Capital Investments quiz

Based on the IRRs, the move to South Carolina will have a positive NPV (the IRR is greater than the discount rate) and the move to Texas will have a negative NPV. In this case, we can rank the two projects based on their IRRs. If the appropriate discount rate was less than both IRRs, for example, 10%, the IRR rankings could not reliably be used to choose between the two proposed moves .

Going concern projects are those to maintain the business or to increase the efficiency of existing operations. The other two projects are business growth investments that increase the size of the company .

The IRR would stay the same because both the initial outlay and the after-tax cash flows double, so the return on each dollar invested would remain the same. All the cash flows and their present values double. The difference between the total present value of the future cash flows and the initial outlay (the NPV) also doubles .

Financing costs are reflected in a project's required rate of return. Project specific financing costs should not be included as project cash flows. The firm's overall weighted average cost of capital, adjusted for project risk, should be used to discount expected project cash flows.

Mutually exclusive means that out of the set of possible projects, only one project can be selected. Given two mutually exclusive projects, the company can accept one of the projects or reject both projects, but cannot accept both projects .

The key is first identifying this as a NPV problem. The minimum price the company should accept for selling the property is the net present value of the mine if the company built and operated it.

Next, the year of each cash flow must be property identified; specifically: CF0 = –430,000 ; CF1-7 = +$200,000 ; CF8 = –$170,000.

Entering these values into the cash flow worksheet:

CF0 = –430,000 ; C01 = 200,000; F01 = 7 ; C02 = –170,000 ; F02 = 1 ; I = 16 ; CPT NPV = 325,858.76

Arranging financing is not one of the administrative steps in the capital budgeting process. The four administrative steps in the capital budgeting process are:

1. Idea generation

2. Analyzing project proposals

3. Creating the firm-wide capital budget

4. Monitoring decisions and conducting a post-audit

Discount rates of 0% and approximately 61.8% both give an NPV of zero

CF0 = – 50 ; CF1 = 100 ;  CF2 = 0 ; CF3 = - 50 ; I = 0 ; CPT NPV = 0

CF0 = – 50 ; CF1 = 100 ;  CF2 = 0 ; CF3 = - 50 ; I = 32 ; CPT NPV = 4.0181

CF0 = – 50 ; CF1 = 100 ;  CF2 = 0 ; CF3 = - 50 ; I = 62 ; CPT NPV = - 0.0321

If demand is “high,” the NPV is as follows:

CF0 = – 190 ; CF1 = 40 ; F1 = 10;  I = 10 ; CPT NPV = 55.78

If demand is “low,” the NPV is

CF0 = – 190 ; CF1 = 20 ; F1 = 10;  I = 10 ; CPT NPV = - 67.11

CF0 = – $336,875

CF1 = $100,000

CF2 = $ 82,000

CF3 = $ 76,000

CF4 = $ 111,000

CF5 = $ 142,000

 I= 8

 CPT → NPV =  $64,582

or

To determine the net present value of the investment, given the required rate of return, we can discount each cash flow to its present value, sum the present value, and subtract the required investment.

Sunk costs are not to be included in investment analysis. Opportunity costs and the project's impact on taxes are relevant variables in determining project cash flow for a capital investment.

CF0 = –$550,000 ;  CF1 = $65,000 ; F1 = 5;  CF2 = $50,000; F2 = 3;   CF3 = $350,000; F3 = 1 . CPT IRR = 7.0152.

Note that the cash flows in year 9 have to be netted to calculate the IRR correctly.

Cf0 = -775,000 , C01 = 0, F01 = 1,  C02 = 300,000, F02 = 2,  C03 = 400,000, F03 = 1;  IRR = 8.6534

or

Cf0 = -775,000 , C01 = 0,  C02 = 300,000,  C03 = 300,000, C04 = 400,000 ;  IRR = 8.6534

There are many factors that can affect the stock price, including whether Ms. Ndereba’s analysis indicates that the project is more or less profitable than investors expected .

The cost of the marketing survey should not be included because it is a sunk cost; it will be incurred whether they decide to do the project or not. The decrease in sales of their current sauce if the spicier version is introduced (cannibalization) should be considered in the analysis. The cost of recipe development should be included because it will only be incurred if they decide to go ahead with the introduction of the new spicier sauce .

