Keen Chapter 9

For the following cash flow pattern of ​-$486 in period ​zero, ​$265 in period ​1, and ​$281 in period ​2, is the IRR ​ above, below or equal to​ 10%?

486=265/1.0x+281/1.0x^2 Hence x=irr=8.04%(Approx). Hence irr is less than 10%

Acorn Corporation is considering a project with an initial cash outlay of​ $50,000 and expected​ after-tax inflows of​ $20,000, $40,000 and​ $6,000 over the​ three-year life of the​ project, respectively. Is​ 13% the IRR of this​ project?

Sum future cash flows @ 13% = -50000 / (1+13%)^0 + 20000 / (1+13%)^1 + 40000 / (1+13%)^2 + 60000 / (1+13%)^3 = 40,607.99 Sum is more than zero hence IRR is more than 13%

A project has the following incremental cash flows for years​ zero, through year​ 4, respectively: ​ -$3,000, $1,900,​ $900, and​ $800. Is​ 9% the IRR of this​ project? If​ not, is where is the IRR compared to​ 9%?

The project should be rejected because the IRR is less than the cost of capital.

The discounted payback period method takes __________ into consideration.

Time Value of Money

Projects that do not compete with one another so that the acceptance of one project will have no bearing on the acceptance of other projects being considered by the firm are known as:

independent projects

MIRR is used when:

cash flows of a project change sign

What is the NPV of a project expected to generate $1,000 a year for 5 years assuming a discount rate of 10% and an initial outlay of $3,250?

$540.79 -The easiest way to solve this problem is to use a financial calculator with the following inputs: PMT = -$1,000; N = 5; I / Y = 10%; CPT PV. PV is equal to $3,790.79 - $3,250 = $540.79. Since the NPV is positive, the project should be accepted.

Assume you have two projects with different lives. Project A is expected to generate present value cash flows of $5.2 million and will last 7 years. Project B is expected to generate present value cash flows of $3.8 million and will last 5 years. Given a required return of 9%, Project A has an equivalent annual annuity of __________ which is __________ than Project B.

-1.03319 million, better -Project A: PV = -$5.2; N = 7; I / Y = 9%; FV = 0; CPT PMT and you get $1.03319 million Project B: PV = -$3.8; N = 5; I / Y = 9%; FV = 0; CPT PMT and you get $.97695 million Project A should be selected since it has a higher EAA.

A firm is evaluating an investment proposal, which has an initial investment of $8,000 and discounted cash flows valued at $6,000. The net present value of this investment is:

-2000

A firm is evaluating a proposal which has an initial investment of $45,000 and has cash flows of $5,000 in year 1, $20,000 in year 2, $15,000 in year 3, and $10,000 in year 4. The payback period of the project is:

-3.5 years -The payback period is the length of time it takes to recover the initial investment so in this case you see that a total of $40,000 is recovered in the first three years, which leaves $5,000 to be recovered. In the fourth year, you will generate $10,000 so the fraction of the year required to capture the remaining $5,000 investment is $5,000/$10,000 or 0.5. The payback period is, therefore, 3.5 years.

Assume that you expect to sell a stock for $50 in two years and your required return is 8%. If the stock is currently selling for $41, what is its NPV?

-The only expected cash flow in this example is the forecasted selling price of the stock which is $50. So, the NPV is equal to the present value of the expected cash flows minus the current price which is: NPV = [$50/(1.08)2] - $41 = $42.87 - $41 = $1.87.

Which of the following decision rules is always correct because it is directly tied to the goal of maximizing shareholder wealth?

NPV rule

​Dice, Inc. is considering a project that has an initial outlay or cost of​ $70,000. The​ project's only expected cash inflow is to occur in year 7 and be equal to​ $124,000. What is the IRR of this​ project?

8.51

The NPV is the PV of all of a​ project's outflows minus the PV of all inflows.

False

The capital budgeting rule is to accept a project if the IRR​ > NPV.

False

To be considered​ acceptable, a project must have an NPV greater than 1.0.

False Greater than 0

A firm's minimum required return on a capital budgeting project is known as the

Hurdle rate

Consider a​ project's incremental cash flows in​ order: ​ -$700, $400,​ $300, $400. Assume a cost of capital of​ 7%. How does the NPV that you get by using​ Excel's NPV function all by itself compare to the correct NPV for this​ project?

Lower Check NOTES

A firm has undertaken a project with an initial investment of $100,000. The firm's cost of capital is 14% What is the NPV for this project?

