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Capital budgeting decision methods

A measure of a company's financial health. Equals cash receipts minus cash payments over a given period of time

it can be showed in graphic matter:

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Example:

Cash Flow- We are going to assume that the project we are considering approving has the following cash flow. Right now, in year zero we will spend 15,000 dollars on the project. Then for 5 years we will get money back as shown below.

|Year |Cash flow |

|0 |-15,000 |

|1 |+7,000 |

|2 |+6,000 |

|3 |+3,000 |

|4 |+2,000 |

|5 |+1,000 |

In a graphic view:

[pic]

|Accounting Rate of Return (ARR) |

PAYBACK PERIOD (PP)

Payback - When exactly do we get our money back, when does our project break even. Figuring this is easy. Take your calculator. But first

the formula for Payback Period

[pic]

the calculator example:

|Year |Cash flow |Running Total | |

|0 |-15,000 |-15,000 | |

|1 |+7,000 |-8,000 |(so after the 1st year, the project has not yet broken even) |

|2 |+6,000 |-2,000 |(so after the 2nd year, the project has not yet broken even) |

|3 |+3,000 |+1,000 |(so the project breaks even sometime in the 3rd year) |

But when, exactly? Well, at the beginning of the year we had still had a -2,000 balance, right? So do this.

|Negative Balance / Cash flow from the Break Even Year |=|When in the final year we break even |

|-2,000 / 3,000 |=|.666 |

So we broke even 2/3 of the way through the 3rd year. So the total time required to payback the money we borrowed was 2.66 years.

Another Payback Period Example

I will begin with an illustration that finds payback period for an example investment proposal. Let us say, we were offered a series of cash inflows at the end of each of the next four years as $5000, $4000, $3000, and $1000. Assuming the initial cash outlay for this proposal is $10,000. We are faced with finding the payback period for this hypothetical investment. Below you will find a tabular format that shows the time period, the corresponding cash flow, and the cummulative sum of the cash flows

| | | |

|Year |Cash Flows |Cumulative Cash Flows |

|0 |-$10,000 | |

|1 |$5,000 |$5,000 |

|2 |$4,000 |$9,000 |

|3 |$3,000 |$12,000 |

|4 |$1,000 |$13,000 |

| | | |

Payback Period Step by Step

We add up the cash inflows beginning after the initial cash outlay in the cumulative cash inflows column

We keep an eye on this last column and track the last year for which the cumulative total does not exceed the initial cash outlay

We compute the part or fraction of the next year's cash inflow need to payback the initial cash outlay by taking the initial cash outlay less the cumulative total in the last step then divide this amount by the next years cash inflow.

E.g., ( $10,000 - $9,000 ) / $3,000 = 0.334

Since we said these were annual cash flows thus to obtain the payback period in years , we take the figure from the last step and add it to the year from the step 2.

Thus our payback period is 2 + .334 = 2.334 years

Instead of representing the years as a decimal value we could represent the payback period in years and months this way We take the fraction 0.334 and multiply it by 12 to get the months which is 4.01 months. Thus our payback period is 2 years and 4 months

PV and FV:

|Present Value |How much you got now. |

|Future Value |How much what you got now grows to when compounded at a given rate |

I give you 100 dollars. You take it to the bank. They will give you 10% interest per year for 2 year.

• The Present Value = $ 100

• Future Value = $121.

|FV= PV (1 + i )N |

• FV = Future Value

• PV = Present Value

• i = the interest rate per period

• n= the number of compounding periods

Determine Future Value Compounded Annually

What is the future value of $34 in 5 years if the interest rate is 5%? (i=.05)

• FV= PV ( 1 + i ) N

• FV= $ 34 ( 1+ .05 ) 5

• FV= $ 34 (1.2762815)

• FV= $43.39.

Determine Future Value Compounded Monthly

What is the future value of $34 in 5 years if the interest rate is 5%? (i equals .05 divided by 12, because there are 12 months per year. So 0.05/12=.004166, so i=.004166)

• FV= PV ( 1 + i ) N

• FV= $ 34 ( 1+ .004166 ) 60

• FV= $ 34 (1.283307)

• FV= $43.63.

Determine Present Value Compounded Annually

You can go backwards too. I will give you $1000 in 5 years. How much money should you give me now to make it fair to me. You think a good interest rate would be 6% ( You just made that number up). (i=.06)

• FV= PV ( 1 + i ) N

• $1000 = PV ( 1 + .06) 5

• $1000 = PV (1.338)

• $1000 / 1.338 = PV

• $ 747.38 = PV

O.K. so you give me $ 747.38 today and in 5 years I'll give you $1000. Sound fair?? You will get 6% interest on your money.

Determine Present Value Compounded Monthly

Here's that last one again, but with monthly compounding instead of annual compouding. (i equals .06 divided by 12, because there are 12 months per year so 0.06/12=.005 so i=.005)

• FV= PV ( 1 + i ) N

• $1000 = PV ( 1 + .005) 60

• $1000 = PV (1.348)

• $1000 / 1.348= PV

• $741.37 = PV

Teachers note:

I have just add the monthly calculation just for example. In Economy / finance at the B2B market, its normally the annually calculation we use.

