Capital Budgeting & Evaluation Techniques Flashcards
Define risk.
Risk is the possibility of loss or other unfavorable result that derives from the uncertainty implicit in future outcomes.
What does the presence of risk for a portfolio of projects mean?
Many outcome are possible.
Define risk-free rate.
Risk-free rate is the reward expected for deferring current consumption and does not change as the perceived risk of an undertaking increases (or decreases)
With regards to the risk-reward relationship graph, when the perceived risk of an undertaking increases, what would be the expected effect on the risk-free rate of return and the risk premium? You can look at graph in formula book to see the risk-reward graph.
Risk-free rate = No change. Risk-free rate is always constant and won’t change when perceived risk increases/decreases.
Risk premium = Increase. An increase in the risk premium would be expected as a result of an increase in perceived risk; it is the “reward” for risk. Thus, the greater the risk, the greater the expected reward (or risk premium).
On the risk-reward relationship graph which shows the relationship between financial risk and expected financial reward, the curve has a ______ slope. Why does it have a slop in this direction?
POSITIVE slope. The more perceived risk a financial investment or undertaking has, the higher the expected return associated with that risk.
Which rate identifies the rate of return required by investors to compensate them for deferring current consumption when making an investment? Also, this rate is the interest that would be charged on a borrowing that carried no risks (e.g., of default, inflation, etc.). This interest is required by lenders, not to cover risks, but to compensate the lender for deferring use of the funds by making an investment.
Risk-free rate
Review definitions for prime rate, discount rate, and effective rate.
Prime rate - interest rate that commercial banks charge their most creditworthy borrowers.
Discount rate - rate at which member banks may borrow short-term funds directly from a Federal Reserve Bank.
Effective rate - rate calculated as the interest received (or charged) divided by the actual cost of the investment (or loan).
Out of the four rates below, one rate charges interest on borrowing. Two rates charges interest on borrowing as well as including premiums for risks associated with making loan. Which rate is associated with interest only? Which two rates are associated with interest and premium?
Choices: Risk-free rate, effective rate, discount rate, and prime rate
Interest Only -Risk-free rate Intertest and Premium Only -Prime rate -Effective rate
Define capital budgeting.
Capital budgeting - Process of measuring, evaluating, and selecting long-term investment opportunities (or projects).
Does accounting rate of return consider time value of money? Yes or no.
No
An efficient portfolio is one that meets investor’s risk preference function which describes the investor’s tradeoff between _____ and ______.
Risk and return
Capital budgeting is based on predictions of an uncertain _______. All capital budgeting methods are based on predictions of ______ income or cash flows. (HINT: same word)
Future
What are three advantages to payback period, discounted cash flow, internal rate of return, and net present value method?
- All consider time value of money
- Don’t require multiple trial and error calculations
- They don’t require knowledge of a company’s cost of capital
(Re-check; may be incorrect)
What is one limitation of payback period, discounted cash flow, internal rate of return, and net present value method?
They rely on forecasting of future data (cash flows)
The relationship between risk and return is _____ or _______.
Direct or positive
This rate is commonly compared to internal rate of return to evaluate whether to make an investment? (Hint: provides a measure of the cost of the funds that the company is considering investing in a project)
Weighted-average cost of capital
This particular type of risk is the level of risk that concerns investors who supply capital to a diversified company. What is the name of this type of risk?
Weighted-average of project risk (betas). A diversified company can be thought of as an investment portfolio. The relevant risk for both management and investors is the weighted average of project risk.
The cost of capital is a composite, or weighted-average, of all financing sources in their usual proportions. It includes both the cost of ___________ and the cost of _________.
- Equity financing
2. After-tax cost of debt
When a company is financing with both debt and equity, the benchmark cost of capital should be? And why?
Weighted-average cost of capital. Because it incorporates all financing sources. Weights are determined by usual financing proportions.
Interest rates that have ______ over the past several years should encourage a company to use short-term loans.
Declined.
The payback period approach to assessing a capital project determines the # of years (periods) needed to recover the initial cash investment in the project and compares resulting time with pre-established maximum period. When would a project be deemed acceptable or unacceptable?
Project Acceptable: When expected payback period for project is less or equal to pre-established maximum
Project Unacceptable: When expected payback period is longer than established maximum.