NPV = $50,000/(1.14) + $65,000/(1.14)2 + $90,000/(1.14)3 - $100,000 = $43,860 + $50,015 + $60,748 - $100,000 = $54,623

Chris has been offered the chance to invest $120,000 in a partnership, which is expected to return $25,000 per year. If Chris is in the 30% tax bracket and limits investments to those with a payback of six years, should Chris invest?

No, because the payback period is 6.86 years. -To calculate the payback you need to calculate Chris' annual cash return which is equal to $25,000 (1 - 0.30) = $17,500 per year in after-tax proceeds from the investment. Given that annual amount, his payback is equal to $120,000 / $17,500 = 6.86 years. Since the payback exceeds his six year cut off he should not make the investment.

Jenna is considering an investment which has a price of $16,000. She expects to receive $3,000 for eight years. What is the investment's internal rate of return?

PV = -$16,000 N = 8; FV = 0 PMT = $3,000 CPT I/Y, which gives you 10.0082 or approximately 10%.

Which of the following decision rules is always correct because it is directly tied to the goal of maximizing shareholder wealth?

hurdle rule

What is the discounted payback of a project that has an initial outlay of $20,000 and will generate $6,000 in year 1, $12,000 in year 2, $9,000 in year 3, and $14,000 in year 4 assuming the cost of capital is 10%?

To compute the discounted payback you have to calculate the present value of each cash flow and subtract these values from the initial outlay to determine how long it takes to recover the investment after considering the time value of money. The PVs of each cash flow using a 10% discount rate are: PV of year 1 = $6,000/(1.1) = $5,455 PV of year 2 = $12,000/(1.1)2 = $9,917 PV of year 3 = $9,000/(1.1)3 = $6,762 PV of year 4 = $14,000/(1.1)4 = $9,562 So the discounted payback is equal to: Initial outlay = $20,000 - $5,455 - $9,917 = $4,628 remaining to be recovered after two years. So, discounted payback = 2 years + $4,628/$6,762 = 2.68 years.

Accept/reject decisions based on the IRR rule usually agree with those based on the NPV rule.

True

Excel's NPV function treats CF in year 1 as the CF in year 2.

True

The Excel function that will yield the correct result without any modificaiton is the IRR function..

True

The NPV tells us the expected dollar impact of a proposed project on the value of a firm.

True

When the IRR exceeds the cost of​ capital, the NPV will be positive.

True

A firm must choose from 5 capital budgeting proposals outlined below. The firm is subject to capital rationing and has a capital budget of $500,000. The firm's cost of capital is 12%. Using the internal rate of return approach to ranking projects, which projects should the firm accept?

Using the internal rate of return approach to ranking projects, the firm should accept projects 1,2,3 and 5. Using IRR, the firm should accept any project that generates an IRR at least as high as the firm's cost of capital. The only project that does not exceed the firm's 12% cost of capital is project 4.

An investment costs​ $875,000 today and is expected to produce a​ one-time inflow at the end of year 8 of​ $1,430,000. What is the IRR of this​ project?

Year Cash Flows 0 -875000 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 1430000 IRR = 6.33%

profile is __________.

a graph of a project's NPV over a range of different discount rates

When using the net present value (NPV) to evaluate capital budgeting projects, you should:

accept all projects with a positive NPV

Incremental cash flows are estimated to be in order​ -$20M, $5M,​ $12M, and​ $7M. If the cost of capital is​ 10%, what is the NPV of this​ project?

cashflow(in million) PVF@10% Discounted cashflow -$20 1 -$20 $5 0.9091 4.5455 $12 0.8264 9.9168 $7 0.7513 5.2591 NPV -0.2786

One method that can be used to evaluate capital budgeting projects with different lives is to convert the project's cash flows to a level annual cash flow that has the same present value as the project's overall cash flows. This annual cash flow is known as the:

equivalent annual annuity

Capital budgeting is the process of:

evaluating a firm's investment choices

Unlike the IRR criteria, the NPV approach assumes an interest rate equal to the:

firm's cost of capital

unlike the IRR criteria, the NPV approach assumes an interest rate equal to the:

firm's cost of capital

When resources are limited you should select the projects with the:

highest NPV

The IRR can lead to incorrect project rankings because projects with much higher NPVs may also have:

longer project lives

As you increase the required return used in an NPV calculation, the likelihood of a __________ NPV __________.

negative, increases

The profitability index is a ratio of the:

present value of benefits to the present value of costs.

In order to calculate a project's NPV, you need to know the appropriate discount rate, the amount of the initial outlay, and:

the amount and timing of the expected cash flows