As a CMA USA aspirant, i made these quick notes to refer the capital budgeting methods it includes equations, notes, and everything regarding the topic. hope this helps. thank you.

1. CAPITAL BUDGETING METHODS (CMA USA PART2)
By shabeelath.

2. CAPITAL BUDGETING METHODS
1. Payback period/method
2. Discounted payback period/method
3. Net present value(NPV)
4. Internal rate of return(IRR)
5. Accounting/average rate of return

3. PAYBACK PERIOD/METHOD;
•PAYBACK METHOD is used to calculate the number of periods that
must pass before the net after tax cash inflows from an investment
will equal or payback the initial investment.
•The company using the payback method choose its desired payback period
I. Projects with payback period of less than the chosen amount of time are
candidates for further considerations
II. While projects with payback periods of excess of chosen amount of time
are rejected
•Assumption;
All cash inflows from the project will be reinvested at the required rate of
return.

4. PAYBACK PERIOD EQUATIONS;
•EQUATION;(IF CASH INFLOWS ARE DIFFERENT);
PAYBACK PERIOD=
NUMBER OF YEARS WHEN THE CASH FLOW IS NEGATIVE
+
AMOUNT FROM THE FINAL NEGATIVE YEAR/CASH INFLOW FOR THE FOLLOWING
YEAR
EQUATION (IF CASH INFLOWS ARE SAME);
INITIAL INVESTMENT/CONSTANT CASH INFLOWS

5. PAYBACK PERIOD;
ADVANTAGES
•It is simple and very easy to understand
•It can be suitable for preliminary
screening when there are many
proposals
DISADVANTAGES
•It ignores all cash flows beyond the
payback period
•It does not consider project profitability
therefore, a project that has large
expected cash flows in the latter years
of its life could be rejected in favor of
less profitable project
•It is more in to the capital recovery
rather than the profitability

6. DISCOUNTED PAYBACK METHOD;
•DISCOUNTED PAYBACK METHOD measure all of the expected cash inflows and
outflows of a project using time value of money
•Time value of money concept is that the money received today is worth more than the
money received in any future period.
•The discounted payback method is also known as BREAKEVEN TIME.
•It is based on the same concept as the payback period, but before calculating the
payback period the expected cash flows are discounted to their present values using
an appropriate interest rate, usually the company’s cost of capital

7. DISCOUNTED PAYBACK METHOD;
•EQUATION;
NUMBER OF YEARS WHEN THE CASH FLOW IS NEGATIVE
+
AMOUNT FROM THE FINAL NEGATIVE YEAR/ DISCOUNTED CASH INFLOW FOR THE FOLLOWING YEAR

8. DISCOUNTED PAYBACK PERIOD;
ADVANTAGES
•It includes time value of money
•It is simple and very easy to understand
•It can be suitable for preliminary
screening when there are many
proposals
DISADVANTAGES
•It does not consider project profitability
therefore, a project that has large
expected cash flows in the latter years
of its life could be rejected in favor of
less profitable project
•It is more in to the capital recovery
rather than the profitability
•It ignores all cash flows beyond the
payback period

9. NET PRESENT VALUE(NPV)
•NPV method is based on the present value of the expected future monetary
gain or loss. All expected cash inflows or outflows are discounted to the
beginning of the project using required rate of return
•It is the present value(PV) of future cash flows less the initial investment in the
project
• NPV is used in capital budgeting and investment planning to analyze the
profitability of a projected investment or project.
•It is assumed that an investment with a positive NPV will be profitable, and an
investment with a negative NPV will result in a net loss.
•If the net after tax cash flows including the depreciation tax shield, are same
every year of the projects life and if discount rate is same through out the
project the net present value of expected cash flows can be discounted as an
ANNUITY.

10. REQUIRED RATE OF RETURN;
•THE PRESENT VALUE OF THE EXPECTED CASH FLOWS IS CALCULATED USING
A DISCOUNT RATE THAT IS THE COMPANY’S REQUIRED RATE OF RETURN
which is one of two options;
1.The return the company can expect to receive in the market for an investment
of comparable risk.
2. The minimum rate of return that the project must earn to justify investment of
the resources
•The RRR is also called DISCOUNT RATE, HURDLE RATE, OR OPPORTUNITY
COST OF CAPITAL

11. RELEVENT EXPECTED CASH FLOWS USED IN NET PRESENT VALUE;
•Initial net cash outflows
•Initial net cash inflows
•Depreciation tax shield
•Operating cash inflows
•Operating cash outflows
•Cash proceeds from sale of the asset
•Working capital released at the end of the year.

12. INTERPRETATION OF NPV ANALYSIS;
1. when a project has a positive NPV. It will be profitable because it will earn more
than it will cost the company the project is acceptable
2. when a project has a negative NPV, the project would be unprofitable because it
would cost the company more than it could earn.
3. if the project has ZERO NPV, the present value of expected future cash inflows is
exactly equal to the amount of the initial investment. Shareholder wealth would
neither increase or decrease.

