discounting and compounding

8/6/2019 Discounting and Compounding

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Christopher B. Stone µ01

Present value of future cash flow

n

r ! 1

FV

PVr = discount raten = number of periods

Discounting: calculation of present valuesDiscounting: calculation of present values

Compounding: calculation of future valuesCompounding: calculation of future values




Internal rate of return

IRR is that unique discount

rate which, when applied toa series of future cashflows, yields a net present

value of 0.




Financial management rate of return

Serie A Serie B Serie

F (100.00)$ (100.00)$ (50.00)$

F1 -$ 7.18$ (42.82)$F2 -$ 7.18$ 7.18$

F3 -$ 7.18$ 7.18$

F4 -$ 7.18$ 7.18$

F5 141.42 117.18 107.18$

7.18% 8.86% 8.12%

Only Series A is a ³pure´ IRR

Series B and Series C have money extracted from the system

Series C has money invested in the system after t0

The IRR model assumes1) That money invested in the system is held in an accountbearing interest at the IRR before being invested;2) That money extracted from the system is re-invested in an

account yielding the IRR.

IRR FMRR

IRR Safe rate

IRR Re-investment rate

Negative cash f low s after t0, before they are

invested, are held in an account that produces

interest at

Money extracted from the system is re-

invested at

FMRR bifurcates negative and positive cash flowsFMRR bifurcates negative and positive cash flows




Financial management rate of return

PV FV

0 0

10 .1.1 .1.1.1

F uture valued at re-investment rate

PV¶ed at safe rate

FMRR > reFMRR > re- -investment rate for worthwhile investmentsinvestment rate for worthwhile investments




Hurdle rates

The earnings you foregoby deploying capital in adifferent way

The rate you must get on an

investment for the deal tomake sense

I f hurdle rate < I RR, NPV is positiveI f hurdle rate < I RR, NPV is positive




Sensitivity analysis

If you discount your cash flo s @ the HRand get a + V the V represents your profit over the life of the deal.

If HR<IRR+ V

V @ HR is the positivecushion you have

nr 1

FV V

Annuitize this figurecalculate mT to get et Uniform Series US




Recourse debt

Creditor can sue debtor if not re paid

Might be secured might not

Most corporate debt is recourseException: real estate

Recourse

Borro er has no personal liability

Must be secured other ise it's nothing

You can still sue for fraudulent conveyances etc.

on recourse

Debt




Compounded interest

At YR1 I o e 1The 1 does not accrue interest if unpaid

Simple

At YR1 I o e 1The 1 interest itself accrues interest

Compound

Interest

I borro 100 @ 1




Capital asset pricing model

f mf e R R R k !

Cost of

capital Risk-freereturn

USG securities

Average rate of returnon common stocks

(S&P 00)

Co-variance

of returns againstthe portfolio

(departure from the average)< , security is safer than S&P 00 average

> , security is riskier than S&P 00 average

Cost of equity capital = return expected on firm¶s common stock Cost of equity capital = return expected on firm¶s common stock

Cost of capital = Risk-free return + compensation for additional risk beyond a USG bondCost of capital = Risk free return + ( x market risk premium)Cost of capital = Risk free return + ( x margin by which stock market exceeds risk-free return




Methods of inventory valuation

o er of cost or r et Cost

I OFirst oo s into in entor

re first oo s o t

Cost Y

LI Ost oo s into in entor

re first oo s o t

n in in entor l tion etho s




Depreciation methods

Str i ht line

S o the e rs

1 0 etho o le e linin l n e

e linin l n e

eler te

epre i tion etho s

= Cost-salvage valueUseful life

= Cost-salvage value * remaining years of useful lifen(n+ )

Keyed off the remaining balance in each year AFT R depreciationDoes N T use salvage value




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Board authorizes and issues 100 shares at§

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s in #

Board bu

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Board authorizes and issues 100 shares o ̈

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Painting is distributed as dividend

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Board declares dividend o ̈

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Scena$

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(pa$

stock issued) Scena$

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(no-pa$

stock issued)

Assets Liabi iites Assets Liabi iites

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(ea$

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Facts

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Assets Liabi iites

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Assets Liabi iites




Liquidity ratios

Currentratio

=Current assets

Current liabilities

Quickratio

= Current assets - inventoryCurrent liabilities

Cash flowliquidity

ratio=

Cash flow from operations*Current liabilities

*From the cash flow statement




Leverage ratios

Debtratio

=LiabilitiesAssets

Debt equityratio

=LiabilitiesNet worth




Financial leverage index

Financialleverage

index

=Return on equity

Adjusted return on assets

= Net earnings* equity**[ arnings + interest ( -tax rate)] assets

* Note this does not include pfd div** r market cap

Is a company trading positively on its leverageI.e. is it bringing in capital at less than the return




Activity ratios

Accountsreceivableturnover

=Net sales*

Accounts receivable

*From the income statement

Inventoryturnover

=C GS*

Inventory

Accountspayableturnover

=Total expenses*Accounts payable




Operating cycle

Capital

infusion$

Sale

InventoryAccounts

receivable

Avg. amount of time inventory is outstanding+

Avg. amount of time receivables are outstanding

Operatingcycle

=




Capital

infusion$

Sale

Cash conversion cycle

Avg. amount of time inventory is outstanding+

Avg. amount of time receivables are outstanding-

(A

vg. amount of time payables are outstanding)

Cashconversion

cycle=

Accountspayable

(Payment)

Accounts

receivable

Inventory




Profitability ratios

Gross profit

margin =

Gross profitGross sales

This is very much driven by variable costs cost of goods sold. Overhead is OT included.

Measures profitability

A business can be profitable and still trade negatively on its leverage A business can be profitable and still trade negatively on its leverage




P ratio

P ratio =Stock price per share

arnings per share

Growth stockHigh E ratio

Value stockLo E ratio

Return ontotal assets

=arnings + interest

Assets

discounting and compounding

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