PROJECTON

DISCOUNTING TECHNIQUES

&ANNUITIES

FINANCE FUNCTION

PROCUREMENT OF FUND DEPLOYMENT OF FUND

DEBT EQUITY LONG TERM SHORT TERM

CAPITAL BUDGETING

WORKING CAPITAL MGT.

TECHNIQUES

TRADITINAL MODERNIgnore time value of money

Consider Time Value Of Money

•ARR •PAYBACK PERIOD

•NPV•PROFITABILITY INDEX •IRR•DISCOUNTED PAYBACK PERIOD

DISCOUNTING TECHNIQUESThe discounting or present value is the exact opposite of compound or future value. While future value shows how much a sum of money becomes at some future period ,present value shows what the value is today of some future sum of money. In compound Or future value approach the money invested today appreciates because the compound interest is added to the principal. The present value of money to be received on future date will be less because we have lost the opportunity of investing it at some interest .Thus , the present value of money to be received in future will always be less. It is for this reason that the present value technique is called DISCOUNTING.

The discounted cash flow technique

*The discounted cash flow value (or what the total capital employed in the business is worth)Has been calculated based on operating profits that do not consider financing costs (forExample, interest expense) or income from nonoperating assets. As a result, the net valueOf the equity is derived by subtracting the market value of debt and adding the market valueOf nonoperating assets.

Year 3Cash Flow

FromOperations

Year 4And BeyondCash Flow

FromOperations

Historical Financial Results

Adjustments forNonrecurring

Items

Prospects For the Future

Cash Flow

Adjustments

Projected SalesAnd Operation Profit

4 Years +

3 Years

1 Years 2 Years

+

+

-

-

Year 2Cash Flow

From Operations

ShareholderValue

MarketValue Of Debt

MarketableSecurities and Excess Assets

Present ValueOf Residual

Value

Present ValueCash Flow

From Operations

Year 1Cash Flow

From Operations

AVERAGE RATE OF RETURN ARR is the rate of return which is very simple and subjectively Used in CAPITAL BUDGETING. ARR is compared with the required rate of return to decide upon project acceptance or rejection . ARR is calculated by dividing average PAT by either capital invested or average capital invested .

•ARR is NON – DISCOUNTED TECHNIQUE.•ARR is not calculated on CFAT but calculated on PAT

ARR is method of evaluating proposed capital expenditure is also known as the ACCOUNTING RATE OF RETURN . ARR is based upon accounting information rather than cash flows .

CALCULATED AS-- ON INITIAL INVESTMENT

ARR =Average PAT

Initial Investment

* 100

ON AVERAGE INVESTMENT

ARR=Average PAT

Average Investment

* 100

EXAMPLE C Ltd. Is considering investing a project. The expected original Investment in the project will be Rs. 2,00,000. the life of the project will be 5 year with no salvage value . The expected Average profit after tax is Rs. 53.900 . Calculate the ARR .

SOLUTION--

ARR =53,900

2,00,000*100

= 26.95%

PAY BACK PERIOD Pay back period is the period within which The project will pay back its cost.

Smaller the pay back period . Better the project . The main advantage of method is its SIMPLICITY . The main disadvantage is that it does not consider the post pay back period profitability.Payback period can be calculated on the basis of simple cash flow or discounted cash flow.PBP method is quite suitable when rate of becoming obsolete is quite high.

EXAMPLE In project A the initial investment is Rs.1,00,000. The Cash flows for 4 years are respectively 30,000 , 40,000,50,000 and 30,000. Calculate the PAYBACK PERIOD OF PROJECT A.

SOLUTION--

1st year = 30,0002nd year = 40,000 70,000 should earn= 1,00,000 – 70,000 3rd year =30,000 time of 3rd year = 30,000/ 50,000 = 6 months PAYBACK PERIOD = 2 YEARS 6 MONTHS

NET PRESENT VALUE This is the first discounted cash flow techniques . NPV can be described as the summation of the present values of cash proceeds (CFAT ). In each year minus the summation of present value of the net cash outflows in each year .

The decision rule for a project under NPV is to accept the project if the NPV is positive and reject if it is negative. Symbolically, (a).NPV>0 = ACCEPT (b).NPV<0 = REJECT ZERO NPV implies that the firm is indifferent to accepting or rejecting the project.

Net Present Value (NPV)

NPV is the present value of an investment project’s net cash flows

minus the project’s initial cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ - ICONPV =

Basket Wonders has determined that the appropriate discount rate (k) for this project is

13%.