Payback period approach determines the # of years needed to recover _________?
The initial investment amount
Quick simple payback period problem. Initial investment = $1,000. Below are the cash inflows for each year. What is the payback period? Year 1: $200 Year 2: $200 Year 3: $400 Year 4: $400
The answer is 3.5 years. It takes you this amount of time to accumulate the $1000 initial investment. (200 + 200 + 400 + 200) = $1,000 or 3.5 years.
What is the formula to calculate payback period of an investment?
Initial cash investment/net cash inflows = # of years needed to recover initial investment
What are three advantages of the payback period?
- Easy to understand and use
- Useful in evaluating liquidity
- Establishing short maximum period reduces uncertainty
What are four disadvantages of the payback period?
- Ignores time value of money
- Ignores cash flows after payback period
- Does not distinguish different sources of cash flow
- Not measure project profitability
Capital budgeting is concerned with capital investments that have prospects for ________ long-term benefits?
Long-term. Capital budgeting does not apply to short-term.
Which of the following approaches to capital project evaluation are concerned with determining economic feasibility of projects?
Choices: Net present value approach, profitability index approach, accounting rate of return approach, internal rate of return approach.
- Net present value approach
- Accounting rate of return approach
- Internal rate of return approach
This approach to capital project evaluation is primarily concerned with the relative economic ranking of projects by taking into account the cost of a project as well as with its net present value. What is it?
Profitability index approach
Regarding determining payback period, when you are given information relating to depreciation and time value of money, would these be considered in your calculation of payback period?
No. Time value of money is not included.
Depreciation is not included as well since it is not a cash inflow/outflow.
Formula: Initial cost/Net Cash Inflows
Regarding payback period, what is the formula to calculate initial investment of a project? You are given net cash inflows and payback period.
Initial cash investment = Net cash inflows x payback period
Regarding payback period, how do you calculate net cash inflows portion of payback period equation when you are given operating expenses and depreciation expenses?
Payback period = Initial cash investment/Net cash inflows (Operating expenses - Depreciation expenses)
What is the formula to calculate straight-line depreciation?
(Cost - Residual Value)/# of year of life = SL Depreciation expense per year
What is the formula to calculate sum-of-the-years digits depreciation?
Depreciable amount (Cost-Residual Value) x fraction of yr (5/15). **5 year example. 5+4+3+2+1= 15. 5/15 for year 1. 4/15 for year 2 and so on**
What is the formula to calculate double declining balance depreciation?
Beg. of period book value (Just cost; no residual value) x (2 x SL rate)
**5 year depreciation would be 20% SL rate. Therefore, 40% used (2 x 20%).
Double declining balance depreciation is calculated by doubling the straight-line rate and multiplying that rate by the declining book value each year.
What is the formula to calculate units of production depreciation?
(Cost - Residual Value)/# of total units x # of units yr 1
The units of production method is calculated by allocating the depreciable amount to production on a per unit basis and multiplying the resulting per unit rate by the level of production each period.
What are the advantages of discounted payback method? How do these compare to advantages for payback period?
Same advantages as payback period, however, it does consider time value of money.
- Easy to understand and use
- Useful in evaluating liquidity
- Establishing short maximum period reduces uncertainty
- Considers time value of money
What are the disadvantages of discounted payback method? How do these compare to advantages for payback period?
- Ignores cash flows after payback period
- Does not distinguish different sources of cash flow
- Not measure project profitability
* *Does measure time value of money**
Discounted payback method and payback method have same advantages and disadvantages, what is the one key difference?
Discounted payback method considers time value of money while the other doesn’t. Because of this it makes discounted payback method better.
The discounted payback period approach to assessing a capital project determines the number of years (or other periods) needed to recover the initial cash investment in the project and compares the resulting time with a preestablished maximum payback period. Does it result in a longer or shorter payback period than undiscounted payback method?
Longer. The cash flows are multiplied by PV factor to determine a discounted amount which is always lower than original cash amount.
Cash flow x PV factor = Discounted amount
Does discounted payback method include all of these? Duration of funds being tied up, project’s cost of capital, and project’s break-even point.
Yes all of these.
This capital budgeting evaluation approach determine the number of periods required for the discounted cash inflows of a project to equal its discounted cash outflows?