Because all Bearing’s projects have a positive NPV, they are all providing a return that is greater than the opportunity COC. Therefore, the ROIC must be greater than the COC .

CFO = -2,2; CF1 = 1,3; CF2 = 1,6 ; CF3 = 1,9; CF4 = 0,8 ;  I = 8 ; CPT → NPV = $2,47

or

Externalities refer to the effects that the acceptance of a project may have on other firm cash flows. Cannibalization is one example of an externality.

Sunk costs should be excluded from cash flows, as they are costs that cannot be avoided even if the project is not undertaken. Externalities, such as positive or negative effects of accepting a project on sales of the company's existing products, should be included in the cash flows.

Using a financial calculator or the trial and error method, the IRR is 28.79%. The COC, which is stated as 10%, is not used to solve the problem.

Using a financial calculator:

Cf0 = -150,000 ;C01 = 100,000 ; C02 = 120,000 ; CPT IRR = 28.7855

Key principles of the capital allocation process are :

1. Decisions are based on cash flows, not accounting income .

2. Cash flows are based on opportunity costs .

3. The timing of cash flows is important .

4. Cash flows are analyzed on an after-tax basis .

5. Financing costs are reflected in the project's required rate of return .

In theory, a positive NPV project should provide an increase in the value of a firm's shares.

NPV of new capital equipment = $50 million - $30 million = $20 million

Value of company prior to equipment purchase = 8,000,000 × $28.00 = $224,000,000

Value of company after new equipment project = $224 million + $20 million = $244 million

Price per share after new equipment project = $244 million / 8 million = $30.50

Note that in reality, changes in stock prices result from changes in expectations more than changes in NPV.

Project X

CF0 = – 15,000 ; CF1 = 2,000 ;  CF2 = 5,000 ; CF3 = 8,000 ; CF4 = 8,000 ; I = 15 ; CPT NPV = 354.0046

IRR= 16 % (given)

Project Y

CF0 = – 13,250 ; CF1 = 200 ;  CF2 = 500 ; CF3 = 7,000 ; CF4 = 15,000 ; I = 15 ; CPT NPV = 480.8972

CF0 = – 13,250 ; CF1 = 200 ;  CF2 = 500 ; CF3 = 7,000 ; CF4 = 15,000 ;  CPT IRR = 16.1542

Because these projects are mutually exclusive, only one can be undertaken: It should be Project Y, which has the highest NPV and thus increases shareholder wealth the most. Both projects’ IRRs exceed the hurdle rate, and the IRR of Project Y exceeds that of Project X. The decision, however, should be based on the superior NPV of Project Y

(Both projects ) is incorrect. Both NPV_X and NPV_Y are positive, but because they are mutually exclusive projects, only the one with higher positive NPV will be chosen

The IRR is the discount rate that makes the NPV = 0. Because the cash flow stream is in perpetuity, it can be solved as follows:

0 = –270 + (30/IRR)

IRR = 11.1%

When valuing mutually exclusive investments, the decision should be made with the NPV method because this method uses the most realistic discount rate—namely, the opportunity cost of funds. In this example, the reinvestment rate for the NPV method (here, 10%) is more realistic than the reinvestment rate for the IRR method (here, 21.86% or 18.92%) .

The option to abandon the project and receive the market value of the facility if actual cash flows are less than expected over the first two years can be viewed as a valuable put option that should be included in the calculation of the project’s NPV. 

A post-audit identifies what went right and what went wrong. It is used to improve forecasting and operations .

In valuing investments, expected cash flows should be discounted at required rates of return that reflect their risk, not at a risk-free rate that ignores risk. NPV is superior to IRR. Choosing projects based on IRR might cause the company to concentrate on short-term investments that do not maximize the company’s NPV . 

Mandatory regulatory or environmental projects may be required by a governmental agency or insurance company and typically involve safety-related or environmental concerns. The projects typically generate little to no revenue, but they accompany other new revenue producing projects and are accepted by the company in order to continue operating .

Project P ⇒ N = 5; PMT = 5,000; FV = 0; I/Y = 12; CPT → PV = 18,024;  NPV for Project A = 18,024 – 15,000 = 3,024.
Project Q ⇒ N = 5; PMT = 7,500; FV = 0; I/Y = 12; CPT → PV = 27,036;  NPV for Project B = 27,036 – 25,000 = 2,036.

