Present Value .

• Present Value

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Net present value

1 In finance, the 'net present value' ('NPV') or 'net present worth'

('NPW') of a time series of cash flows, both incoming and outgoing, is

defined as the sum of the present values (PVs) of the individual cash

flows of the same entity.


Net present value

1 Used for capital budgeting and widely used throughout economics,

finance, and accounting, it measures the excess or shortfall of cash flows,

in present value terms, above the cost of funds.


Net present value

1 NPV can be described as the “difference amount” between the

sums of discounted: cash inflows and cash outflows. It compares the

present value of money today to the present value of money in the future,

taking inflation and returns into account


Net present value - Alternative capital budgeting methods

1 * Adjusted present value (APV): adjusted present value, is the net

present value of a project if financed solely by ownership equity plus the present value of all the benefits of

financing.


Hyperbolic discounting - Present Value of an Standard Annuity

1 The present value of a series of equal annual cash flows in arrears discounted

hyperbolically:


Hyperbolic discounting - Present Value of an Standard Annuity

1 Where V is the present value, P is the annual cash flow, D is the number of annual payments and k is the factor

governing the discounting.


Time value of money - Present value of a future sum

1 The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula. For example, the

annuity formula is the sum of a series of present value calculations.



1 The present value (PV) formula has four variables, each of which can be solved for:



1 The cumulative present value of future cash flows can be calculated

by summing the contributions of FVt, the value of cash flow at time t


Adjusted present value

1 'Adjusted Present Value' ('APV') is a business valuation method. APV is the

net present value of a project if financed solely by ownership equity plus the present value of all the benefits of

financing. It was first studied by Stewart Myers, a professor at the MIT Sloan

School of Management and later theorized by Lorenzo Peccati, professor

at the Bocconi University, in 1973.


Adjusted present value - APV formula

1 Take Present Value (PV) of FCFs discounted by Return on Assets %

(also Return on Unlevered Equity %)


Adjusted present value - APV formula

1 + Present Value of Debt's Periodic Interest Tax Shield discounted by Cost of Debt Financing

%


Present value

1 The initial amount of the borrowed funds (the present value) is less than

the total amount of money paid to the lender.


Present value

1 The project with the least present value, i.e


Present value - Years' Purchase

1 This equates to a present value

discounted in perpetuity at 5%


Present value - Background

1 If a 100 note, payable in one year, sells for 80 now, then 80 is the

present value of the note that will be worth 100 a year from now


Present value - Background

1 The operation of evaluating a present value into the future value is called a

capitalization (how much will 100 today be worth in 5 years?). The

reverse operation—evaluating the present value of a future amount of money—is called a discounting (how much will 100 received in 5 years—at

a lottery for example—be worth today?).


Present value - Nominal Annual Rate of Interest

1 The present value of an annuity immediate is the value at time 0 of the stream of cash

flows:


Present value - PV of a Bond

1 The present value of a bond is the purchase

price


Present value - Technical details

1 Present value is Additive inverse|additive. The present value of a

bundle of cash flows is the sum of each one's present value.


Present value - Technical details

1 The full Laplace transform is the curve of all present values, plotted as

a function of interest rate


Present value - Variants/Approaches

1 There are mainly two flavors of PV. Whenever there will be uncertainties

in both timing and amount of the cash flows, the expected present value approach will often be the

appropriate technique.



1 * 'Traditional Present Value Approach' – in this approach a single set of

estimated cash flows and a single interest rate (commensurate with the risk, typically a weighted average of

cost components) will be used to estimate the fair value.



1 * 'Expected Present Value Approach' – in this approach multiple cash flows

scenarios with different/expected probabilities and a credit-adjusted risk free rate are used to estimate

the fair value.


Present value - Present Value Method of Valuation

1 An investor, the lender of money, must decide the financial project in which to invest their money, and

present value offers one method of deciding.


Present value - Present Value Method of Valuation

1 The project with the smallest present value – the least initial outlay – will

be chosen because it offers the same return as the other projects for the

least amount of money.


Bond valuation - Present value approach

1 Below is the formula for calculating a bond's price, which uses the basic present value (PV) formula for a

given discount rate:http://www.investopedia.com/university/advancedbond/advancedbond

2.asp


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