Finance Exam 2: Entire Thing

The amount of the interest that has been repaid at that point in time. It's cumulative.

In loan amortization problems, what does INT indicate?

the periodic interest rate

APR / number of periods compounded per year = what?

expansion

Are replacement or expansion capital budgeting projects riskier?

Determine the net investment cash outlay

At time 0 of the Capital Budgeting process, what is the first step?

When interest isn't reinvested, so interest is only earned on the principle amount

Describe simple interest

project B because NPV is higher.

If projects are INDEPENDENT, but you can only chose 1, what would we chose and why? PROJECT A cost = $5 PV of future CF = $10 NPV = 5 IRR = 100% PROJECT B cost = $100 PV of future CF = $150 NPV = 50 IRR = 50%

RANK THEM based on NPV if no budget constraint or IRR if budget constraint.

Since you can't choose more than 1 project for mutually exclusive projects, what do you do?

Salvage value of asset (sales price) (+/-) tax benefit or expense (+) original change in NWC

The final step in conducting a capital budgeting analysis is finding the terminal cash flows. How do you calculate this final number?

the value that we ultimately sell the asset for, not the book value

The salvage value of an asset is

PV = FV/(1+r)^n

Describe the mathematical relationship between present and future value...

YES, because the opportunity to invest the money is always available, you're just choosing not to.

Even if you chose not to invest money, does your money still have time value?

Old remaining interest - new mortgage total interest

For the really long and hard amortization problems that have to do with analyzing two different mortgages, how could you determine how much you'll be saving with the new mortgage versus the old one?

the INTEREST RATE

How do you measure the time value of money?

simple interest

Interest earned on principal sum

MORE because money received today can be invested to receive a return

TVM refers to the fact that a dollar in hand today is worth ______ than a dollar promised some time in the future. Why?

0

The IRR sets the PV of inflows = PV of outflows, meaning at that rate, the NPV would be....

PV of all cash inflows = PV of all cash outflows

The IRR sets what equal to what to get an NPV of 0?

pure discount

Treasury bills are an example of what kind of loan?

The effect of compounding interest

an EAR is an EAR because of what?

erosion

A negative spillover is called

APR (annual percentage rate)

Also known as the stated rate, quoted rate, or NOMINAL INTEREST RATE

perpetuity

An annuity in which the cash flows continue forever

cost of capital

Another word for "discount rate" is...

C

CH 10 MC: Which one of the following best illustrates erosion as it relates to a snack stand located on the beach? A. Providing free ice and condiments for customers B. Repairing the canopy over the snack stand because of wind damage C. Selling fewer cookies because ice cream was added to the menu D. Offering french fries but not onion rings E. Losing sales due to bad weather

C

CH 10 MC: Which one of the following types of costs was incurred in the past and cannot be recouped? A. Incremental B. Side C. Sunk D. Opportunity E. Erosion

E

CH 9 MC: A project has a net present value of zero. Given this information: A. the project has a zero percent rate of return. B. the project requires no initial cash investment. C. the project has no cash flows. D. the summation of all of the project's cash flows is zero. E. the project's cash inflows equal its cash outflows in current dollar terms.

D

CH 9 MC: The internal rate of return is defined as the: A. maximum rate of return a firm expects to earn on a project. B. rate of return a project will generate if the project is financed solely with internal funds. C. discount rate that equates the net cash inflows of a project to zero. D. discount rate which causes the net present value of a project to equal zero. E. discount rate that causes the profitability index for a project to equal zero.

be indifferent to accepting or rejecting

If NPV is 0, financial managers would....

It will be more than 1 BECAUSE the future cash flows must be bigger than the initial investment

If a project has a positive NPV, what does that mean for its profitability index?

It has cash flow consequences related to the tax bill.

If depreciation is a non-cash expense, why do we include it?

Take PRN + INT

In a loan amortization problem, it may ask the total amount of money that has been repaid at that point. How might you find that?

Enter the payment amount, N, and interest rate to calculate what the future value of your cash flows will be by the end. Then, find the FV of the value of the mortgage. Take the FV of the mortgage - FV of payments to find what amount in the future you will have to pay.

Let's say you can only afford "x" amount in annual payments for a mortgage, but that means you will have to make a balloon payment at the end to make up for what you couldn't pay. How would you solve this?

Enter the payment amount, N and interest rate. Calculate the present value of the cash flows to find out how much you would pay off now. Then, take the cost of the entire mortgage - PV of payments (what you just found) to see how much you need to pay upfront.

Let's say you can only afford "x" amount in annual payments for a mortgage, but that means you will have to make an initial payment upfront to make up for it. How would you solve for the initial payment value?

- Closely tied with NPV - Contains information about margin of safety - Objective decision criteria makes it easy to chose - We don't need to know the discount rate

List some PROS of using the IRR

TRUE

T/F: Time value of money allows us to compare can flows at different points in time by finding their equivalent values through time by compounding or discounting

profitability index

The PV of future cash flows divided by the absolute value of its initial costs

Net Present Value (NPV)

The difference between an investment's market value and its costs TODAY, aka a measure of how much value is created TODAY by undertaking an investment

internal rate of return

The discount rate that makes the nPV of a project = 0, AKA the single rate of return that summarizes the merits of a project

DECREASES

The discounted payback period ______ as the discount rate decreases

discounted payback period

The length of time required for an investment's discounted cash flows to equal its initial costs

discounting

The process by which future money is reduced over time to today's smaller value

Typically the one with the larger MIRR. However, if these projects are different sizes, you need to use NPV because conflicts with MIRR and NPV occur.

What are the criteria for using the MIRR when accepting or rejecting for mutually exclusive projects?

When a borrower pays interest each period and also repays the principal at maturity

What is an interest only loan?

An annuity with payments that occur at the end of each period

What is an ordinary annuity?

1,180.49 because we would choose Project F based on NPV, so doing Project F's NPV - Project D's NPV = opportunity cost.

What is the opportunity cost of choosing the best project over the next best, if these are mutually exclusive projects? Project D NPV = 2,834.74 IRR = 25% Project F NPV = 4,015.23 IRR = 21%

The required rate of return

When NPV = 0, the IRR is equivalent to what?

Spillover

When the cash flows of a project impact existing cash flows either positively or negatively

complex annuity

When the dollar amount, frequency of payments, and/or frequency of compounding/discounting is different

simple annuity

When the frequency of payments and the frequency of compounding/discounting is identical

Pure discount

Which loan is the most short term?

Because a higher NPV means more cash is going to be used, so the higher the NPV isn't always the ideal choice

Why don't we use NPV with mutually exclusive projects and a limited capital budget?