Cost of capital

The cost of capital is the required rate of return that a firm must achieve in order to cover the cost of generating funds in the marketplace

The firm must earn a minimum of rate of return to cover the cost of generating funds to finance investments; otherwise, no one will be willing to buy the firm’s bonds, preferred stock, and common stock

In connecton with an investment.

Cost of capital refers to the opportunity cost of making a specific investment. It is the rate of return that could have been earned by putting the same money into a different investment with equal risk. Thus, the cost of capital is the rate of return required to persuade the investor to make a given investment.

Example:

Let's assume Company XYZ is considering whether to renovate its warehouse systems. The renovation will cost $50 million and is expected to save $10 million per year over the next 5 years. There is some risk that the renovation will not save Company XYZ a full $10 million per year. Alternatively, Company XYZ could use the $50 million to buy equally risky 5-year bonds in ABC Co., which return 12% per year.

Because the renovation is expected to return 20% per year ($10,000,000 / $50,000,000), the renovation is a good use of capital, because the 20% return exceeds the 12% required return XYZ could have gotten by taking the same risk elsewhere

Difference i definitions:

Cost of Capital A:

The difference in return between an investment one makes and another that one chose not to make. This may occur in securities trading or in other decisions. For example, if a person has $10,000 to invest and must choose between Stock A and Stock B, the cost of capital is the difference in their returns. If that person invests $10,000 in Stock A and receives a 5% return, while Stock B makes a 7% return, the cost of capital is 2%

Cost of capital B:

The overall percentage cost of the funds used to finance a firm's assets.

Teacher note: We use variant B. Also inlignment with the initial words.

Variant of payback:

Discounted Payback - is almost the same as payback, but before you figure it, you first discount your cash flows. You reduce the future payments by your cost of capital. Why? Because it is money you will get in the future, and will be less valuable than money today. For this example, let's say the cost of capital is 10%.

|Year |Cash flow |Discounted Cash flow |Running Total |

|0 |-15,000 |-15,000 |-15,000 |

|1 |7,000 |6,363 |-8,637 |

|2 |6,000 |4,959 |-3,678 |

|3 |3,000 |2,254 |-1,424 |

|4 |2,000 |1,366 |-58 |

|5 |1,000 |621 |563 |

So we break even sometime in the 5th year. When?

|Negative Balance / Cash flow from the Break Even Year |=|When in the final year we break even |

|-58 / 621 |=|.093 |

So using the Discounted Payback Method we break even after 4.093 years.

FORMULA:

In discounted payback period we have to calculate the present value of each cash inflow taking the start of the first period as zero point. For this purpose the management has to set a suitable discount rate. The discounted cash inflow for each period is to be calculated using the formula:

|Discounted Cash Inflow = |Actual Cash Inflow |

| |(1 + i)n |

Where:

i is the discount rate;

n is the period to which the cash inflow relates

|Discounted Payback Period = A + |B |

| |C |

Where,

A = Last period with a negative cumulative discounted cash flow;

B = Absolute value of discounted cumulative cash flow at the end of the period A;

C = Discounted cash flow during the period after A.

Net Present Value (NPV) - Once you understand discounted payback, NPV is so easy! NPV is the final running total number. That's it. In the example above the NPV is 563. That's all. You're done, baby. Basically NPV and Discounted Payback are the same idea, with slightly different answers. Discounted Payback is a period of time, and NPV is the final dollar amount you get by adding all the discounted cash flows together. If the NPV is positive, then approve the project. It shows that you are making more money on the investment than you are spending on your cost of capital. If NPV is negative, then do not approve the project because you are paying more in interest on the borrowed money than you are making from the project

see excel file:

Internal Rate of Return (IRR)

The formula for IRR is: 0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n

where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and IRR equals the project's internal rate of return.

Example:.

Assume Company XYZ must decide whether to purchase a piece of factory equipment for $300,000. The equipment would only last three years, but it is expected to generate $150,000 of additional annual profit during those years. Company XYZ also thinks it can sell the equipment for scrap afterward for about $10,000. Using IRR, Company XYZ can determine whether the equipment purchase is a better use of its cash than its other investment options, which should return about 10%.

Here is how the IRR equation looks in this scenario:

0 = -$300,000 + ($150,000)/(1+.2431) + ($150,000)/(1+.2431)2 + ($150,000)/(1+.2431)3 + $10,000/(1+2431)4

The investment's IRR is 24.31%, which is the rate that makes the present value of the investment's cash flows equal to zero.

From a purely financial standpoint, Company XYZ should purchase the equipment since this generates a 24.31% return for the Company --much higher than the 10% return available from other investments.

Teacher note: use excel file to find IRR.

Compare two options

To see how this definition is applied, consider two competing investments in computer equipment. Each calls for an initial cash outlay of $100, and each returns a total a $200 over the next 5 years making a net cash flow gain of $100 in each case. But the timing of the returns is different, as shown in the table below (Case A and Case B), and therefore the present value of each year’s return is different. The sum of each investment’s present values is the investment's Net Present Value. Using a discount rate (interest rate) of 10% for the discounting, we find:

Comparing the two investments, the early large returns in Case A lead to a better net present value (NPV) than the later large returns in B. Note especially the Total line for each present value column in the table. This total is the net present value (NPV) of each cash flow stream.

