Chapter 6 Principles of Corporate Finance Tenth Edition Making Investment Decisions With the Net Present Value Rule Slides by Matthew Will McGraw-Hill/Irwin

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

6-3

What To Discount

Rule 1

Only Cash Flow is Relevant

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


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


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)

6-13


Details of cash flow forecast in year 3 ($1000s)

6-14


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


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

6-16


Revised cash flow analysis ($1000s)

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


28.37

21.00

6-24


Another Example

Select one of the two following projects, based on highest “equivalent annual cash flow” (r=9%).

4.107.81.820

2.69.52.59.415

Project 43210

D

C

EAANPVCCCCC

2.82

2.78

.87

1.10

Documents

Chapter 6 Principles of Corporate Finance Tenth Edition Making Investment Decisions With the Net Present Value Rule Slides by Matthew Will McGraw-Hill/Irwin