Chapter 12
NPV Formula
NPV = (P - I) ... where: P = present value of a project's future cash inflows, I = Present value of a project's cost. * The present value of a of a project's future cash inflows is calculated by using a discount factor.
NPV, IRR & Mutually Exclusive (competing) Project's
NPV deals in terms of absolute dollars at the required rate of return. IRR deals in terms of relative dollars at the internal rate of return. So... because final analysis is concerned with absolute profits (total dollars earned) NPV should be used to compare competing, mutually exclusive projects.
Net Present Value (NPV)
Net present value is a type of discounting model that accounts for the time value of money. It helps managers make capital investment decisions in terms of a project's present value of cash inflows and outflows.
Non Discounting Methods (2):
Non Discounting: 1. Payback Period 2. Accounting Rate of Return (ARR)
Using the IRR
Once IRR is computed managers compare it to the firms required rate of return. IRR > required rate of return ... ACCEPT IRR < required rate of return ... REJECT IRR = required rate of return ... indifferent
Payback Period Formula
Payback Period = Original Investment / Annual Cash Flow *only when cash flows are an equal amount for each period.
Internal Rate of Return (IRR)
The IRR is a discounting model that accounts for the time value of money and is the most widely used of the capital investment techniques. The IRR is the discount rate that sets the present value of a project's cash inflows equal to the present value of the project's cost so... IRR = discount rate where NPV is zero
Flaws with the Payback Period
FLAWS: 1. It ignores the time value of money 2. It incentivizes managers to undertake projects w/ short payback periods to reflect well on their short-run performance measures. 3. It ignores the cash flow performance of the project beyond the payback period.
What are the components of making a capital investment decision?
1. Estimate the timing and quantity of cash flows 2. Asses the risk of the investment 3. Consider the impact of the project on a firms profit.
Debt Covenants
A covenant is a promise or indenture so in terms of debt it is essentially a "debt agreement" or money owed/borrowed.
Non Discounting Models
A type of capital investment decision model that does NOT consider the time value of money.
Discounting Models
A type of capital investment model that DOES explicitly consider the time value of money.
The Payback Period
A type of non discounting model that presents the time required for a firm to recover its initial investment.
ARR Formula
ARR = Average Income / Initial Investment
Post Audit Benefits
BENEFITS: 1. Resource Allocation: if a project is doing well managers may decide to use additional funds to further invest/commit... or the opposite. 2. Positive Impact on Manager Behavior: the post audit is a follow up analysis that holds managers accountable for the results of their decisions. 3. Independent Perspective: Usually post audits are done by an independent party or audit staff who are independent of all other operations yielding an unbiased and objective analysis.
How to choose the BEST project out of several competing options:
Choosing the best project: 1. Assess the cash flow patterns for each project 2. Compute NPV for each project 3. Identify project w/ greatest NPV
Finding the Discount Factor (df) for IRR
Discount Factor for IRR: 1. Investment (I) = Annual Cash Flow (CF) x Discount Factor (df) ... I = CF(df) 2. df = I / CF ... OR ... Investment / Annual Cash Flow Ex: (I = $205,570.50 CF = $50,000 / year) So... df = 205,570.50 / 50,000 = 4.11141
Discounted Cash Flows
Discounting models use discounting cash flows which are future cash flows expressed in terms of their *present value*.
Discounting Methods (2):
Discounting: 1. Internal Rate of Return (IRR) 2. Net Present Value (NPV)
Flaws with using the ARR:
FLAWS: 1. It ignores the time value of money (non discounting model) 2. It is dependent on net income which is a figure that is most likely to be manipulated by managers 3. Manager incentives may lead managers to commit to projects that yield the highest dollar return of net income to investment, rather than an investment that produce the greatest cash flow and long-term investment.
NPV, IRR & Independent (Non Competing) Project's
For independent projects or projects which are non competing NPV and IRR will yield the same managerial decision. Oppositely, when considering mutually exclusive (competing) projects NPV and IRR may yield different results.
Making Capital Investment Decisions
Generally, any new project must cover the opportunity cost of the funds being invested. Managers Must: 1. Estimate quantity & timing of cash flows 2. Assess the risk of the investment 3. Consider the project's impact on firm profits
IRR Formula *(uniform cash flows)
IRR: I = CF(df) *uniform cash flows* Investment = Annual Cash Flows / Discount Factor
IRR Formula *(non uniform cash flows)
IRR: I = SUM x [ CF,t / (1+i)^t ] *non uniform cash flows* TO SOLVE: guess a value of (i), adjust random value of (i) accordingly until present value of cash flows = initial investment.
Choosing the Required Rate of Return
If future cash flows are known with certainty then the correct rate of return = firm's cost of capital. This is often not the case in practice so... Managers will choose a rate of return higher than the cost of capital to account for uncertainty but if the rate chosen is excessively high it will biasly favor short-term investments.
Capital Decision Making Models & Mutually Exclusive (competing) Projects
In the case of choosing between mutually exclusive or competing projects the NPV model is judged as superior to the IRR model.
Positive NPV means:
Positive NPV shows: 1. Initial investment is recovered 2. Required rate of return is recovered 3. A return in excess of both of the above will be realized.
How to find the average income of a project:
Project Avg. Income = (Sum of net income for each year of project) / (Number of years)
Who does a post audit?
The best and most objective post audit results are normally found when an independent party with no bias is used to perform the post audit. An internal audit staff is typically used for this task.
Capital Investment Decisions
The decisions are concerned with planning, setting goals and priorities, arranging financing, and using criteria to select long-term assets.
Relationship b/w discount rate & present value of future cash inflows:
The discount rate and present value of a project's future cash inflows move inversely. As the discount rate increases, the present value of future cash inflows would decrease, and vice-versa.
Post Audit
The post audit is a key follow up analysis that compares the estimated benefits and operating costs to the actual benefits and operating costs after a project is implemented. It evaluates the the overall outcome of the investment and proposes corrective action if needed.
Capital Budgeting
The process of making capital investment decisions often. There are two types, independent and mutually exclusive projects.
NPV Analysis for Mutually Exclusive (competing) Projects
The project being proposed with the HIGHEST value for NPV should be chosen when deciding between projects.
Independent Projects
These are capital budgeting projects that do not affect cash flow of other projects whether they are accepted or rejected. (non competing projects)
Mutually Exclusive Projects
These are capital budgeting projects that preclude the acceptance of other projects if they are accepted. (competing projects)
Accounting Rate of Return (ARR)
This is a type of non discounting model that measures the return on a project in terms of income rather than the project's cash flow. It can be used to screen investments to be sure they do not adversely affect debt covenants.
Required Rate of Return ("discount rate, hurdle rate, cost of capital").
This is the minimum acceptable rate of return. If future cash flows are known with certainty then the (correct rate of return = firm's cost of capital).
Using NPV:
To effectively use NPV measurements managers would ACCEPT projects w/ POSITIVE net present value and REJECT those with a NEGATIVE value. Positive NPV = increases in a firm's wealth