Discounted payback period approach
Regarding discounted payback period approach, how do you determine payback period when given initial investment, cash flows, and PV factor for each flow.
SUM of (Net cash flow x present value for each year). Determine the # of years to recover initial investment. For the balance needed on last year, divide remaining balance/PV for last year. See notes on formula book for more details.
With discounted payback approach, how do you determine the cash flow for one of the years? You are given the following info. Payback period = 2 years Initial cost = $30,000 Cash flow year 1 = $20,000 Cash flow year 2 = Y PV year 1 = 0.9524 PV year 2 = 0.9070
Set up a formula and solve for variable Y.
Initial cost = Cash flow Yr 1 x PV Yr 1 + Cash flow Yr 2 x PV Yr 2
$30,000 = $20,000 × (.9524) + (Y)year 2 cash inflow × (0.9070) Year 2
Solve for Y = $12,075
This approach to capital project evaluation assesses a project by measuring expected annual incremental accounting income as a percentage of the initial or average investment?
Accounting rate of return approach
This capital project evaluation approach is one of the few approaches that recognizes depreciation expense? Takes into account depreciation expense in computing annual incremental income.
Accounting rate of return approach.
Note: Takes into account depreciation expense in computing annual incremental income.
What is the formula to calculate accounting rate of return?
(Average annual incremental income - Average annual incremental Expenses)/Initial or Average cost
Depreciation counts as an expense
How does accounting rate of return approach treat depreciation expense and time value of money?
- Depreciation is taken into account as an expense when you are calculating annual incremental income (numerator in ARR formula)
- Time value of money: ARR does not consider time value of money
What are three advantages of accounting rate of return approach?
- Easy to understand and use
- Considers entire life of projects
- Assumes that incremental net income is the same each year
- Performance evaluation measure
What are three disadvantages of accounting rate of return approach?
- Ignores time value of money
- Uses accrual accounting values; not cash flows
- Use of different depreciation methods have different results
You are given the following variables below. Which ones would be included in the numerator or denominator in accrual accounting rate of return formula?
Average annual operating income = $40,000
Initial increase in required investment = $60,000
Average increase in required investment = $30,000
ARR = Average annual incremental income/Initial or average investment
Annual operating income ($40,000) = Numerator
Initial investment ($60,000) = Possible denominator
Average investment ($30,000) = Possible denominator
How do you calculate accounting rate of return given the following info. Initial cost = $100,000 Cash flows/Income = $20,000 per year SL Depreciation for 10 years Info regarding time value of money.
-Time value of money irrelevant in ARR
-Depreciation relevant in ARR
Depreciation expense equals $100,000 cost/10 years = $10,000
ARR=Income-Expenses/Cost
$20,000 (Income) - $10,000 (depreciation) / $100,000 (cost) = 10%
In the ARR portion of formula, how do you determine annual average incremental income given tax rate and income before taxes?
Tax rate = 30%
Income before taxes = $7,200
ARR=Avg. Ann. Inc. Income/Initial or Avg. Cost
Average annual incremental income = Income before taxes x (1 - Tax rate)
or
$7,200 x .70(1-.3) = $5,040
With regards to Accounting rate of return, what is a formula to calculate average cost (denominator)?
(Hint: Given initial investment + salvage/residual value + Net working capital)
Average cost = Initial cost + Salvage/residual value + Net Working Capital/2
With regards to ARR formula, how do you calculate initial investment?
ARR = Annual Inc. Income/Initial investment
You are given info below
ARR = 10%
Annual Incremental income= $3,000
10 year straight line depreciation
By rearranging the formula: Initial investment = Incremental annual income (Income - Depreciation %)/ARR
or
$3,000 (Income) - .10 (Depreciation %)/.10 (ARR) = Initial Investment
-Solve for initial investment
Answer: $15,000
In ARR formula, is revenue over life of project and depreciation expense used?
Yes in numerator. Average annual incremental income = revenue - Depr. Expense.
This capital project evaluation approach provides a way of ranking projects by taking into account both cash flow benefit expected from projected and the cost of each project?
Profitability Index (PI)
Also know as cost/benefit ratio or present value index
This computes the expected return for each dollar (present value) invested?
Profitability approach
What are the two formulas used to calculate profitability index (PI)?