FINDING THE NUMBER OF PERIODS 1. 10,000 → PV 2. 2183.55 → +/- → PMT 3. 3 → I/Y 4. CPT → N → 5

You borrowed $10,000 from your parents and have agreed to repay it in equal annual payments of $2,183.55 each, which includes the 3% interest you have agreed to pay. How many years will it take you to repay this loan?

strategic asset allocation

capital budgeting is also called

opportunity cost

The interest rate reflects the _______________ of choosing not to invest one's money

It is an annual interest rate expressed as if interest were compounded once per year.

What is the true definition of the EAR?

APR excludes the impact of compounding interest, while EAR includes this impact

What is the difference between APR and EAR?

The greater the PI, that's the project we will chose. However, if they're both under 1, we would reject both

For mutually exclusive projects, what makes us accept or reject based on profitability index?

1. Find the PV of the desired annual payments 2. Use this number as the FV and calculate the value of payments needed today

For the retirement savings problems, break the process to solving it down into qualitative steps.

principal

The amount of an original investment

payback period

The amount of time required for an investment to generate cash flows sufficient to recover its initial costs

future value

The amount that an investment is worth after one or more periods

relevant (related to project) incremental (impacts future cash flows)

The cash flows that are considered in the capital budgeting process are...

Divide the interest by 12 and multiply n by 12 to solve for the problem

A monthly payment with an interest compounded monthly means you do what?

Divide the interest number by 12 and multiply n by 12 to solve for the problem

A monthly payment with an interest rate not specified as monthly/yearly means you do what?

Rank the options using IRR, highest IRR should be chosen

ASSUMING YOU HAVE A LIMITED BUDGET (capital constraint), With mutually exclusive projects, how do you go about accepting or rejecting?

Rank the options using NPV, highest NPV should be chosen

ASSUMING YOU HAVE AN UNLIMITED BUDGET, With mutually exclusive projects, how do you go about accepting or rejecting?

B

CH 6 MC: Your local pawn shop lends money at an annual rate of 24% compounded weekly. What is the true value of these loans? A. 25.16 B. 27.05 C. 26.49 D. 27.56 E. 28.64

These are the row headings year - depreciable basis - depreciation % - depreciation expense - end book value

Describe how to set up (not solve, just set up) a depreciation schedule

they stay fixed

Do the payments for amortized loans stay fixed or do they vary?

No. Only include the [transportation, installation and cost of asset]+[change in NWC with assets positive and liabilities negative]

Do you include the effect of opportunity costs within the NICO?

Use the CF registers, but hit IRR instead of NPV when everything is input.

How do you calculate an IRR given the cost of a project and its cash flows?

Balance: -1,000 400/1.1 = 363 -> 1,000 - 363 = -637 remaining 300/1.1^2 = 248 -> 637 - 248 = -389 remaining 400/1.1^3 = 300 -> 389 - 300 = -89 remaining Bal remaining year 3 / DISCOUNTED CF for year 4 200/1.1^4 89/136 = .6544 3.6544 years to pay off

How do you calculate the discounted payback period for this stream of cash flows? Assume 10% discount rate T0 - (1,000) T1 - 400 T2 - 300 T3 - 400 T4 - 200

Balance remaining from last year / DISCOUNTED cash flow this year

How do you calculate the fraction of time it will take in the year that the discounted payback period will be reached?

If it's independent projects

NPV and PI, IRR and MIRR will always lead to the same accept/reject decisions when?

present value of future cash flows, the present value of the cost to aquire.

NPV is the __________ net of __________

B

RANDOM MC: Which one of the following is an example of a sunk cost? A. $2,000 in lost sales because an item was out of stock B. $2,000 paid last year to rent equipment C. $2,000 project that must be forfeited if another project is accepted D. $2,000 reduction in Product A revenue if a firm commences selling Product B E. $2,000 increase in comic book sales if a store ceases selling puzzles

Compounding

The process by which money today grows over time into a larger future value.

FINDING EAR 1. 2nd → ICONV (above 2) 2. (NOM shows) → 14 3. ENTER → down arrow → down arrow 4. (C/Y shows) → 12 (number of compounding periods) 5. ENTER → down arrow → down arrow 6. (EFF shows) → CPT → 14.9342

Your credit card company charges you a stated annual percentage rate (APR) of 14% on your balance, but they charge you interest monthly. What is the effective annual rate you are paying? In other words, what is the interest rate you are really paying each year?

E

RANDOM MC: A new sports coupe costs $41,750 and the finance office has quoted you an APR of 7.7 compounded monthly for 36 months. What is the EAR? A. 7.81% B. 8.02% C. 7.94% D. 8.13% E. 7.98%

True

T/F: An APY is the same as an EAR

FALSE

T/F: Differing sized mutually exclusive events means the MIRR and NPV lead to the same decision

True

T/F: In the depreciation schedule, the depreciable basis for all years stays the same

FALSE, only when it can earn a positive return.

T/F: Money can have time value if it can be invested to earn a negative return

True, it's an opportunity cost

T/F: The option to lease out the manufacturing facility instead of launching a new product is a relevant cash flow

True, but ONLY if the MIRRs are calculated using the same terminal year

T/F: equal size + different life of mutually exclusive events means the MIRR and NPV lead to the same decision

interest-only

Corporate bonds are an example of what kind of loan?

With mutually exclusive projects, The project with the shorter payback period should be accepted With independent projects, If the payback period is less than the "policy maximum" number of years it should take, we accept. If payback is longer than what the firm prescribes, we reject.

Describe the difference in the payback period acceptance/rejection with mutually exclusive vs independent projects.

Last year's EBV - this year's depreciation expense

For all years besides Y1, how do you find the end book value of an asset in the depreciation schedule?

In compounding you take the total amount of years and subtract the number of the current year to get the value of the exponent. If there are 5 years, then year 1 will have an exponent of 4

For compounding cash flows with multiple years, what is the rule for the exponent in the compounding equation?

One of them will have to be negative. Negative implies a cash outflow from the person with the money, while positive indicates gains.

In the financial calculator, if you're using PV and FV in the same problem, what is the rule in terms of signs?

FINDING PMT OF LOAN 1. 210,000 - 20,000 → +/- → PV 2. 7.5 / 12 → I/Y 3. 30 x 12 → N 4. CPT → PMT → 1,328.5076 FINDING INTEREST PAID 1. 2nd → AMORT 2. P1 = 1 → enter → down 3. P2 = 180 → enter → scroll to INT 4. INT = 192,442.0207

LOAN AMORTIZATION PROBLEM You have arranged a 30-year mortgage with a 7.5% annual interest rate in order to buy a home at a price of $210,000. You will make a down payment of $20,000 but you must borrow the rest. You will make monthly payments. How much will your monthly payments be? After you have made half of your payments, how much interest will you have paid?

E

RANDOM MC: An investment costs $152,000 and has projected cash inflows of $71,800, $86,900, and −$11,200 for Years 1 to 3, respectively. If the required rate of return is 15.5 percent, should you accept the investment based solely on the internal rate of return rule? Why or why not? A. Yes; The IRR exceeds the required return. B. Yes; The IRR is less than the required return. C. No; The IRR exceeds the required return. D. No; The IRR is less than the required return. E. You should not apply the IRR rule in this case.

