Sebastian Perrier

Calculation for one period:

• FV=PV + PV. r -> FV=PV(1+r) -> PV=FV/(1+r)

Calculation for multiple periods:

• PV=[FCF1/(1+r) + FCF2/(1+r)'2 + ... + FCFn/(1+r)'n]

Calculation of NPV:

• NPV = PV – Initial Investment

Calculation of IRR:

• Solve “r” (the discount rate) that gives an NPV of zero

NOTES:

• FCF1, FCF2, FCFn – Projected Yearly Free Cash Flows
• r – Interest Rate or Cost of Capital (carefully use the project’s WACC, not the company’s one bc risks are different)
• I – Initial Investment
• n – Project Life (years, months, etc, but put r according to period specified)

Mathematical Problems with the IRR

(a) Negative Cash Flows and Multiple Rates of Return; e.i. when cash flows are +-+, gives multiple IRR, and thus mathematical calculation gives an error.

(b) The Re-investment Problem: bc when you borrow, WACC can change due to different risks.

(c) Ranking Differences: cannot decide in terms of size of projects and timing of cash.

Investment Appraisal and Inflation

(a) Adjust projected cash flows, to account for anticipated fall in value of money

(b) Re-state the discount rate, to allow for anticipated impact of expected inflation

APPENDIX – Future Values and Discount Rate Table

There are four steps in the investment decision:

1. Identify investment opportunities
2. Put numbers to each opportunity (this is the most difficult part!)
3. Evaluate and make a decision (NPV calculation)
4. Monitor investment and control

In point 3, how to make a decision, there are 3 possible analyses:

• PAYBACK PERIOD (ignores time value of money and ignores cash flows after payback period)
• INTERNAL RATE OF RETURN (good to compare, but doesn’t allow + – + flows bc of maths error)
• NET PRESENT VALUE (forces you to get WACC, considers time value of money and has not maths problems).

Decision criteria:

• Choose project that maximizes NPV
• Choose project in which IRR is higher than WACC

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CFO’s objective: MAXIMIZE SHAREHOLDERS VALUE (while complying with law and ethic values):

a. Do not run out of cash! Cash-flow management.

b. Make good investment decisions!

c. Make good financing decisions!