PI = PV (Present Value of cash inflows)/Project cost
or
PI = NPV (Net Present Value: cash inflows - cash outflows)/Project cost
You are given several projects with the cost and NPV given. Under profitability Index, how do you determine the most desirable project?
The project with the highest profitability index. A project with PI over 1 is deemed acceptable.
PI = NPV/Cost
Rank these in order of highest PI
In profitability index for ranking projects, the _____ the percentage, the higher the project rank.
Higher
Does profitability index ignore or use time value of money?
The profitability index does not ignore the time value of money. By using present values of cash flows, the profitability index takes into account the time value of money.
What are two advantages of profitability index (PI)?
- Uses free cash flows
2. Consistent with goal of shareholder wealth maximization
What is a disadvantage of profitability index?
It requires detailed long-term forecasts of the project’s cash flows. The longer the projection period, the greater the uncertainty of those cash flows.
Dividing the present value of annual after-tax cash flows by original cash invested in project is called?
Profitability index
What is the formula to calculate excess present value?
Excess present value = PV of cash inflows/Initial Investment x 100
How do you calculate after-tax cash flows with the following information?
What is the formula?
Also is depreciation deductible for tax purposes for profitability index?
Cash flows = $30,000
Depreciation = $20,000
Tax rate = 30%
After-tax cash flows = before-tax cash flow - income taxes.
Income tax calculation = ($30,000 before tax - $20,000 depreciation) x .30 tax rate = $3,000
After tax cash flow = $30,000 - $3,000
This capital evaluation approach assesses projects by comparing the present value of expected cash inflows (revenues, savings, residual values, etc.) of project with expected cash outflows (initial investment/other payments).
Net Present Value Approach
In Net Present Value method, PV (present value) of expected cash inflows is by determined by discount (or known as hurdle rate) based on weighted average cost of capital to firm. When you are given a net present value of a project, when is the project deemed economically acceptable or unacceptable?
NPV >/= 0; acceptable
NPV = 0; unacceptable
NPV = Present value of cash inflows - present value of cash outflows. What are four different things that constitute cash inflows?
Highly important when calculating NPV.
- After-tax net cash inflows/revenues/savings (After tax revenues x PV of annuity for # of periods)
- Residual/salvage values (Residual/salvage value x PV of single sum or $1)
- Depreciation savings (Depreciation expense x tax rate)
* *Depreciation savings are only applicable when income taxes are involved** - Terminal Value (Total terminal value x PV of $1)
NPV = Present value of cash inflows - present value of cash outflows. What are the three things that constitute cash outflows?
Highly important when calculating NPV.
- Initial cash investment
- Other payments of project
- Additional investment in working capital
What is the formula to calculate net present value? Relating to Net Present Value Approach.
Net Present Value (NPV) = PV of cash inflows - PV of cash outflows
When calculating PV of cash inflows in Net Present Value Approach, you are given expected sales, operating expenses, and tax rate. How do you determine total cash inflows?
First, determine operating income by sales - operating expenses. Second, determine net income by operating income x (1 - tax rate) = net cash inflows Operating Income (Before Taxes) = Sales - Operating expenses Net Income (After Taxes) = Operating Income x (1 - Tax rate)
With regards to net present value approach, which of the following is considered a cash flow (inflow/outflow)?
A. Proceeds from sale of asset
B. Carrying amount of asset
C. Amount of annual depreciation of asset
D. Amount of annual depreciation on fixed assets
Proceeds from sale of asset is a cash inflow.
NPV - PV of cash inflows - PV of cash outflows
You are given a problem in net present value approach, where amount of cash inflows is given per year as well as initial cost of investment. You are given PV of annuity for # periods as well as PV of $1 or sing sum. Which PV do you use to calculate NPV?
PV of annuity for # of periods (higher number)
NPV = net cash flows x PV of annuity - Initial cost
NPV Approach. Calculate expected cash inflow for project given following variables. Expected sales = $1,500 Cash operating expense = $700 Depreciation = $150 Tax rate = 30%
Cash inflows is part of NPV equation (NPV = Cash inflows - Cash outflows).
Expected sales - operating expenses = Operating Income
-Operating income x (1 - tax rate) = Net Cash Flows
-Add depreciation savings (depreciation expense x tax Rate)
1,000 x (1-.30) = $800 x (1 - .30) = $560 + (250 x .30) = $635
Why would depreciation be used in the determination of net present value? Given income taxes are related to the problem.