D

RANDOM MC: The net present value of a project will increase if: A. the required rate of return increases. B. the initial capital requirement increases. C. some of the cash inflows are deferred until a later year. D. the aftertax salvage value of the fixed assets increases. E. the final cash inflow decreases.

E

RANDOM MC: Which one of the following statements correctly defines a time value of money relationship? A. Time and future values are inversely related, all else held constant. B. Interest rates and time are positively related, all else held constant. C. An increase in a positive discount rate increases the present value. D. An increase in time increases the future value given a zero rate of interest. E. Time and present value are inversely related, all else held constant.

TRUE

T/F: APR is the interest rate charged per period multiplied by the number of periods per year

CF0 = (+/-) 100 CF1 = 60 CF2 = 60 IRR -> CPT = 13.0662% If the discount rate is less than this number, we would accept.

The cost of a project is $100. It is expected to return 60 dollars per year for 2 years. What is the IRR of this project?

The frequency of the payments made. If they're monthly payments, and the interest rate is given __% per year, no matter if it's compounded monthly or annually, you just divide this % by 12 to find the monthly interest rate. On the other hand, if the payments are annual, but the interest rate is __% per year compounded monthly, you must use the calculator to change it to an EAR.

The key with figuring out EAR vs APR comes down to what?

Take the original cash flow for that year and divide it by 1.[discount rate decimal]^the year number for example, at 8%, if year 3 has a cash flow of 244,820, to discount it you would do 244,820/1.08^3

When discounting in the discounted payback period method, what formula do you use to discount back to PV?

risk and liquidity

the payback period measures....

project B because NPV is higher.

If projects are mutually exclusive, what would we chchooseose and why? PROJECT A cost = $5 PV of future CF = $10 NPV = 5 IRR = 100% PROJECT B cost = $100 PV of future CF = $150 NPV = 50 IRR = 50%

We will receive tax refund

If the end book value ends up being MORE than what we sell the asset for, will we owe or receive taxes?

True

T/F: equal size + life of mutually exclusive events means the MIRR and NPV lead to the same decision

FALSE: PB period measures RISK and LIQUIDITY

T/F: the payback period is a measure of profitability

You can either use an EAR or match (divide interest by 12 and multiply n by 12)

A lump sum payment and interest compounded monthly means you do what?

positive, because it shows that value will be added to the company if it's undertaken TODAY...

A project that has a _______ NPV should be accepted because.....

Finding the operating cash flows for each year

After a depreciation schedule is made in capital budgeting, what is the next step?

- At time 0, it's the negative NICO value - For the years in between, its the OCF found each year - For the last year, it's the OCF for the year plus the terminal cash flow calculated.

After all of the steps of the capital budgeting process is done, you put all of the numbers on a timeline. Describe which numbers go on it.

2nd -> ICONV NOM = 3.45 -> ENTER -> down down C/Y = 12 -> ENTER -> down down CPT -> EFF = 3.5051

An APR is 3.45% compounded monthly. What is the effective annual interest rate?

Find the EAR to plug into I/Y

An annual payment with interest compounded monthly means you do what?

decreases

As an amortized loan is paid off, the interest paid in each fixed payment ____________

increases

As an amortized loan is paid off, the principal paid in each fixed payment ____________

If IRR > the discount rate/cost of capital, ACCEPT If IRR < the discount rate/cost of capital, REJECT

For independent projects, how do you determine wether to reject or accept the project based on IRR?

E

CH 10 MC: 4. Cerda Diagnostics spent $5,000 last week repairing equipment. This week the company is trying to decide whether the equipment could be better utilized by assigning it to a proposed project. When analyzing the proposed project, the $5,000 should be treated as which type of cost? A. Opportunity B. Fixed C. Incremental D. Erosion E. Sunk

B because the opportunity cost is that amount

CH 10 MC: Six years ago, Hendershot Stables paid $84,000 in cash for equipment. Last year, the company spent $7,600 on equipment upgrades. The company no longer uses this equipment and has received a cash offer of $39,600 from a buyer. The current book value of the equipment, including all updates, is $32,200. If the company decides to keep the equipment and use it for a new project, what value, if any, should the company assign to the equipment? A. $0 B. $39,600 C. $39,800 D. $84,000 E. $91,600

B

CH 10 MC: The fact that a proposed project is analyzed based on the project's incremental cash flows is the assumption behind which? A. Underlying value principle B. Stand-Alone principle C. Equivalent cost principle D. Salvage principle E. Fundamental principle

E

CH 5 MC: Claire's coin collection contains 50 1948 silver dollars. Her grandparents purchased them at face value. These coins have appreciated by 7.6% annually. How much will the collection be worth in 2025? A. $13,611.18 B. $18,987.56 C. $14,122.01 D. $11,218.27 E. $14,077.16

C

CH 5 MC: Nirav just opened a savings account paying 2% interest compounded annually. After four years, the savings account will be with $5,000. Assume there are no additional deposits or withdrawals. Given this info, Nirav: A. Will earn the same amount of interest each year for 4 years B. Will earn simple interest on his savings every year for 4 years C. Could have deposited less money today and still had 5,000 in four years if the account paid a higher interest rate D. Has an account already valued at $5,000 E. Could earn more interest on this account if the earning were withdrawn annually.

If it's greater than 1, we accept. If less than 1, we reject

For independent projects, what makes us accept or reject based on profitability index?

C

CH 5 MC: This morning, Clayton deposited $2,500 into an account that pays 5% interest, compounded annually. Also that morning, Jada deposited $2,500 at 5% interest annually. Clayton will withdraw his interest earnings and spend it asap. Jada will reinvest her interest earnings into her account. Which statement is correct? A. Jada will earn more interest in Y1 than Clayton B. Clayton will earn more interest in Y3 than Jada C. Jada will earn more interest in Y2 than Clayton D. After five years, they will both have earned the same amount of interest E. Clayton will earn compound interest

B

CH 6 MC: On this date last year, you borrowed $3,900. You have to repay the loan with a lump sum payment of $6,000 six years from now. What is the interest rate? A. 6.01 B. 6.35 C. 6.78 D. 5.47 E. 5.38

C

CH 6 MC: You are comparing two investment options that each pay 6% compounded annually. Both options will provide you with $12,000. Option A pays $2,000 in the first year followed by 2 payments of $5,000 each. Option B pays 3 payments of $4,000. Which of the following is correct? A. Both options are of equal value since they both provide $12,000 B. Option A has the higher FV at the end of year 3 C. Option B has a higher PV at time 0 D. Option B is a perpetuity E. Option A is an annuity

C

CH 9 MC: In actual practice, managers most frequently use which two types of investment criteria? A. Net present value and payback B. Average accounting return and internal rate of return C. Internal rate of return and net present value D. Internal rate of return and payback E. Net present value and profitability index

C

CH 9 MC: Mutually exclusive projects are best defined as competing projects that: A. would need to commence on the same day. B. have the same initial start-up costs. C. both require the total use of the same limited resource. D. both have negative cash outflows at time zero. E. have the same life span.

