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Payback Period (Non-Discounted)

Topic: Investment DecisionsChapter: Chapter 2
Payback Period=Initial InvestmentAnnual Cash Inflow (if inflows are uniform)\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}} \text{ (if inflows are uniform)}
Calculates the time required to recover the initial investment from the cash inflows. If inflows are uneven, it is calculated by cumulative cash flows.

Accounting Rate of Return (ARR)

Topic: Investment DecisionsChapter: Chapter 2
ARR=(Average Annual Profit After TaxAverage Investment)×100\text{ARR} = \left( \frac{\text{Average Annual Profit After Tax}}{\text{Average Investment}} \right) \times 100
Measures the profitability of an investment based on accounting profits rather than cash flows. Average Investment is often calculated as \frac{\text{Initial Investment} + \text{Salvage Value}}{2}.

Net Present Value (NPV)

Topic: Investment DecisionsChapter: Chapter 2
NPV=∑t=1nCFt(1+k)t−I0NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+k)^t} - I_0
The difference between the present value of cash inflows and the initial investment. A positive NPV indicates the project should be accepted.

Profitability Index (PI)

Topic: Investment DecisionsChapter: Chapter 2
PI=Present Value of Cash InflowsInitial Investment\text{PI} = \frac{\text{Present Value of Cash Inflows}}{\text{Initial Investment}}
Also known as the Benefit-Cost Ratio. It measures the relative profitability per unit of investment. Accept if PI > 1.

Internal Rate of Return (IRR)

Topic: Investment DecisionsChapter: Chapter 2
0=∑t=1nCFt(1+IRR)t−I00 = \sum_{t=1}^{n} \frac{CF_t}{(1+IRR)^t} - I_0
The discount rate at which the Net Present Value (NPV) of a project becomes zero. It represents the project's break-even rate of return.

Discounted Payback Period

Topic: Investment DecisionsChapter: Chapter 2
Discounted Payback=Time taken to recover initial investment using discounted cash flows\text{Discounted Payback} = \text{Time taken to recover initial investment using discounted cash flows}
Similar to the Payback Period, but it accounts for the time value of money by discounting each cash inflow before cumulative calculation.

Payback Period (PBP) - Even Cash Flows

Topic: Investment DecisionsChapter: Chapter 2
PBP=Initial InvestmentAnnual Cash Inflow\text{PBP} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}}
Calculates the time required for the cumulative cash inflows from a project to equal the initial investment. Applicable when annual cash inflows are constant.

Payback Period (PBP) - Uneven Cash Flows

Topic: Investment DecisionsChapter: Chapter 2
PBP=Full years before recovery+Unrecovered amount at the beginning of the yearCash flow during the year\text{PBP} = \text{Full years before recovery} + \frac{\text{Unrecovered amount at the beginning of the year}}{\text{Cash flow during the year}}
Calculates the time required for the cumulative cash inflows to recover the initial investment when cash flows are not constant. Involves identifying the year of recovery and interpolating within that year.

Discounted Payback Period (DPBP)

Topic: Investment DecisionsChapter: Chapter 2
DPBP=Full years before recovery (discounted)+Unrecovered amount at the beginning of the year (discounted)Discounted cash flow during the year\text{DPBP} = \text{Full years before recovery (discounted)} + \frac{\text{Unrecovered amount at the beginning of the year (discounted)}}{\text{Discounted cash flow during the year}}
Similar to Payback Period, but uses discounted cash flows to account for the time value of money. It measures the time taken for the present value of cash inflows to equal the initial investment.

Accounting Rate of Return (ARR) / Return on Investment (ROI)

Topic: Investment DecisionsChapter: Chapter 2
ARR=Average Annual Accounting ProfitAverage Investment×100\text{ARR} = \frac{\text{Average Annual Accounting Profit}}{\text{Average Investment}} \times 100
Measures the average annual accounting profit generated by a project as a percentage of the average investment. Average Investment can be (Initial Investment + Salvage Value) / 2 or Initial Investment.

IRR (Interpolation Method)

Topic: Investment DecisionsChapter: Chapter 2
IRR=L+NPVLNPVL−NPVH(H−L)\text{IRR} = L + \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} (H - L)
Used to approximate the IRR when it cannot be calculated directly. L is the lower discount rate, H is the higher discount rate, NPV_L is the NPV at the lower rate, and NPV_H is the NPV at the higher rate.

Equivalent Annual Annuity (EAA)

Topic: Investment DecisionsChapter: Chapter 2
EAA=NPVPVIFAr,n=NPV[1−(1+r)−nr]\text{EAA} = \frac{\text{NPV}}{\text{PVIFA}_{r,n}} = \frac{\text{NPV}}{\left[ \frac{1 - (1+r)^{-n}}{r} \right]}
Converts the NPV of a project into an equivalent annual cash flow over its life. Useful for comparing projects with unequal lives. PVIFA is the Present Value Interest Factor for an Annuity.

Payback Period (PBP)

Topic: Capital BudgetingChapter: Chapter 2
Payback Period=Initial InvestmentAnnual Cash Inflow (if inflows are uniform)\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}} \text{ (if inflows are uniform)}
The time required to recover the initial investment from the net cash inflows. If inflows are uneven, it is calculated by cumulative cash flows.