$10,000 $7,000

EXAMPLE

$10,000 $12,000 $15,000 (1.13)1 (1.13)2 (1.13)3

+ +

+ - $40,000(1.13)4 (1.13)5

NPV = +

SOLUTION

NPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) + $15,000(PVIF13%,3) + $10,000(PVIF13%,4) + $

7,000(PVIF13%,5) – $40,000NPV = $10,000(0.885) + $12,000(0.783) +

$15,000(0.693) + $10,000(0.613) + $ 7,000(0.543) – $40,000NPV = $8,850 + $9,396 + $10,395 +

$6,130 + $3,801 – $40,000 =- $1,428

NPV Acceptance Criterion

No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject

as NPV < 0 ]

The management of Basket Wonders has determined that the required rate is 13%

for projects of this type.Should this project be accepted?

Profitability Index (PI)

PI is the ratio of the present value of a project’s future net cash flows to the

project’s initial cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ ICOPI =

PI = 1 + [ NPV / ICO ]<< OR >>

Method #2:

Method #1:

PI Acceptance Criterion

No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI <

1.00 ]

PI = $38,572 / $40,000= .9643 (Method #1, previous

slide)

Should this project be accepted?

Internal Rate of Return (IRR)

IRR is the discount rate that equates the present value of the future net cash flows from an

investment project with the project’s initial cash outflow.

CF1 CF2 CFn (1 + IRR)1 (1 + IRR)2 (1 + IRR)n

+ . . . ++ICO =

$15,000 $10,000 $7,000

IRR Solution

$10,000 $12,000(1+IRR)1 (1+IRR)2

Find the interest rate (IRR) that causes the discounted cash flows to equal $40,000.

+ +

++$40,000 =

(1+IRR)3 (1+IRR)4 (1+IRR)5

IRR Solution (Try 10%)

$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $7,000(PVIF10%,5)

$40,000 = $10,000(0.909) + $12,000(0.826) + $15,000(0.751) +

$10,000(0.683) + $7,000(0.621)

$40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347

= $41,444 [Rate is too low!!]

IRR Solution (Try 15%)

$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) +

$10,000(PVIF15%,4) + $ 7,000(PVIF15%,5)

$40,000 = $10,000(0.870) + $12,000(0.756) + $15,000(0.658) + $10,000(0.572)

+ $7,000(0.497)$40,000 = $8,700 + $9,072 + $9,870 +

$5,720 + $3,479 = $36,841 [Rate is too high!!]

0.10 $41,4440.05 IRR $40,000

$4,6030.15 $36,841

X $1,4440.05 $4,603

IRR Solution (Interpolate)

$1,444X

=

0.10 $41,4440.05 IRR $40,000

$4,6030.15 $36,841

X $1,4440.05 $4,603

IRR Solution (Interpolate)

$1,444X

=

0.10 $41,4440.05 IRR $40,000

$4,6030.15 $36,841

($1,444)(0.05) $4,603

IRR Solution (Interpolate)

$1,444X

X = X = 0.0157

IRR = 0.10 + 0.0157 = 0.1157 or 11.57%

IRR Acceptance Criterion

No! The firm will receive 11.57% for each dollar invested in this project at a cost of

13%. [ IRR < Hurdle Rate ]

The management of Basket Wonders has determined that the hurdle rate is 13% for

projects of this type. Should this project be accepted?

DISCOUNTED PAYBACK PERIOD

DPB refers to a period within which the PRESENT VALUE OF CASH INFLOWS completely recover the PRESENT VALUE of cash outflow.

NOTE- COC is the cost of capital which refers to the minimum rate of return a firm must earn on its investments.

RELATIONSHIP b/w NPV, IRR & PI ?(a) IF NPV IS +VE , PI>1 IRR>COC

(b) IF NPV IS –VE, PI<1 IRR<COC

(c) IF NPV =0, PI=1 IRR=COC

ACCEPT

REJECT

IRRELEVANT

ANNUITIESANNUITY refers to a series of equal periodical periods . If the Payments are made at the end of each period, we call itREGULAR ANNUITY . If the payments are made at the beginning of each period, we call it ANNUITY DUE.

ANNUITY

PRESENT VALUE OF FUTURE AMOUNT

FUTURE VALUE OF PRESENT AMOUNT

TABLE A3+ A4 TABLE A1+ A2

PVIF PVIFA FVIF FVIFA

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