E

CH 9 MC: The internal rate of return: A. may produce multiple rates of return when cash flows are conventional. B. is best used when comparing mutually exclusive projects. C. is rarely used in the business world today. D. is principally used to evaluate small dollar projects. E. is easy to understand.

B

CH 9 MC: The length of time a firm must wait to recoup the money it has invested in a project is called the: A. internal return period. B. payback period. C. profitability period. D. discounted cash period. E. valuation period.

B

CH 9 MC: When the present value of the cash inflows exceeds the initial cost of a project, then the project should be: A. accepted because the payback period is less than the required time period. B. accepted because the profitability index is greater than 1. C. accepted because the profitability index is negative. D. rejected because the internal rate of return is negative. E. rejected because the net present value is positive.

E

CH 9 MC: Which one of the following methods of analysis provides the best information on the benefits to be received from a project per dollar invested? A. Net present value B. Payback C. Internal rate of return D. Average accounting return E. Profitability index

A

CH 9 MC: Which one of the following methods predicts the amount by which the value of a firm will change if a project is accepted? A. Net present value B. Discounted payback C. Internal rate of return D. Profitability index E. Payback

C

CH 9 MC: Which one of the following statements related to the internal rate of return (IRR) is correct? A. The IRR yields the same accept and reject decisions as the net present value method given mutually exclusive projects. B. A project with an IRR equal to the required return would reduce the value of a firm if accepted. C. The IRR is equal to the required return when the net present value is equal to zero. D. Financing type projects should be accepted if the IRR exceeds the required return. E. The average accounting return is a better method of analysis than the IRR from a financial point of view.

D

CH 9 MC: Which one of the following will decrease the net present value of a project? A. Increasing the value of each of the project's discounted cash inflows B. Moving each cash inflow forward one time period, such as from Year 3 to Year 2 C. Decreasing the required discount rate D. Increasing the project's initial cost at Time 0 E. Increasing the amount of the final cash inflow

D

CH 9 MC: Which one of these statements related to discounted payback is correct? A. Payback is a better method of analysis than discounted payback. B. Discounted payback is used more frequently in business than payback. C. Discounted payback does not require a cutoff point. D. Discounted payback is biased towards short-term projects. E. The discounted payback period increases as the discount rate decreases.

discounted cash flow valuation

Calculating the present value of a future cash flow to determine its worth today is called.....

Independent projects have no competing alternatives, and taking it doesn't impact any alternatives. Mutually exclusive projects have competing alternatives and by choosing one, you can not accept any others.

Capital budgeting projects can either be independent or mutually exclusive. What is the difference?

estimates

Decision making calculations like NPV, IRR and PI are ___________

1. Label the years for how long you plan on having the asset 2. Put the depreciable basis (the same number) for all of the rows 3. Put the MACRS depreciation % corresponding to each year starting at year 1 4. Find the depreciation expense for all rows by multiplying the depreciable basis by the depreciation % 5. For YEAR 1, the end book value is the depreciable basis - the depreciation expense 6. For the rest of the years, the end book value is last year's EBV - this year's depreciation expense. 7. The last end book value number is the book value when we sell it.

Describe how to solve a depreciation schedule

YES, it shows the ned addition or reduction to wealth in the present value

Does NPV measure profitability of a decision?

Discounted, as the values we discount back to present become smaller than the original cash flows.

Does it take longer to pay back using normal or discounted payback period?

NPV assumes reinvestment of cash flows at the cost of capital, while IRR assumes reinvestment of cash flows at IRR rate.

Explain why NPV and IRR can lead to different rankings if they are mutually exclusive projects

Note: You can NOT find EAR in this problem because payments are monthly so you must find a monthly rate. You must make the other variables match the frequency of payments! 1. 500 → +/- → PMT 2. 6 → / → 12 → I/Y (or .5 → I/Y) 3. 3 → x → 12 → N (or 36 → N) 4. CPT → FV → -19,688.0525

Find the future value of payments of $500 per month if they are invested in an account that earns a rate of 6% per year compounded monthly for 3 years.

Note: Interest is compounding more frequently (monthly) than the payments (made yearly), so we HAVE to use EAR. 1. 6,000 → +/- → PMT 2. 3 → N 3. 2nd → ICONV → 6 4. ENTER → down → down 5. 12 → ENTER → down → down 6. CPT → CE/C → I/Y 7. CPT → FV → 19,133.0255

Find the future value of payments of 6,000 per year for 3 years with an interest rate of 6% compounded monthly.

Note: DON'T find an EAR because the payments (monthly) match the compounding interest (monthly), so make the other variables match the frequency of your payments. 1. 10,000 → FV 2. 10 → x → 12 → N (or 120 → N) 3. 10 → / → 12 → I/Y (or .833 → I/Y) 4. CPT → PMT

Find the monthly payment needed to obtain $10,000 in 10 years given an interest rate of 10% compounded monthly.

Note: With a lump sum of money, you can use EAR or you can just calculate a new N and I/Y. No frequency of payments to match! 1. 10,000 → FV 2. 10 → N 3. 2nd → ICONV → 10 4. ENTER → down → down 5. 4 → ENTER → down → down 6. CPT → CE/C → I/Y 7. CPT → PV → -3,724.3062

Find the present value of $10,000 to be received 10 years from now, given an interest rate of 10% compounded QUARTERLY.

lower

For a borrower, the ______ the interest rate, the better

The exponent in the denominator matches the year number when discounting.

For discounting cash flows with multiple years, what is the rule for the exponent in the discounting equation?

With mutually exclusive projects, The project with the shorter discounted payback period should be accepted With independent projects, If the discounted payback period is less than the "policy maximum" number of years it should take, we accept. If discounted payback is longer than what the firm prescribes, we reject.

For the discounted payback period, what are the rules for mutually exclusive projects vs independent projects?

1. Find the value of your current payments for OG mortgage 2. Find out how much money we still need to repay for OG mortgage (P1 = 1, P2 = today's period. Find BAL) 3. Find out how much interest we would still have to pay for the rest of the life of the OG mortgage (P1 = 1 period from today, P2 = end. Find INT) 4. Find the value of the monthly payments of the new mortgage (use the remaining money we need to repay as the PV) 5. Find the total interest that we would have to pay for the new loan (INT)

For the really long and hard amortization problems that have to do with analyzing two different mortgages, break the process to solving it down into qualitative steps.

TIME and INTEREST. So if time goes up, or interest rate increases, then the future value will increase.

