present value analysis note: examples are from analysis for financial management, robert c. higgins,...

Present Value AnalysisNote: examples are from Analysis for Financial

Management, Robert C. Higgins, 8th Edition, McGraw-Hill

“Back of the Envelope” methodsPayback periodReturn on Investment %When to use?Limitations?

Strategic PlanningInvestment/Performance planning process for

an organizationWhat do we need to invest in, in the next

quarter/year, and what benefits can we expecting in return?

Involves “capital budgeting” – the financial evaluation of investment proposals

Discounted Cash FlowRelevant when

A company contemplates an action entailing costs/benefits that extend beyond the current year

IncludesAnalyzing equipment acquisitions or salesChoosing among competing technologies

Financial EvaluationEstimate the relevant cash flows (benefit $

and cost $)Calculate a “figure of merit” for this

investmentCompare the figure of merit to an acceptance

criterion

Challenges?Estimating relevant cash flows

E.g. depreciation, financing costs, shared resources, etc.

Many important costs/benefits cannot be measured in $ so must be evaluated qualitatively (evaluating $ is simpler!)

TABLE 7-1 Cash Flows for Container-Loading Pier ($ millions)TABLE 7-1 Cash Flows for Container-Loading Pier ($ millions)

Year 0 1 2 3 4 5 6 7 8 9 10

Cash flow ($40) 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 17

1 2 3 4 5 6 7 8 9 10

7.5

17

40

Eg: Container Loading PierFirst, “back of the envelope”:Payback?

In year 6 (accum ben – accum costs is > 0)(7.5M*6 – 40M) = 45M – 40M = 5M

Time value of Money: CompoundingCompounding Example

10% interest rate, invest $1End of year 1:

$1 + (10% of $1) = $1 + .10 = $1.10End of year 2:

$1.10 + (10% of $1.10) = $1.20 +11 = $1.21

Time Value of Money: Discounting (present value)Discounting

Finding the present value of a future sum Example

10% return; Promised $1 in one year—what would you have to invest today?

.909 i.e. $1 = $.909 + (10% of $.909)

Calculating Present ValueUse present value tables calculators,

spreadsheet.Present Value Table

Shows the present value of $1 to be received at the end of any number of periods from 1 to 50, at interest rates ranging from 1% to 50%

In present value “interest rate” often called “discount rate”

What is the “discount rate”?If a company already has cash “in hand”:

The rate of return available on similar risk investments

If a company must raise cash (by selling securities):Rate of return expected by buyers of the

securities

Discount Rate & RiskDiscount rate is often adjusted to reflect risk

in an investment’s cash flowIf an investment is higher risk, a “risk

premium” is often added to the discount rate to compensate for the risk (e.g. that the investment will not meet projected cash flows). This means that the discount rate for a higher risk investment will typically be higher.

Example: Baseball CatcherNew, young catcher signed to a contract

promising $2M a year for 4 years.What is the contract worth today assuming the

catcher has a similar risk investment opportunity yielding 15% per year?

0 1 2 3 4

Using Present Value Tables:• Must find P at 15% of each individual payment

P?P = present value of the contract

P = (.870 x $2M) + (.756 x $2M) + (.658 x $2M) + (.572 x $2m)P = $5,710,000

Example: Baseball Catcher cont’dMuch simpler approach:

This amount happens to be an annuity (same $ every year) so we can use the present value annuity table (appendix B).

P = 2.855 x $2M = $5,710,000

P = $5,710,000 means that:$5,710,000 today is equivalent to the future

cash flows of $2M per year for 4 years at 15%

Year

Beginning- of-Period Principal

Interest at

15%

End-of -Period

Principal

Withdrawal 1 $5,710,000 $856,500 $6,566,500 $2,000,000 2 4,566,500 684,975 5,251,475 2,000,000 3 3,251,475 487,721 3,739,196 2,000,000 4 1,739,196 260,879 2,000,075 2,000,000

Note: The $75 remaining in the account after the last withdrawal is due to round-off error in the present value tables.

$5,710,000 Today is Equivalent to $2 million a Year for 4 Years When the Interest Rate is 15 %$5,710,000 Today is Equivalent to $2 million a Year for 4 Years When the Interest Rate is 15 %

Back To the Pier ExampleCalculate P, over 10yrs using 10%

$7.5M for 9 yrs – an annuity$7.5M + $9.5M = $17M for the 10th yearP = (5.759 x $7.5M) + (.386 x $17M)P = $43.1925M + $6.562MP = $49.75M

1 2 3 4 5 6 7 8 9 10

$7.5M

$17M

Investment of $40M

P = $49.75M at 10%

Net Present Value (NPV)

NPV = Present Value ofCash Inflows

Present Value ofCash Outflows

-

NPV for Pier =$49.75M - $40M =

$9.75M

NPV Rule of ThumbNPV > 0

Accept the investment!NPV < 0

Reject the investment!NPV = 0

Investment is marginal (does not create or destroy wealth)

Benefit:Cost Ratio (BCR)BCR = (present value of cash inflows) / (present value of cash outflows)BCR for Pier = $49.75M / $40M = 1.24

BCR Rule of ThumbBCR > 1, attractive investmentBCR < 1, unattractive investmentBCR = 1, marginal

Internal Rate of Return (IRR)IRR is the discount rate at which an

investment’s NPV is zeroOften tricky with the tables; calculator or

computer are easierThe IRR is equivalent to the interest rate on a

bank account that would yield the same $ as the investment being considered

TABLE 7-2 NPV of Container Pier at Different Discount RatesTABLE 7-2 NPV of Container Pier at Different Discount Rates

Discount Rate NPV ($ millions)

10% $9.7512% 5.44

IRR = 15%18% -4.48

FIGURE 7-2 NPV of Container Pier at Different Discount RatesFIGURE 7-2 NPV of Container Pier at Different Discount Rates

-20

-10

0

10

20

30

40

50

0 4 8 12 16 20 24

Discount rate (%)

NP

V (

$ m

illi

on

s)

IRR

IRR Rule of ThumbIf K% is the “opportunity cost of capital)IRR > K, accept the investmentIRR < K, reject the investmentIRR = K, the investment is marginal