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• Discounted Cash Flow continued

MIN E 408: Mining Enterprise Economics

Project Evaluation Methods

1. Discounted Cash Flow (DCF):

Cash flow discounted at an investor arbitrarily selected discount rate

– Net Present Value (NPV).

– Internal Rate Of Return (IRR).

– Profitability index or benefit cost ratio.

– Payback and discounted payback period.

2. Capital Asset Pricing Method (CAPM):

Discount rate quantitatively modeled using the beta of a security or project with

comparable risk as project.

3. Option Pricing Method:

Uses Portfolio replication to duplicate the project as consisting of certain basicassets that are risk free. The resulting portfolio of assets must have a returnequal to the risk f ree rate.

Project Evaluation Methods

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• IRR is the discount rate that sets the NPV to zero

• Independent of the interest rates in the capital market and sointrinsic to project cash flow

• Solution by tr ial and error

• Solver or goal seek in Excel does it!

• Accept Pro ject i f IRR > discount rate (MARR)

Investment Decision Criteria:Internal Rate of Return (IRR)

0

1

01

T

t

t

t

CF NPV I

RRR

NPV=-$9,325

-$30,000

$0

$30,000

$60,000

$90,000

0 0.04 0.08 0.12 0.16

Rate of Return

N P V

IRR = 8.445%

Investment Decision Criteria:

Internal Rate of Return (IRR)

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1. No IRR

This project has no IRR:

1 2

+ 1,000 – 3,000 2,500

0

• NPV at 10%:

84.3381.1

500,2

1.1

000,3000,1 2

IRR (Some Problems)

2. Implied reinvestment

Project I0 C1 C2 C3 C4 IRR

A $-100m $10m $50m $60m $70m 24.73%

• Misconception that 24.73% is return on 100million; thus

7074.8477.7919.40

01yr 2yrs3yrs

70m60m50m10m

Amount (m$)

Reinvestment

242.03

Total

IRR (Some Problems)

4100 (1 0.2473) $242.03m

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3. Scale problems: similar to PI’s problem

4. Timing Problems

– Projects with back-loaded cash flows may look worse with IRRwhen both IRRs > discount rate

Project I0 C1 C2 C3 C4 IRR MARR NPV

A $-100 $10 $50 $60 $70 24.7% 12% $35.98

B $-100 $70 $50 $30 $10 30.5% 12% $30.07

IRR (mutually exclusive projects)

35.98

24.73%

30.07

30.46%0

20

40

60

80

100

0% 4% 8% 12% 16% 20% 24% 28% 32% 36%

r- discount rate %

N P V

( m i l l i o n $ )

Project A

Project B

IRR (Mutually Exclusive Projects)

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Find the difference between the alternatives. The resulting cash flowshould depict net investment

Project I0 C1 C2 C3 C4 IRR NPV

A-B 0 -60 $0 $30 $60 16.54% $5.91

If the difference between alternatives depict

a net borrowing, reverse decision criteria.

Choose A

IRR – Incremental Approach

• Payback Period:- The number of years required to recover initialinvestment on a project.

• The decision rule: Accept all projects with payback periods

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Year A B C

0 -$100m -$100m -$100m

1 $20m $50m $50m

2 $30m $30m $30m

3 $50m $20m $20m

4 $60m $60m $99m

PBP 3 3 3

• With DPBP cash flows are discounted by the appropriate discount rateand the payback rule applied.

Payback Period and DiscountedPayback Period

• The payback period (PBP) and the discounted paybackperiod (DPBP) are used to reduce the time exposure ofinvested capital to risk.

• For every project,

DPBP estimate > PBP estimate

• If DPBP is > project li fe

– NPV

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• Contemplating which of two dozers to buy.

• Very similar in terms of output.

• Will not directly effect cash flow except through costs.

• r =10%.

Initial Cost Operating costs per year Life

$100,000 $28,500 5

$145,000 $24,000 7

Projects with Different Life Spans

Machine 1

Machine 2


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• Replacement Chain

– Find common life for the tw o and calculate NPV over that life.

• Uniform Annual Series (UAS) or Equivalent Annual Cost (EAC)


5

1 1208,037.42 1

0.10 1.10

$54,879.75

A

A

7

1 1261,842.05 1

0.10 1.10

$53,783.8

A

A

Machine 1

Machine 2

Equivalent Annual Cost

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Review Of Main Points

• Discounted Cash Flow (DCF) Methods:

– Net Present Value

– Internal Rate of Return

• DCFROR and DCFROI

• Commonly used in practice

– Pay Back Period (PBP) and Discounted Pay BackPeriod (DPBP)

• Simple and common

Documents

408-2012-Lec04 DCF3