Future value is positively correlated to what two factors?

FIND VALUE OF CURRENT MONTHLY PAYMENTS 1. 325,000 → PV 2. 30 x 12 → N 3. 10.75 / 12 → I/Y 4. CPT → PMT → 3,033.8144 This is the payments we have to make monthly. FIND OUT HOW MUCH WE STILL OWE ON CURRENT MORTGAGE 1. 2nd → AMORT 2. P1 = 1, P2 = 120 (we are 10 years in already) 3. BAL = 298,830.57 This is the amount of money we still have to pay off, thus it's the total amount of money the new mortgage would begin to pay off... FIND OUT HOW MUCH INTEREST WE WILL STILL HAVE TO MAKE IF WE KEPT THE ORIGINAL MORTGAGE 1. 2nd → AMORT 2. P1 = 121, P2 = 360 3. INT = $429,284.9541 This is the amount we would still have to pay in interest in original loan FIND THE VALUE OF THE MONTHLY PAYMENTS OF NEW MORTGAGE 1. 298,830.57 → PV (the BAL remaining on old) 2. 15 x 12 → N 3. 7.25 / 12 → I/Y 4. CPT → PMT → $2,727.9134 This is the monthly payments for new mortgage FIND TOTAL INTEREST WE WOULD HAVE TO PAY FOR NEW LOAN 1. 2nd → AMORT 2. P1 = 1, P2 = 180 3. INT = 192,193.8297 So you should take the new loan because the amount of interest left to pay, along with the monthly payments, are less than remainder of OG loan.

HARD LOAN AMORTIZATION PROBLEM You have had a $325,000 30 year mortgage with a 10.75% interest rate for 10 years now. You are considering refinancing this mortgage because a reputable loan company has offered you a new mortgage loan at 7.25% for 15 years. All payments in either case are paid MONTHLY. Should you refinance with this company?

1,000 - 400 = -600 in year 1 remaining 600 - 300 = -300 in year 2 remaining 300 - 400 = + 100 Bal remaining Y2 / CF in Y3 300 / 400 = .75 It will take 2.75 years to pay back...

How do you calculate the payback period for this stream of cash flows? T0 - (1,000) T1 - 400 T2 - 300 T3 - 400 T4 - 200

FV = (1+r)^n

How do you find the FUTURE VALUE with an equation?

1. Discount all NEGATIVE cash flows back to PV using rate of return 2. Compound all POSITIVE cash flows to FV using rate of return 3. Add up all of the negative and positive values 4. The sum of the negative values is our new PV 5. The sum of the positive values is out new FV 6. Use the TVM registers to compute a new I/Y

How do you find the MIRR (in words)

Put all cash flows (DISCLUDING the negative initial investment) into the CF registers and solve for NPV. Then divide by the POSITIVE version of the NICO that you discluded in that initial calculation. OR, use the NPV value you calculated to find NPV. Add to it the cost of the initial investment (positive) because that is a negative value in NPV calculation. Then, divide by that same number

How do you find the PV of future cash flows for finding the profitability index?

balance remaining in last year / cash flow for year it will end

How do you find the decimal amount of time it takes to pay back in the payback period?

The PV of the future cash flows is set equal to the cost of acquiring those cash flows, solving for the discount rate (IRR) that makes it happen.

How does the IRR work?

FINDING PV 1. 2nd → CLR TVM → CE/C 2. 15000 → FV 3. 5 → N 4. 6 → I/Y 5. CPT → PV → -11,208.8726

How much would you pay today to receive $15,000 in 5 years if the appropriate interest rate is 6%?

Higher NPV - next best NPV = opportunity cost for choosing next best NPV due to capital restraints

How to calculate opportunity costs associated with capital rationing decisions?

CF REGISTERS: CF -> 2nd -> CE|C TVM REGISTERS 2nd → CLR TVM → CE/C (x2)

How to clear cash flows register versus TVM registers on your calculator?

1. The project has negative outflow at time 0 and positive subsequent cash flows (conventional cash flows) 2. The project is independent

IRR and NPV have identical accept/reject decisions ONLY IF....

present value of future cash flows = the initial investment

IRR is the rate at which the _______________ = _____________

APR - 5% EAR - 5.0945%

If an annual interest rate is 5% compounded quarterly, what's the APR and what's the EAR?

$100 each year (3) plus the principal = 1,300

If an interest-only loan was 3 years at 10% interest, and the amount borrowed was 1,000, how much would be repaid at maturity?

USE THE CASH FLOW REGISTERS. In CF0 (at time 0), you would input the cost to do the project (the NICO) as a negative number. In the rest of the registers, you would put the OCF cash flows in (typically positive). The last CF register would include the last OCF and the terminal cost as a positive number. Click NPV, put in the "discount rate" or interest rate and CPT

If given a stream of cash flows and the cost of the project, how would you find the NPV?

Project A because it has a higher IRR Low initial costs, so limited budget means we will make our money back faster

If projects are mutually exclusive, and you have a limited capital budget, what would we chose and why? PROJECT A cost = $5 PV of future CF = $10 NPV = 5 IRR = 100% PROJECT B cost = $100 PV of future CF = $150 NPV = 50 IRR = 50%

project B because NPV is higher.

If projects are mutually exclusive, and you have an unlimited capital budget, what would we chose and why? PROJECT A cost = $5 PV of future CF = $10 NPV = 5 IRR = 100% PROJECT B cost = $100 PV of future CF = $150 NPV = 50 IRR = 50%

Choose higher IRR because this indicates larger cash flows are likely to come sooner, and typically NPV will be higher for higher costing projects, so doesn't really make sense.

If there is capital rationing, and you are given NPV and IRR, which would you choose and why?

Choose higher PI, especially if the initial outlay is smaller.

If there is capital rationing, and you are given NPV and PI, which would you choose and why?

Project D because it has a higher IRR. We can't choose both, even though they're independent, as we have a limited budget

If these projects are independent and there's a limited budget, which would you choose and why? Project D NPV = 2,834.74 IRR = 25% Project F NPV = 4,015.23 IRR = 21%

Both, as they're independent and both have a positive NPV

If these projects are independent, which would you choose and why? Project D NPV = 2,834.74 IRR = 25% Project F NPV = 4,015.23 IRR = 21%

Project F because higher NPV

If these projects are mutually exclusive, which would you choose and why? Project D NPV = 2,834.74 IRR = 25% Project F NPV = 4,015.23 IRR = 21%

550,000 - 468,700 = 81,300 81,300 x .3 = $24,390 that we owe in taxes

If we sell an asset for 550,000 but the end book value was 468,700, and the tax expense was 30%, how much taxes do we owe?

gain, owe (we over depreciated the asset in our books)

If we sell an asset for 550,000 but the end book value was 468,700, this is a _____ so we _______ taxes

Divide the APR given by 4, multiply the number of years by 4 to match the frequency of the payment. Don't find the EAR!

