Capital Budgeting

Capital Budgeting Techniques

This lesson illustrates four capital budgeting techniques. These techniques are used to evaluate capital expenditures--purchases of long term fixed assets. A distinguishing feature of a capital expenditure is that such an expenditure involves cash inflows or outflows over several years' time. Typical capital expenditures include the purchase of buildings, computers, and equipment. Additionally, very large capital projects--a bridge, a highway, or a super ferry would be planned using these techniques.

An example of a capital budgeting situation is one in which a company purchases an expensive piece of equipment because the equipment is expected to produce savings each year over a ten-year period. The equipment requires a cash outlay now, and will require a tune-up in year five. At the end of the ten-year period, the equipment can be sold for its salvage value. Capital budgeting provides a way to evaluate the purchase price, the savings, the tune up, and the salvage value of such an investment, despite the fact that these cash flows happen at different points in the investment's life. Furthermore, if there are several investments that might be made, each with a different pattern of cash flows, we would like to be able to compare those investments objectively even if the project lives of the investments or cash flow patterns are different.

Four Capital Budgeting Methods

The capital budgeting methods covered in Chapter 26 are:

  1. Average Rate of Return Method

  2. Payback Period Method

  3. Net Present Value Method (NPV)

  4. Internal Rate of Return Method (IRR)

Methods 1 and 2 are fairly trivial methods, from the standpoint that they ignore the time value of money. Payback and the Accounting Rate of Return treat dollars received in later years of the investment as being of equal value to dollars received in earlier years.

Methods 3 and 4 are examples of discounted cash flow methods. NPV and IRR apply a discount to dollars received in the future. The further out in time a cash flow is expected, the bigger the discount. A strength of the NPV and IRR methods is that dollars to be spent or received later in the investment's life are considered less valuable that dollars to be spent or received earlier. We will focus on discounted cash flow techniques because they take into account the time value of money.

One element that always must be considered is a company's cost of capital. In other words, money costs money. The cost of capital is a weighted average cost of debt and equity. You might think of the cost of capital as the cost of money. For an individual, the cost of capital might be the interest rate on a bank loan. For a corporation, there may be several sources of money, including the bond market, issuance of common stock, or issuance of preferred stock. For each source, a borrowing rate could be computed, and a composite rate calculated. Such calculations are a subject for a finance course; for our purposes, we will treat the cost of capital, or "hurdle rate" as a given. In the problems for this chapter, the cost of capital will be stated clearly.

You will have to become familiar with the concepts of present value in order to successfully handle the NPV and IRR techniques. As part of this lesson, you may need to review the material on present value calculations.

1. Average Rate of Return Method

This method calculates the ratio of the annual net income divided by the average investment in the project. For example, a company is planning to purchase new equipment that will generate net income of $60,000 per year for six years, and will have an initial cost of $240,000. With a $240,000 cost and six-year life, the depreciation expense each year will be $40,000. This means that the net income will be $60,000-$40,000=$20,000 per year.

The average investment amount goes in the denominator. The average investment is found by adding the original investment amount, $240,000 to the expected salvage value ($0 for this example) and dividing by 2. The denominator works out to ($240,000+$0)/2=$120,000

A ratio is computed: average operating income/average amount invested in the asset = ($60,000-$40,000)/ $120,000 = .167 or 16.7%.

The Annual Rate of Return Method has some inherent weaknesses:

  1. It focuses upon net income, rather than cash flow;

  2. It ignores the time value of money, because income to be earned in the early years is weighted exactly equally to income to be earned later in the investment life;

  3. This numerator of this ratio is usually net income, rather than cash flow; better investment-analysis techniques focus on the cash to be received from an investment;

  4. It is inflexible with respect to evaluating fluctuating income amounts during the project.

2. Cash Payback Method

The Cash Payback Method determines how long it will take to recover the original investment, based on the savings generated each year by the investment. It focuses on cash flows, so depreciation charges must be added back to net income. (This is similar to the calculation of cash flows from operations in the construction of a cash flow statement.)  

Using the previous example, the investment has an original cost of $240,000 and generates cash flow of $60,000 per year.  If you asked the question, "how long will it take to recoup the investment?", the answer would be $240,000/$60,000 or 4 years.

The Cash Payback Method also has a number of weaknesses:

  1. It ignores the time value of money;

  2. It is biased in favor of projects that have a short payback period;

  3. The measurement provided is in years, rather than a dollar amount or a rate of return, making this method difficult to use when choosing between investments;

  4. It ignores the timing of cash inflows and outflows.

Although the Average Rate of Return method and the Cash Payback method are described in this chapter, I encourage you to spend the bulk of your time studying the discounted cash flow methods. Both the NPV and IRR methods properly weigh the timing and amount of both cash inflows and outflows over an investment's life.  Additionally, if you take further courses in accounting or finance, you will find that both of these methods are emphasized.

Present Value Concepts

Net Present Value and Internal Rate of Return are applications of present value thinking.

A basic premise of present value is this question: Which would you rather receive--$1,000 today, or $1,000 one year from now? This situation can be modeled as follows.
 