13. EQUATIONS OF NET PRESENT VALUE(NPV);
1.SERIES OF UNEQUAL CASH FLOWS;
NPV= PV OF FUTURE EXPECTED CASH FLOWS($1 FACTOR) – INITIAL INVESTMENT
2. SERIES OF EQUAL CASH FLOWS;
NPV= PV OF FUTURE EXPECTED CASH FLOWS($1 FACTOR, ANNUITY) – INITIAL
INVESTMENT
3. SERIES OF EQUAL CASH FLOWS WITH UNEQUAL AMOUNT AT THE END;
NPV=[ PV OF ANNUITY(1 TO 6 YEARS OF THE SAME CASH FLOW) X THE CONSTANT CASH
FLOW] + [PV OF $1 FACTOR(BECAUSE IT IS DIFFERENT AT THE END) X [CASH FLOW
AMOUNT+ AFTER TAX CASH FLOW FROM DISPOSAL] – INITIAL INVESTMENT

14. 4. A PERPETUAL ANNUITY; (A perpetuity is a type of annuity that lasts forever,The
stream of cash flows continues for an infinite amount of time.)
PV= ANNUAL CASH FLOW/ REQUIRED RATE OF RETURN
NPV= PV – INITIAL INVESTMENT
5. A PERPETUAL GROWING ANNUITY; A growing perpetuity is a stream of cash
flow that is expected to be received every year forever but also grow at the
same growth rate forever.
PV= ANNUAL CASH FLOW/ REQUIRED RATE OF RETURN – GROWTH RATE

15. INTERNAL RATE OF RETURN
•INTERNAL RATE OF RETURN(IRR) for a project is the interest rate i.e discount rate at which the
NPV IS ZERO(0). Or at which the present value(PV) of its expected cash inflows equals the
present value of expected cash inflows.
•If the IRR is greater than the projects required rate of return the investment is acceptable
If the IRR is less than the projects required of return then the investment should not be made.
•Assumptions;
IRR assumes that cash flows from the project will be reinvested by at the IRR itself.
The modified IRR assumes that cash flows from the project will be reinvested by the RRR.
•CROSS-OVER RATE; IT IS THE HURDLE RATE WHERE NPV OF TWO PROJECTS ARE EQUAL.

16. INTERNAL RATE OF RETURN
CONVENTIONAL PROJECT AND NON CONVENTIONAL PROJECT;
•CONVENTIONAL PROJECT;
A conventional project begins with a cash outflow followed by the several cash inflow
•NON-CONVENTIONAL PROJECT;
If a project has a negative cash flow after year 0 then it is called NON
CONVENTIONAL PROJECT

17. CALCULATING INTERNAL RATE OF RETURN(IRR)
•ANNUAL CASH FLOWS SAME FOR EVERY YEAR;
Step 1 =INITIAL INVESTMENT/ANNUAL CASH FLOW= ANNUITY FACTOR
Step 2 = Locate a required rate of return in annuity table which provides the similar
annuity factor we got with the projects estimated life(given in the question)
Step 3 = if the internal rate of return we got is greater than the hurdle rate then it is
acceptable (prefer hock textbook page no. 176)

18. CALCULATING INTERNAL RATE OF RETURN
•ANNUAL CASH FLOWS DIFFERENT FOR YEARS;
STEP 1; CALCULATE TWO NPV OF THE PROJECT WITH TWO COST OF CAPITAL
STEP 2; USE THE FOLLOWING FORMULA TO FIND THE IRR
WHERE, L= LOWER DISCOUNT RATE H= HIGHER DISCOUNT RATE
NL= NPV AT LOWER RATE
NH= NPV AT HIGHER RATE

19. INTERNAL RATE OF RETURN
ADVANTAGES
•It includes time value of money
DISADVANTAGES
•If a project is non conventional it will
have more than one IRR and it may not
be able to calculate

20. ACCOUNTING RATE OF RETURN
• ACCOUNTING RATE OF RETURN(ARR); it is the rate of the amount of the expected
increase in annual average accounting income as a result of the project relative to the
required investment
•It does not take time value of money in to the consideration.
EQUATION;
AVERAGE RATE OF RETURN=AVERAGE PROFIT/AVERAGE INVESTMENT
AVERAGE PROFIT= SUM OF CASHFLOWS – SUM OF DEPRECIATION – TAX/NO.OF
YEARS
AVERAGE INVESTMENT= [INITIAL INVESTMENT+SCRAP VALUE/2]+ADDITIONAL
WORKING CAPITAL

21. ACCOUNTING RATE OF RETURN
ADVANTAGES
•The computations are easy to do and
understand
•Convenient to use it to evaluate project
DISADVANTAGES
•It does not include time value of money
in to the consideration
•The result of ARR are effected by the
method of depreciation used.

22. THANK YOU.