Depreciation increases cash flow by reducing income taxes. Depreciation savings (cash inflows) = (Depreciation expense x tax rate)
In NPV problem, how do you calculate investment cost when given NPV and cash inflows?
Since NPV is the difference between cash inflows and cash outflows. Calculate cash inflows and subtract NPV from that number to calculate investment cost.
Or simply…..
Investment cost = PV of cash inflows - NPV
In NPV approach, residual/salvage value (same thing) are used to calculate cash inflows. Which PV is used to calculate the PV of residual/salvage value?
A. PV of annuity of # of periods
B. PV of $1
B. PV of $1
This will be added with PV of revenue/savings/cash inflows
You are given PV of cash outflows. How do you determine the PV of cash inflows given following variables?
Cash outflow = $12,000
PV of $1 = 0.5674
PV of annuity = 1.7623
PV of inflow = Cash outflow x PV of $1
or
12,000 x .5674 = $6,809
Regarding NPV approach, when you are given a present value table, how do you determine which PV value to use in equation?
You choose the number based of discount (hurdle rate) or cost of capital.
With regards to NPV approach, which of these would result in highest present value? A. Decrease in taxes B. Decrease in cash outflow C. Increase disposal value D. Increase cash inflow
A. Decrease in taxes
This capital evaluation approach consistently provides the best solutions even when considering mutually exclusive projects?
Net present value
Which capital evaluation approach requires the discount rate (hurdle rate) to be determined in advance?
Net Present Value Method
The two most important methods of capital budgeting that consider time value of money are?
- Net present value method
2. Internal rate of return
With regards to NPV approach, would depreciation expense and salvage value be included or excluded ignoring tax considerations? How about including tax considerations?
Ignoring tax considerations -Salvage value = included -Depreciation = excluded Considering tax considerations -salvage value = included -Depreciation = included as tax deduction
What is considered the best capital evaluation method is considered the best method concerning maximizing shareholder value and considering profitability of the project?
Net Present Value
When a project has a positive net present value, its internal rate of return is _______ than the required rate of return?
Greater
What are four advantages of net present value method?
- Recognizes time value of money (accounts for compounding returns)
- . Relates project rate of return to cost of capital
- Considers entire life of project
- Easier to compute than internal rate of return
What are two disadvantages of net present value method?
- Requires estimation of cash flows over entire life of project
- Assumes cash flows are immediately reinvested at hurdle or discount rate
What is the formula to calculate PV of annuity given project cost and annual cash inflow? NPV method.
PV of annuity = Project cost/annual cash inflow
In NPV, when solving for cash inflows to determine the amount of income taxes owe, how do you calculate this when given cash flows, depreciation, and tax rate?
Income taxes owed = (Cash flows - depreciation) x Income tax rate
Depreciation is tax deductible
IMPORTANT. When calculating cash inflows. You have to multiply your after-tax cash flows x PV of annuity. It is important to deduct taxes from cash flows then you can multiply by PV of annuity. What is the formula to calculate after tax cash flows? What is formula to calculate income tax owed?
After-tax cash flows = Cash flows - income tax owed
Income taxes owed = (cash flows - depreciation) x tax rate
In NPV approach, when you are given a different amount of cash flow each year, which PV percentage do you use?
A. PV of $1 at end of periods
B. PV of annuity at end of # periods
B. PV of $1 at end of # of periods
PV of annuity would be if cash flows was the same for each year
Regarding NPV, increases in taxes would ______ both benefits and costs. Why?
Decrease. The determination of net present value takes into account both inflows of cash (benefits) and outflows of cash (costs).
NPV method. How do you calculate expected value/expected contribution of a product when given the amounts of each outcome and probability of each outcome?
Outcome amount x Probability of outcome. Sum the total amount.
How is an additional investment in working capital treated? With regards to NPV approach.
As an additional initial investment
Regarding NPV, what is the formula to calculate total issue price of bonds?
You are given principal of bond, interest rate, and yield %.
Total issue price for bond = PV of the maturity value (principal) + PV of interest annuity
PV must be computed at yield rate
PV maturity = principal x PV of $1/value of one (yield rate)
PV interest annuity = Interest (Principal x interest rate) x PV of annuity (yield rate)