If the investment choice were based solely on NPV, other things being equal, the one with the higher NPV (Case A) is the better investment. You can take this as a signal that Case A will also have the higher IRR.

IRR asks a different question of the same two cash flow streams. Instead of proposing a discount rate and finding the NPV of each stream (as with NPV), IRR starts with the net cash flow streams and finds the interest rate (discount rate) that produces an NPV of zero for each. The easiest way to see how this solution is found is with a graphical summary:

These curves are based on the Case A and Case B cash flow figures in the table above. Here, however, we have used nine different interest rates, including 0.0 and 0.10, on up through 0.80. As you would expect, as the interest rate used for calculating NPV of the cash flow stream increases, the resulting NPV decreases. For Case A, an interest rate of 0.38 produces NPV = 0, whereas Case B NPV arrives at 0 with an interest rate of 0.22. Case A therefore has an IRR of 38%, Case B an IRR of 22%.

Which is the better Investment? Other things being equal, and using IRR as the decision criterion, the one with the higher IRR is the better choice.

Another way to think of IRR is this: IRR tells you just how high inflation rates have to go in order to eliminate the present value of this investment.

← For the Case A cash flow, the prevailing inflation rate would have to rise all the way to 38% to make this investment worthless.

← The Case B investment would become worthless if interest rates rose to 22%.

Funding a company's needs:

• Receive credit from suppliers

• Obtain lease financing

• Obtain bank loans

• Issue bonds

• Issue stock

• Factor Business Debts

other EXTERNAL sources:

Loans from family and/or friends*

New Investor/ Partner

Venture Capital

* In generel this is only valid in new started operation where the needed capital is limited, so its left out for the rest of the paper.

EXTERNAL: For both new investor / venture capital is called external, is refering to that people outside the company will have impact at the ownership/decicions.

EXPLANATIONS:

Supplier credit

This is the easiest way that companies obtain funding. Companies buy goods and services and have anywhere from seven days till 6 months to pay for them; when companies need more credit from suppliers the financial controllers will negotiate longer credit terms or larger credit lines. The payment terms can also be stretched and this can work well because the creditors do not want the customer to go into bankruptcy taking their money with them.

Lease financing

Instead of buying equipment, many companies choose to lease equipment - this is a form of financing. Cars,computers and heavy equipment can be financed for short periods or indeed longer periods.

If it is a short period it is referred to as an operating lease and at the end of the lease the property is still useful and is returned to the finance company.

Long term leases are, in substance, ways are ways of funding a purchase rather than buying the temporary services of a piece of equipment. These are often referred to as capital leases.

For capital leases the leased assets and the financing liability are recorded on the leasing company's books as though the company had bought the equipment outright.

Bank financing

The next level of financing involves banks. If a company has a credit line or revolver with a bank it draws down and pays back up to set limits of credit as cash is needed and generated by the business. The credit is often secured by assets of the firm however if a business runs into trouble it may not be able to pay the bank and go into bankruptcy

Bond Insurance

Bonds have fixed interest rate contractual payments and a principal maturity. The risk comes to the firm's owners if they cannot be serviced. The principle bond owners can then exchange them for ownership of the company and oust the owners.

The After-Tax cost of Borrowing

Interest payments for borrowing from vendors, bankers or bondholders are tax-deductible, while dividends to shareholders are not. The after-tax cost of borrowing is the interest cost less the tax benefit.

Stock Issues

Stock issues have non-contractual, non tax deductible dividend payments. Stock represents an ownership in the business and in all of its assets. If additional shares of stock are issued to raise cash, this is done at the at the expense of the current shareholders' ownership interest. New shareholders share their ownership interest equally on a per-share basis with the current shareholders - this is why analysts say that the new shareholders dilute the interest of existing shareholders.

Factoring Business Debts

Factoring companies generally pay up to eighty percent of the value of outstanding invoices straight away provided that they are satisfied that the business debtor is capable of paying the sums due.

The externals:

New Investor/ Partner

Neither a speculator (who takes on high risks for high rewards) nor a gambler (who takes on the risk of total loss for out of proportion rewards) but one whose primary objectives are preservation of the original. ""investment (the principal), a steady income, and capital appreciation.

Individual who joins with other individuals (partners) in an arrangement (partnership) where gains and losses, risks and rewards, are shared among the partners.

Venture Capital

Startup or growth equity capital or loan capital provided by private investors (the venture capitalists) or specialized financial institutions (development finance houses or venture capital firms).

Venture capital can also include managerial and technical expertise. This form of raising capital is popular among new companies or ventures with limited operating history, which cannot raise funds by issuing debt. The downside for entrepreneurs is that venture capitalists usually get a say in company decisions, in addition to a portion of the equity.

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ECONOMY

2. SEMESTER

SPRING 2013

EASJ CAMPUS ROSKILDE

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