Accounting Rate of Return (ARR)

Topic: Capital BudgetingChapter: Chapter 2
ARR=(Average Annual Profit after TaxAverage Investment)×100\text{ARR} = \left( \frac{\text{Average Annual Profit after Tax}}{\text{Average Investment}} \right) \times 100
Measures the profitability of an investment based on accounting profits rather than cash flows. Average Investment is typically calculated as \frac{\text{Initial Investment} + \text{Salvage Value}}{2}.

Net Present Value (NPV)

Topic: Capital BudgetingChapter: Chapter 2
NPV=∑t=1nCFt(1+k)t−I0NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+k)^t} - I_0
The difference between the present value of cash inflows and the initial investment. A positive NPV indicates the project should be accepted.

Profitability Index (PI)

Topic: Capital BudgetingChapter: Chapter 2
PI=Present Value of Cash InflowsInitial InvestmentPI = \frac{\text{Present Value of Cash Inflows}}{\text{Initial Investment}}
Also known as the Benefit-Cost Ratio. It is used to rank projects when capital is rationed. A PI > 1 indicates a viable project.

Internal Rate of Return (IRR)

Topic: Capital BudgetingChapter: Chapter 2
0=∑t=1nCFt(1+IRR)t−I00 = \sum_{t=1}^{n} \frac{CF_t}{(1+IRR)^t} - I_0
The discount rate at which the Net Present Value (NPV) of a project becomes zero. It represents the project's intrinsic rate of return.

Discounted Payback Period

Topic: Capital BudgetingChapter: Chapter 2
Discounted Payback=Time taken to recover investment using discounted cash flows\text{Discounted Payback} = \text{Time taken to recover investment using discounted cash flows}
Similar to the Payback Period, but it accounts for the time value of money by discounting each cash inflow before calculating the recovery period.

Payback Period (Uniform Annual Cash Inflows)

Topic: Capital BudgetingChapter: Chapter 2
Payback Period=Initial InvestmentAnnual Cash Inflow\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}}
Calculates the time required to recover the initial investment when annual cash inflows are constant. It measures the liquidity of a project.

Payback Period (Uneven Annual Cash Inflows)

Topic: Capital BudgetingChapter: Chapter 2
Payback Period=Years before full recovery+Unrecovered amount at the beginning of the yearCash flow during the full recovery year\text{Payback Period} = \text{Years before full recovery} + \frac{\text{Unrecovered amount at the beginning of the year}}{\text{Cash flow during the full recovery year}}
Calculates the time required to recover the initial investment when annual cash inflows are not constant. It involves accumulating cash flows until the initial investment is recovered.

Accounting Rate of Return (ARR) / Return on Investment (ROI) - Based on Initial Investment

Topic: Capital BudgetingChapter: Chapter 2
ARR=Average Annual Accounting ProfitInitial Investment×100\text{ARR} = \frac{\text{Average Annual Accounting Profit}}{\text{Initial Investment}} \times 100
Measures the average annual accounting profit (Profit After Tax) generated by a project as a percentage of the initial investment.

Accounting Rate of Return (ARR) / Return on Investment (ROI) - Based on Average Investment

Topic: Capital BudgetingChapter: Chapter 2
ARR=Average Annual Accounting ProfitAverage Investment×100\text{ARR} = \frac{\text{Average Annual Accounting Profit}}{\text{Average Investment}} \times 100
Measures the average annual accounting profit (Profit After Tax) generated by a project as a percentage of the average investment. Average Investment = (Initial Investment + Salvage Value) / 2.

Profitability Index (PI) / Benefit-Cost Ratio (BCR)

Topic: Capital BudgetingChapter: Chapter 2
PI=Present Value of Future Cash InflowsInitial InvestmentorPI=1+NPVInitial Investment\text{PI} = \frac{\text{Present Value of Future Cash Inflows}}{\text{Initial Investment}} \quad \text{or} \quad \text{PI} = 1 + \frac{\text{NPV}}{\text{Initial Investment}}
Measures the present value of future cash inflows per rupee of initial investment. A PI greater than 1 indicates an acceptable project.

Internal Rate of Return (IRR) - Interpolation Method

Topic: Capital BudgetingChapter: Chapter 2
IRR=L+NPVLNPVL−NPVH(H−L)\text{IRR} = L + \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} (H - L)
The discount rate at which the Net Present Value (NPV) of a project becomes zero. It represents the project's expected rate of return. L = Lower discount rate, H = Higher discount rate, NPV_L = NPV at lower rate, NPV_H = NPV at higher rate.

Discounted Payback Period (DPBP)

Topic: Capital BudgetingChapter: Chapter 2
DPBP=Years before full recovery of discounted cash flows+Unrecovered discounted amountDiscounted cash flow during the full recovery year\text{DPBP} = \text{Years before full recovery of discounted cash flows} + \frac{\text{Unrecovered discounted amount}}{\text{Discounted cash flow during the full recovery year}}
Calculates the time required to recover the initial investment using discounted cash flows. It considers the time value of money, unlike the traditional payback period.
Chapter 2 Formulas — CA Intermediate | Kartavvya