For independent projects the NPV decision rule is to accept all projects with a positive NPV. Therefore, accept both projects.

or

Project P  ⇒ Cf0 = -15,000, C01 = 5,000, F01 = 5,  I = 12 ;  CPT NPV = 3,024.

Project Q  ⇒ Cf0 = -25,000, C01 = 7,500, F01 = 5,  I = 12 ;  CPT NPV = 2,036.

CFO = -100; CF1 = 40 ; CF2 = 80 ; CF3 = 120 ; I = 20 ; CPT → NPV = $ 58.33

or

For these investments, a discount rate of 13.16% would yield the same NPV for both (an NPV of 6.73).

We subtract the two investments from each other:

CF0 = – 100 - (– 100)  = 0

CF1 = 36 - 0 = 36   ; F1 = 3

CF2 = 36 - 175 = - 139   ; F1 = 1

CPT IRR = 13.159

CF0 = – 100 - (– 100)  = 0

CF1 = 36 - 0 = 36   ; F1 = 3

CF2 = 36 - 175 = - 139   ; F1 = 1

I= 13.159

CPT NPV = 6.7282

Rescheduling and prioritizing projects is part of the planning stage of the capital budgeting process, not the post-audit. The post-audit’s purpose is to explain any differences between the actual and predicted results of a capital budgeting project. This process can aid in indicating systematic errors, improve business operations, and provide concrete ideas for future investment opportunities.

The IRR is computed by identifying all cash flows and solving for the rate that makes the NPV of those cash flows equal to zero.

CF0 = – 4,662,005  ; CF1 = 22,610,723  ; CF2 = ‒ 41,072,261  ; CF3 = 33,116,550  ;CF4 = ‒ 10,000,000  ;  I = 8  ; CPT NPV = ‒ 307.7589

CF0 = – 4,662,005  ; CF1 = 22,610,723  ; CF2 = ‒ 41,072,261  ; CF3 = 33,116,550  ;CF4 = ‒ 10,000,000  ;  I = 15  ; CPT NPV = 99.9354

CF0 = – 4,662,005  ; CF1 = 22,610,723  ; CF2 = ‒ 41,072,261  ; CF3 = 33,116,550  ;CF4 = ‒ 10,000,000  ;  I = 8  ; CPT NPV = ‒ 0.0120

Using either the IRR function in Excel or a financial calculator, IRR is determined by setting the NPV equal to zero for the cash flows shown in the following table

CFO = -1,000; CF1 = 200; CF2 = 200; CF3 = 900;  CPT →  IRR = 11.0258

Calculate the PV of the project cash flows

N = 5, PMT = -3,000, FV = 0, I/Y = 9.7, CPT → PV = 11,460

Calculate the project NPV by subtracting out the initial cash flow

NPV = $11,460 – $10,000 = $1,460

or

CF0 = –$10,000 ; CF1 = $3,000 ; F1 = 5 ; I= 9.7  CPT → NPV = $1,460

or

CF0 = –$10,000

CF1 = $3,000 

CF2 = $3,000

CF3 = $3,000 

CF4 = $3,000 

CF5 = $3,000 

 I= 9.7

 CPT → NPV = $1,460

The projects are independent, meaning that either one or both projects may be chosen. Both projects have positive NPVs, therefore both projects add to shareholder wealth and both projects should be accepted.

The NPV of the new equipment is $700 million - $400 million = $300 million.

The NPV of this project is added to Fullen’s current market value.

On a per share basis, the addition is worth $300 million / 200 million shares, for a net addition to the share price of $1.50.  $36.00 + $1.50 = $37.50.

Stock prices reflect investor expectations for future investment and growth. A new positive-NPV project will increase stock price only if it was not previously anticipated by investors .

Expansion projects increase the scale of a firm’s existing activities and/or extend a firm’s reach into new product or service categories and markets, in the hopes of generating longer-term expected gains. Regulatory/compliance projects are required for the business to continue operations but otherwise might not be undertaken by a company. Going concern projects benefit the company through improved efficiencies and cost savings over time .