If you have a payment that is quarterly, what do you do with the problem?

use the MIRR

If you have unconventional cash flows, instead of finding the IRR what do you do?

depreciable basis - depreciation expense

In Y1, how do you find the end book value of an asset in the depreciation schedule?

You ADD the tax expense to the negative EBIT, as it's a tax benefit. If EBIT is -8,000, and tax is 40%, then the tax expense is 3,200. We would do -8,000 + 3,200 to get -4,800 as our NI. Then we would add back the depreciation.

In calculating operating cash flows in step 3 of the capital budgeting process, what happens to the tax expense if EBIT is negative?

1. Find the total cost of the asset, including cost and additional transportation/setup costs associated. This is your DEPRECIABLE BASIS 2. Find the change in NWC, like inventory, A/P or A/R. NOTE: If an asset needs to increase, it's positive. If a liability needs to increase, it's a negative number 3. Add the depreciable basis to the change in NWC to find the NICO. Make the NICO number NEGATIVE

In determining the NICO at time 0, what must you do?

financing costs like interest paid, dividends paid, or principal repaid.

In estimating incremental cash flows, we do not include

[projected revenue each year] - [any opportunity costs or negative spillovers] + [any positive spillovers]

In finding each year's projected OCF in capital budgeting, the first row is the net incremental revenue. What does this number encompass?

It is a given % in the problem. You will multiply the EBIT of that year by the percentage of tax, and subtract the tax percentage from EBIT to find net income.

In finding each year's projected OCF in capital budgeting, the fourth row is the tax expense. What does this number encompass?

It's the depreciation expense we found with the depreciation schedule

In finding each year's projected OCF in capital budgeting, the second row is the depreciation expense. What does this number encompass?

Multiply the EBIT by the decimal of tax expense and take that number away from EBIT

In finding each year's projected OCF in capital budgeting, the sixth row is the tax expense. What does this number encompass?

1. net incremental revenue (projected annual revenue - opportunity costs or negative spillovers + positive spillovers) 2. (-) depreciation expense 3. (=) EBIT 4. (-) tax expense 5. (=) net income 6. (+) depreciation expense 7. (=) OCF

In finding the operating cash flows for each year in capital budgeting, name the different rows...

Enter the details of the loan in the TVM registers, like PV, N, I/Y, and PMT

In loan amoritization problems, what is the first step?

The balance remaining on the mortgage at that point in time

In loan amortization problems, what does BAL indicate?

Allows you to set the range of periods. For example, if there were 24 periods for monthly payments (2 years), then finding the interest paid in year 1 would mean P1 = 1 and P2 = 12.

In loan amortization problems, what does P1 and P2 indicate?

The amount of the principal that has been repaid at that point in time, it's cumulative

In loan amortization problems, what does PRN indicate?

NEGATIVE CASH FLOWS: - Do nothing to 450, it's already the PV - 50/1.1^3 would get 50 to PV POSITIVE CASH FLOWS - Do 20 x 1.1^2 for year 1 - Do 30 x 1.1 for year 2 In discounting, you match the exponent to the year number. In compounding you take the total amount of years and subtract the number of the current year to get the exponent.

In the MIRR method of evaluating capital budgeting decisions, you have to discount negative cash flows and compound positive cash flows. Cost of capital is 10%. Y0 = -450 Y1 = 20 Y2 = 30 Y3 = -50 How would you do this?

Y0 would remain the same: -450 Y1: 60/1.1 = 50 450 - 50 = 400 Y2: 70/1.1^2 = 62 400 - 62 = 338... The exponent matches the year number for discounting It's balance remaining - discounted cash flow that year.

In the discounted payback method of evaluating capital budgeting, you must discount all future cash flows to the present value. Say you have a 10% cost of capital and the following cash flows... tell me how you would discount these numbers: Y0 = -450 Y1 = 60 Y2 = 70

No, because it's already embedded in the cost of capital. We would be counting it twice.

Is interest paid included in the calculation of incremental operating cash flows in capital budgeting? Why or why not?

Never change the payment amount because doing so ignores the time value of money. This is why we don't need to calculate the EAR for problems that provide a monthly payment with a yearly rate that compounds monthly, since we can just divide this rate by 12 and multiply the number of years by 12.

Is it okay to change the value of a payment in a TVM problem?

For every dollar invested in the project, $1.30 is made in profit. Also that $0.30 in NPV is added.

Let's say a project has a profitability index of 1.3. What does that mean?

- Doesn't quantify the addition to wealth in $ - Unconventional cash flows lead to multiple IRRs - Can't compare mutually exclusive events easily, have to use NPV as well

List some CONS of using the IRR

- Provides no information about the AMOUNT of capital at risk - Doesn't tell us anything about the margin of safety - Not ideal with a limited capital budgeting

List the CONS of using NPV for capital budgeting decision making

- Takes into account the time value of money - Provides the best indication of how much each project will increase the value of the firm because it gives $ amount of wealth increase/decrease - Takes into account all cash flows - incorporates risk in the discount rate - Uses cost of capital in reinvestment rate

List the PROS of using NPV for capital budgeting decision making

sunk cost

Money spent in the past that cannot be removed nor changed

1. Determining the NICO - Finding the depreciable base (startup costs and cost of asset) - Finding the change in NWC (+assets, -liabilities) 2. Making a depreciation schedule for each year - Using the depreciable base - Discovering if we will receive a tax benefit or loss upon selling the asset 3. Finding the incremental operating cash flows for each year - Including effects of opportunity costs or spillovers in revenue number 4. Finding the terminal cash flows - salvage value (+/-) tax consequence + change in NWC

Name the 4 general steps of the capital budgeting process...

TIME and INTEREST. So if time goes up, PV decreases, just like how if interest goes down, PV increases.

Present value is inversely correlated to what two factors?

B

RANDOM MC: An amortized loan: A. requires the principal amount to be repaid in even increments over the life of the loan. B. may have equal or increasing amounts applied to the principal from each loan payment. C. requires that all interest be repaid on a monthly basis while the principal is repaid at the end of the loan term. D. requires that all payments be equal in amount and include both principal and interest. E. repays both the principal and the interest in one lump sum at the end of the loan term.

D

RANDOM MC: You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why? A. You should accept the $89,500 today because it has the higher net present value. B. You should accept the $89,500 today because it has the lower future value. C. You should accept the first offer as it is a lump sum payment. D. You should accept the second offer because it has the larger net present value. E. It does not matter which offer you accept as they are equally valuable.

FIND THE PV OF THE HYPOTHETICAL ANNUAL PAYMENTS 1. 30,000 → PMT 2. 15 → N 3. 9 → I/Y 4. CPT → PV → -241,820.65 This means that at the point of retirement, Alex will need 241,820.65 to sustain this need. FIND THE ANNUAL PAYMENTS NEEDED TODAY 1. 241,820.65 → FV 2. 25 → N 3. I/Y → 9 4. CPT → PMT → 2,854.9952 each year.

