FinMathSlides5.pdf

# FinMathSlides5.pdf - FINANCIAL MATHEMATICS Theory Chapter 5...

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1 FINANCIAL MATHEMATICS Theory – Chapter 5 NPV, IRR & Depreciation Universitat Pompeu Fabra Dr. Roland Umlauft Corresponds to Chapter 7 in Brown/Kopp/Zima

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2 Chapter 5.1 Net Present Value 5.1 Net Present Value (NPV) Most business managers and investors are required to decide on a regular basis whether a particular business or investment should be undertaken. In many cases, a comparison between alternative investment projects is required, so a financial valuation of each proposal is necessary before a decision can be made. To use compound interest and calculate the present value of cash flows at a particular interest rate is one method of valuing a project that involves future cash flows.
3 Chapter 5.1 Net Present Value We have seen how to calculate the time value of money. In general, the value of a cash flow at a time t is calculated as follows: Payment F k is done at time t k , so it accumulates interest for t t k time units (this number is negative when discounting). The value of payment F k at time t is: Summing over all payments yields that the value of the entire cash flow at time t is given by: Of particular importance is the case where t is zero. The value of the net cash flow at t* = 0 is called the Net Present Value (NPV) F k (1 + i ) t * t k k F k + i ) t * t k

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4 Chapter 5.1 Net Present Value The interest rate used for this kind of calculations is called the cost of capital . It should be considered to be the cost of borrowing money or the return the investor would obtain if the money would be invested at a similar level of risk. For risk free cash flows this would be the rate that can be obtained by investing money at the risk-free rate. When valuing risky projects a cost of capital reflecting similar risk should be used.
5 Chapter 5.1 Net Present Value This valuation procedure is known as calculating the Net Present Value for the project and can be represented as: where F t =estimated cash inflows – estimated cash outflows (for period t ) and i is the cost of capital per period. F t is often referred to as the estimated net cash flow for the project at the end of period t . When F t >0 , then cash inflows (gains) for period t exceed cash outflows (or costs). The opposite is true when F t <0 . In many examples the first cash flow F 0 (=the investment) is negative, while future cash flows during the term of the project are positive (=benefit). NPV = F 0 + F 1 (1 + i ) 1 + F 2 + i ) 2 + F 3 + i ) 3 + ... + F n + i ) n

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6 Chapter 5.1 Net Present Value The net present value can be used to make a business decision. If NPV 0 , we can conclude that the rate of return from the cash inflows is greater than or equal to the cost of cash outflows, and the project should proceed . If NPV < 0 then the project should not be undertaken , since the cost of cash outflows can not be recovered by the income generated by the project.
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