Review: Net Present Value

Presentation by:

Heather Collins & Michael Maur

Agenda

• Capital Budgeting - why we use NPV

• Value of Money Over Time

• Net Present Value

• Investment Decisions

• The Discount Rate

• Example

• NPV vs. IRR

Capital Budgeting

• Analysis of potential additions to fixed assets. Long-term decisions, involve large expenditures

• NPV is a tool used in capital budgeting, along with IRR.

• Types of projects: Brand new line of business Expansion of existing line of business Replacement of existing asset

• Independent vs. Mutually Exclusive

Value of Money Over Time

$ 1 M

$ 1 M

Value of Money Over Time

A different point of view:• An investment promises to yield a $1M

one-time profit, one year from now• How much of today‘s dollars am I willing to

pay today to have $1M in a year?• p_max = $1M/(1+r)• r is the discount rate• p_max is the Net Present Value (NPV)

Net Present Value

• Net present value: a project’s net contribution to wealth – present value minus initial investment.

• In other words, the present Value in "today's dollars" of the future net cash flow of a project NPV = PV cash inflows - PV cash outflows

t1

C1

2

C2

3

C3

n

Cn

. . .0todayC0

Using NPV to Make Decisions

• r = rate of return of alternative investment• NPV > 0: Investment promises additional returns • NPV < 0: Investment will yield less return than

alternative investment• NPV = 0: Investment will yield an equal return to

an alternate investment

• As a general rule of thumb, choose project with higher NPV

Discount Rate

• How does the management team determine a reasonable discount rate? What information do they use to estimate it? How do they account for future changes? What are some possible bias?

• Interest that can be earned from an alternative investment

• Incorporate adjustments for Inflation Risk - specifically the risk that the expected cash flows will not be

the actual cash flows

Discount Rate

Other factors that can be used to estimate the discount rate:

• 30 year treasury bond rate• Investment Funds target rate of return• Consumer Price Index (CPI)• Max of highest risk-adjusted rate of return that

can be obtained by investing the money & lowest rate at which money can be borrowed

• Average cost of capital in the company

Review: Types of Annuities

• Ordinary (immediate) annuity: The payments are made at the end of each

period

• Annuity due: The payments are made at the beginning of

each period

• If the cash flows are an annuity due instead of an ordinary annuity, it changes the NPV.

Review: Types of Annuities

• The NPV changes because the number of periods that each CF is discounted changes.

• If it is an ordinary annuity, the January payment would be made on January 31, and thus discounted once. If it is an annuity due, the January payment would be made on January 1, and not discounted. i.e. annuity dues end up discounted one less period than

ordinary annuities, thus the NPV changes.

tFeb Mar Apr n

. . .

Jan

Review: Types of Cash Flows

• Normal vs. Non-normal Cash Flows Normal: Cost (negative CF) followed by a

series of positive cash flows - one change of signs.

Non-normal: Cost (negative CF), a series of positive cash flows, & cost to close project - two or more changes of signs.

Example: Marge’s Decision

• Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. NPV: I = 12, CPT NPV = 16,510

• Pretzel: CF0 = -20,000, C01 = 2,000, C02 = 2,500, C03 = 3,000, C04 = 50,000. NPV: I = 12, CPT NPV = 17,690

Time Falafel-Full PV(CF) How 'Bout A Pretzel? PV(CF)

0 (20,000) (20,000) (20,000) (20,000) 1 15,000 13,393 2,000 1,786 2 15,000 11,958 2,500 1,993 3 13,000 9,253 3,000 2,135 4 3,000 1,907 50,000 31,776

NPV 16,510 17,690

Example: Marge’s Decision

• If projects are independent, Marge should select both. Both have positive NPV.

• If the projects are mutually exclusive, select How ‘Bout A Pretzel? Pretzel NPV > Falafel NPV.

Three Things to Remember

• The NPV rule recognizes that a dollar today is worth more than a dollar tomorrow

• NPV depends solely on the forecasted cash flows from the project and the opportunity cost of capital. Better than other investment rules that depend on

choice of accounting method, profitability of existing business, etc.

• Because present values are all measured in today’s dollars, you can add them up. NPV (A + B) = NPV (A) + NPV (B)

NPV vs. IRR

• The next group will go over IRR, however, NPV and IRR sometimes rank projects differently. Size differences: smaller projects free up funds at t=0 Timing differences: projects with faster payback provides more CF

in early years for reinvestment.

• Reinvestment Rate Assumption: NPV assumes cash flows are reinvested at company’s cost of

capital (i.e.: the investors’ required rate of return).

• IRR assumes cash flows are reinvested at IRR. The NPV reinvestment rate assumption is more realistic. Why? Because NPV represents the investor’s required rate of

return and corporations should act to maximize shareholder wealth.

Review: Net Present Value

Thank you for your attention!

Any Questions?