RETIREMENT SAVINGS PROBLEM For retirement, Alex needs an additional $30,000 per year for his retirement years, which would be for about 15 years. He has 25 years until retirement. How much money should Alex save at the end of each year if they earn 9% per year?

FINDING ANNUAL PAYMENT OF ORDINARY ANNUITY 1. 6 → I/Y 2. 30 → N 3. 1,000,000 → FV 4. CPT → PMT → -12,648.9115

Suppose you earn a 6% annual return on your investments. You intend to retire in 30 years and want to make annual payments (starting at the end of this year) to accumulate $1,000,000 upon retirement. What should your minimum annual payment be?

FINDING MONTHLY PAYMENT OF ORDINARY ANNUITY 1. 1,000,000 → FV 2. 6 → / → 12 → = → I/Y (or .5 → I/Y) 3. 30 → x → 12 → = → N (or 360 → N) 4. CPT → PMT → -995.5053 per month

Suppose you earn a 6% annual return on your investments. You intend to retire in 30 years and want to make monthly payments (starting at the end of this month) to accumulate $1,000,000 upon retirement. What should your minimum MONTHLY payment be?

FALSE, it's a sunk cost

T/F: A marketing study done to determine if customers would want a new flavor is a relevant cash flow for the project

FALSE: It's fixed, so it's indifferent and independent to the cost of capital

T/F: An IRR value is affected by the cost of capital

FALSE: must be more than 1 year to be a capital budgeting decision

T/F: Capital budgeting is typically a short-erm process

FALSE: after-tax cash flows because taxes are cash outflows

T/F: In capital budgeting decisions, we are interested in pre-tax cash flows

TRUE

T/F: The IRR is a profitability measure

FALSE - this would be double counting the compounding

T/F: You can take an EAR and divide it by 12 to make a monthly rate

STEP 1: Discount all negative CF to PV -60 / (1.2)^0 = -60 -100 / (1.2)^2 = -69 STEP 2: Compound the positive CF to FV 155 x (1.2)^1 = 186 STEP 3: Add up all the positive and the negative numbers -60+-69 = -129 186 STEP 4: Put these values into the calculator to find new I/Y 1. -129 → PV 2. 186 → FV 3. 2 → N 4. CPT → I/Y → 19.87 WE WOULD REJECT BECAUSE ITS LESS THAN 20%, the required rate of return

The cash flows for a project are: T0 = -60 T1 = 155 T2 = -100 Find the MIRR given a 20% rate of return

opportunity cost

The next best alternative that is given up if a particular investment is undertaken

compounding

The process of finding the future value is called

discounting

The process of finding the present value is called

discounted cash flow valuation, used in NPV calculations

The process of valuing an investment by discounting its future cash flows is called ___________, and is the process used in _________.

opportunity cost

The value of the most valuable alternative activity that was given up if a particular investment is undertaken

Trick question: you would use NPV to determine. However, if that's not an option, we would chose the second option

There are 2 mutually exclusive projects. One has an IRR of 10.57% and the other has an IRR of 16.4%. Which would you choose?

Neither. Firstly, we would want to use NPV to rank mutually exclusive events, not IRR. However, the IRRs are below the firm's cost of capital/discount rate, so no matter if we could use IRR or not, neither would be chosen.

There are 2 mutually exclusive projects. The cost of capital is 17% at a firm. One project has an IRR of 10.57% and the other has an IRR of 16.4%. Which would you choose?

IRR and NPV

Typically, these two measures of accepting/rejecting projects return the same accept/reject conclusion:

PV OF UNEVEN CASH FLOWS: 1. CF → 2nd → CE|C 2. CF → enter → down 3. 300 → enter → down → 1 → down 4. 200 → enter → down → 1 → down 5. 600 → enter → down → 1 → down 6. 500 → enter → down → 1 → down 7. NPV → 6 → enter → down → CPT → $1,360.8366 FV OF UNEVEN CASH FLOWS 1. STO → 1 2. RCL → 1 → PV 3. 6 → I/Y 4. 4 → N 5. CPT → FV → $1,718.0248

UNEVEN CF PROBLEM Suppose an investment will produce the following cash flows: $300 one year from today, $200 two years from today, $600 three years from today, and $500 four years from today. Given 6% interest rate, what is the investment worth today? How much will it be at the end of year 4?

NWC and long-term assets

Undertaking a capital budgeting project will require investments in what?

The singular value of NPV ignores the fact that different projects have different initial outlays, this number does not tell us important starting information.

We don't choose NPV with a limited capital budget because....

Additional cash flow if any, if and only if the project is taken

What are incremental cash flows?

- Doesn't quantify $ amount addition to wealth - Provides no information about amount of capital at risk

What are some CONS of the profitability index?

- MIRR isn't truly an internal rate of return because it uses the required rate of return to discount/compound - Doesn't quantify the amount of $ added - provides no information about capital at risk

What are some CONS of using MIRR?

- Doesn't consider cash flows after payback - Might as well find the NPV - Subjective because of varying payback period requirements - Biased against long term investments

What are some CONS of using the discounted payback method?

- Uses the cost of capital as the re-investment rate - Useful when investment funds are limited - Closely related to NPV

What are some PROS of the profitability index?

- Adresses TVM - Allows us to look at it from a financial sense (takes into account TVM) - Allows us to assess liquidity + risk?

What are some PROS of using the discounted payback method?

1. sunk costs 2. financing costs like interest or dividends

What are some cash flows or costs that we exclude from relevant and incremental cash flows in capital budgeting?

1. Opportunity costs 2. Positive/negative spillovers 3. Investments in NWC 4. Depreciation 5. Start-up and set-up costs

What are some cash flows that we include in relevant and incrememntal cash flows in capital budgeting?

- Always a single MIRR, solves unconventional cash flow problem - Contains information about margin of safety - Objective decision criteria makes it easy to chose - Better indicator of TRUE EXPECTED RETURN, as it assumes cash inflows are reinvested at the cost of capital

What are some of the PROS of using MIRR?

- Does not take into account the TVM - It ignores the cash flows after the payback period - It's subjective since every firm has a different payback period policy - Ignores risk (no discount rate) - Biases us to short-term investments

What are the CONS of the payback period method

- It's intuitive - It's simple and easy to calculate - Leads us to projects that will pay back quickly (liquidity)

What are the PROS of the payback period method

If the MIRR is greater than the cost of capital/required rate of return, then accept If the MIRR is less than the cost of capital/required rate of return then we would reject

What are the criteria for using the MIRR when accepting or rejecting for independent projects?

1. Pure discount loan 2. Interest only loan 3. Amortized loan

What are the three types of loans?