Since the sale was not anticipated by the market, the share price should rise by the NPV of the project per common share. NPV is already calculated using after-tax cash flows.

Using either the IRR function in Excel or a financial calculator

CFO = -50,000; CF1 = 15,000; CF2 = 15,000; CF3 = 20,000; CF4 = 10,000 ; CF5 = 5,000  I = 8; CPT → NPV = $3,378.83

CFO = -50,000; CF1 = 15,000; CF2 = 15,000; CF3 = 20,000; CF4 = 10,000 ; CF5 = 5,000   CPT → IRR = 10.8795 

or

NPV = -50, 000 + 13, 888.89 + 12, 860.08 + 15, 876.64 + 7, 350.30 + 3, 402.92

NPV = -50, 000 + 53, 378.83 = 3, 378.83

The project should be accepted on the basis of its positive NPV and its IRR, which exceeds the cost of capital.

CF0 = – $28,000 ; CF1 = $7,000 ; F1 = 4 ; CF2 = $6,000 ; F2 = 2 ; CPT → IRR = 11.6175% .

Cash flows are based on opportunity costs. Financing costs are recognized in the project’s required rate of return. Accounting net income, which includes non-cash expenses, is irrelevant; incremental cash flows are essential for making correct capital allocation decisions .

CF0 = –5,000 ; CF1 = 3,000 ; CF2 = 2,000 ; CF3 = 2,000 ; I / Y = 10 ; NPV = $883 

Using a financial calculator :

CF0 = – 750 ; CF1 = 175 ; F1 = 7; CPT IRR = 14.0198

CF0 = – 750 ; CF1 = 175 ; F1 = 7;  I = 10 ; CPT NPV = 101.9733

A new project reducing the cash flows of an existing project is an externality called cannibalization .

NPV for Project X ⇒ CF0 = – 100,000 ; C01 = 50,000; C02 = 40,000; C03 = 30,000; C04 = 10,000; I = 15; CPT NPV = -833

NPV for Project Z ⇒ CF0 = – 100,000 ; C01 = 10,000; C02 = 30,000; C03 = 40,000; C04 = 60,000; I = 15; CPT NPV = - 8,014

Reject both projects because neither has a positive NPV.

CFO = -100,000;  CF1 = 10,000;  CF2 = 15,000;  CF3 = 138,000;  I = 12; CPT → NPV = $19,112.

The NPV sums the investment’s expected cash flows (CF) discounted at the opportunity COC. The NPV calculation is 

where

CFt = the expected net cash flow at time t

N = the investment’s projected life

r = the discount rate or opportunity COC

When the NPV = 0, this means the discount rate used is equal to the IRR. If a discount rate is used that is higher than the IRR, the NPV will be negative. Conversely, if a discount rate is used that is lower than the IRR, the NPV will be positive

Costs to finance the investment are taken into account when the cash flows are discounted at the appropriate COC; including interest costs in the cash flows would result in double-counting the cost of debt .

he given cash flows are inserted into a financial calculator along with the 10% discount rate:

CF₀ = −1,500, CF₁ = 300, CF₂ = 600, CF₃ = 1,000, CF₄ = 200, CF₅ = 500, CF₆ = 300, I = 10. Computing NPV the result is 636.32 ~ 636 .

The NPV rule’s assumption about reinvestment rates is more realistic and more economically relevant than the IRR rule because it incorporates the market-determined opportunity cost of capital as a discount rate. In contrast, the IRR calculation assumes reinvestment at the IRR, which sometimes cannot be achieved because it is too high. Time-weighted rate of return suffers similar shortcomings as IRR.

It is quite possible that offering a matching dryer will increase sales of their washers, because some consumers will prefer a matching set. The increased sales of their washers is a positive externality, and those incremental sales should be considered in the analysis. Cannibalization would be a consideration if the introduction of dryers was expected to decrease washer sales. Sunk costs should not be considered in project analysis .

Introducing a new product or entering a new market involves sales and expense projections that can be highly uncertain, and therefore require the greatest degree of detailed analysis. Addressing safety or regulatory concerns or replacing old machinery typically involve less uncertainty and do not require the same depth of analysis as developing a new product or entering a new market .

he study is a sunk cost, and the possible increase in sales of a related product is an example of a positive externality.