Profitability

What does profitability index measure? (risk, liquidity or profitability)

If the project adds value on a stand-alone basis, then it will also add value to the firm overall.

What does the stand-alone basis mean for proposed capital budgeting projects?

Price of asset + delivery cost + installation cost + set-up cost + initial training costs

What elements go into the depreciable base of an asset in capital budgeting?

The projected increase in sales (if not given net revenue) - any change in expenses or costs (if not given net revenue) - any opportunity costs - any erosion + any positive spillovers

What elements go into the incremental revenue number at the top of the incremental operating cash flows?

An annuity in which cash flows continue forever, an example being preferred stock

What is a perpetuity and an example of it?

Borrowing money today and paying it all back in 1 sum plus interest in the future

What is a pure discount loan?

When the borrower repays the principal over the life of the loan, along with interest. The payments are fixed but the amount of principal/interest ratio paid off changes every year

What is an amortized loan?

An annuity with payments that occur at the beginning of each period Before you start an annuity due problem, do this: 2nd → BGN → 2ND → SET Then clear everything and it should say "BGN" up top. Calculate as normal and you can find the value as an annuity due. DON'T FORGET to clear the "BGN" by doing the same pattern of buttons to clear this setting before moving to your next problem.

What is an annuity due? How do you set this problem up on the calculator?

A series of equal payments which occur each period over a specified number of periods

What is an annuity?

the term (1+r)^n

What is the "future value interest factor"?

the term 1/(1+r)^n

What is the "present value interest factor" or the "discount factor"

PV = 1/(1+r)^n

What is the equation for manually finding the present value?

PI = [PV of future cash flows] / [PV of initial costs/investment]

What is the equation for the profitability index?

PV = PMT/r

What is the formula for finding the present value of a perpetuity?

Preferred stock is a perpetuity PV = PMT/r PV = 6/.063 PV = 95.24

What is the price of Westhampton Co's preferred stock if it pays a dividend of $6 per year and investors in the stock require a 6.3% return on their investment?

Calculate the EAR every time interest compounds more frequently than the payment.

What is the rule for using EAR versus APR?

An interest rate expressed in terms of the interest payment made EACH PERIOD. It excludes the impact of compounding.

What is the true definition of APR?

INT and PRN indicate the amount of interest and principal already paid off.

What two labels in the AMORT section of the calculator indicate values already paid?

MACRS (Modified Accelerated Cost Recovery System)

What type of depreciation system do we use in capital budgeting decisions?

It will always be less than the cost of capital

When NPV is negative, what will IRR look like?

It will always be greater than the cost of capital

When NPV is positive, what will IRR look like?

It will always be equal to the cost of capital

When NPV is zero, what will IRR look like?

NPV, type the interest rate, enter, down, CPT.

When calculating a stream of uneven cash flows, what is the last button you will press that will get you the PRESENT VALUE?

When there is more than 1 sign change in the cash flows... Example: - + + - + cash flows would produce 2 different IRRs

When can you NOT use conventional IRR?

No. Only for however long you plan on keeping the asset.

When creating the depreciation schedule, do you do it for the asset's entire life?

Increases in inventory or A/R will be positive. An increase in A/P will decrease the [inventory+A/R] number because it's a benefit and not an investment.

When figuring out the value for the total change in NWC for step 1 of capital budgeting, how do you handle increases in inventory, increases in A/R and increases in A/P?

compounding interest

When interest in earned on interest

A change in the firm's overall future cash flow that comes about as a DIRECT CONSEQUENCE of the decision to take that project

When making capital budgeting decisions, determining relevant cash flows is an important step. What are relevant cash flows?

stand-alone basis

When we evaluate proposed capital budgeting projects, we evaluate them on a ____________ basis

The periodic rate, which is equal to the APR/the number of periods per year.

When we find an interest rate per month, what is it called?

Annuity due because you benefit from having that initial payment upfront that begins earning interest asap.

Which creates more money saved: annuity due or ordinary annuity?

Because we made the initial investment in NWC by buying inventory or supplies, so it's negative in the beginning. By the end, we are reaping the benefits of this investment, thus, this number turns positive in the final calculations

Why do we add back the change in NWC when finding terminal cash flows in capital budgeting decisions?

NPV, IRR, MIRR and profitability index

With independent projects, which measures all lead to the same accept/reject decision?

FINDING INTEREST RATE 1. 3 → +/- → PV 2. 98 → FV 3. 10 → N 4. CPT → I/Y → 41.7133

You bought a stock 10 years ago for $3 per share and the same stock is now selling for $98 per share. What is the compound annual rate of growth of this stock?

FINDING FV 1. 2nd → CLR TVM → CE/C 2. 7000 → +/- → PV 3. 6.1 → I/Y 4. 5 → N 5. CPT → FV → 9,411.8492

You have $7,000 to invest into a bond fund that currently has a return of 6.1% per year. Assuming the fund continues to have similar returns each year, how much money will you have in your investment fund at the end of a 5-year period??

FINDING PV ORDINARY ANNUITY 1. 2nd → CLR TVM → CE/C 2. 10000 → PMT 3. 20 → N 4. 8 → I/Y 5. CPT → PV → -98,181.4741

You have inherited some money and want to set up an annuity to allow yourself to enjoy this money over time instead of using it all at once. You would like to pay yourself $10,000 per year for the next 20 years and your money will be invested at a rate of 8% per year during this time. How much money must you invest in this account today to make this happen?

Note: You HAVE to find an EAR because the interest compounds more frequently (monthly) than the payments that we are trying to find (annual). 1. 5,000 → FV 2. 2 → N 3. 2nd → ICONV → 9 4. ENTER → down → down 5. 12 → ETNER → down → down 6. CPT → CE/C → I/Y 7. CPT → PMT → -2,387.9948

You want to save $5,000 for a trip that you plan to take in 2 years. You can invest your savings at a rate of 9% compounded monthly. What ANNUAL payment must you make to have $5,000 in this account after 2 years?

FINDING FV OF ORDINARY ANNUITY 1. 2nd → CLR TVM → CE/C 2. 1500 → +/- → PMT 3. 18 → N 4. 6.5 → I/Y 5. CPT → FV → 48,615.1011

You wish to save $1,500 per year to use for a European vacation you have planned for your 20th wedding anniversary, which will be in 18 years. If you can invest your savings at 6.5% per year, how much money will you have when it is time for your vacation?

FINDING FV OF ANNUITY DUE 1. 2nd → BGN → 2nd → SET → CE/C 2. 2400 → +/- → PMT 3. 18 → N 4. 5.75 → I/Y 5. CPT → FV → 76606.2549

Your parents are going to deposit $2,400 per year, at the beginning of each year, in a college fund for your newborn child's education. If you child will start college at age 18, how much money will your parents have in this fund when your child begins college? (i=5.75%)

NPV

__________ is considered the "superior" decision making technique in capital budgeting.