Alternative 1: $1,000 now    
Time Period
0
1
Cash Flow
$1,000
 
OR...
Alternative 2: $1,000 in 1 year    
Time Period
0
1
Cash Flow  
$1,000

Alternative 1 is more desirable than Alternative 2. An amount of $1,000 received in time period 0 (now) is considered to be worth $1,000. However, if $1,000 is to be received after one year, it will be worth less than $1,000. Why is this so? And how much less will it be worth?

Here is the reasoning. If the $1,000 is received now, it can be invested at some rate of interest so that it grows to more than $1,000 in one year. Assuming that the prevailing interest rate is 10%, we could invest the money and earn interest of $100. We could calculate the "future value" of this investment by multiplying $1,000 times 1.10. So, the $1,000 would grow to $1,000 + $100 = $1,100 in one year. In general, the calculation of the future value of $1,000 at interest rate r for n years is $1,000 times (1+r)^n. The expression (1+r)^n means "take one plus the interest rate and raise that sum to the nth power." So the future value of $1,000 at 10% for 2 years = $1,000 times (1+.10)^2. And the future value of $1,000 at 10% after three years is $1,000 times (1+.10)^3.

Conversely, we could say that $1,000 is the present value of $1100 to be received one year from now, discounted at 10%. The $1000 invested today and the $1100 received in one year are economically equivalent to one another, if the interest rate we can earn is 10%. In a present value problem, we know the amount we will receive in the future, but we must calculate how much we should be willing to pay for it today, in order to earn a certain interest rate.

Present Value Table

Let's examine alternative 1 again, but let us state the problem in a different way. Suppose we expect a cash flow of $1,100 at the end of one year. What is the present value of this cash flow, discounted at 10%? You already know the answer is $1,000 because $1,000 is the amount that will grow to $1,100 in one year at 10%. But how would you compute this present value directly? Fortunately, a table exists, called a Present Value table, that will make the calculation easy. Here is an abbreviated PV table:
  PV $1         PV Annuity of $1  
6%
8%
10%
....
6%
8%
10%
1
.9434
.9259
.9091
...
1
.9434
.9259
.9091
2
.8900
.8573
.8264
...
2
1.8334
1.7833
1.7355
3
.8396
.7938
.7513
...
3
2.6730
2.5771
2.4869
4
.7921
.7350
.6830
...
4
3.4651
3.3121
3.1699
5
.7473
.6806
.6209
...
5
4.2124
3.9927
3.7908

The formula for the PV $1 table above is 1/(1+r)^n, which is the inverse of the future value calculation described earlier. To derive the first three interest factors at 10%, the formulas would be 1/(1+.1)^1=.9091, then 1/(1+.1)^2=.8264, and finally, 1/(1+.1)^3=.7513.

To determine the present value of a cash flow of $1,100 to be received at the end of one year, look up the present value factor corresponding to 10% and 1 period. The factor is .9091. The present value of $1,100 to be received at the end of one year, discounted at 10% is found by multiplying the cash flow times the present value factor:
 
Alternative 1: $1,100 in one year    
Time Period
0
1
Cash Flow  
$1,100
PV Factor  
.9091
Present value of cash flow  
$1,000

The present value of $1,100 received in one year, discounted at 10% is $999.99, which rounds to $1,000.

But what about alternative 2? To reiterate, this was the receipt of $1,000 at the end of year 1. The present value of $1,000 to be received at the end of one year is .90909 times $1,000 = $909.10.

Conclusion:  the present value of $1,000 received today is $1,000.  The present value of $1,000 to be received in one year, discounted at 10%, is $909.09.  Any cash flows to be received (or paid!) in the future must be discounted prior to comparing them to dollars we expend today.  This is the foundation of discounted cash flow methods.

Lump Sum vs. Annuity

In the previous examples, we were dealing with lump sums. On some investments, the cash stream is the same amount every year. A cash stream of equal amounts every year is called an annuity. Here is an example of an annuity:
 
Year
0
1
2
3
Cash Flow  
$1,000
$1,000
$1,000
PV Factor 10%  
.90909
.82645
.75132
Present Value
$2,486=
$909
$826
$751


Present Value of an Annuity

You could use the Present Value of $1 table to calculate the present value of this annuity. Simply look up the present value factors at 10% for years one, two, and three. Then, multiply each factor times the $1,000 cash flow and add them up. The present value of this three-year annuity is $909+$826+$751= $2486. The table above shows an orderly way to organize this calculation. Note that you take the present value of each cash flow, and then add up those present values. In the example, the present value of this annuity is $909 + $826 + $751 = $2,486.

Interpretation: the present value of a $1,000 annuity for three years discounted at 10% is $2,486. This means that if I require a 10% return on my investment, I would not spend more than $2,486 for this 3-year annuity. (If you spent $2,600 for this annuity, for example, your return would be less than 10%).

Another way to calculate the present value of an annuity is to use the PV Annuity table. I have included the PV Annuity table above. For a 3-year annuity at 10%, the interest factor from the Annuity table is 2.4869. Take $1,000 (the amount of the annuity) times this factor, 2.4869 and you will get $2,486, the same present value we calculated above. In fact, you will find that the PV annuity table simple adds up the interest factors from the PV $1 table. The annuity interest factor for 10% for 3 years is 2.486. The same figure can be derived from the PV $1 table--by adding up the interest factors for years 1, 2 and 3--we add .9091 +.8262 + .7513=2.486.

The PV annuity table, is to be used only for annuities. So, if the cash flows over the three year period were $1,000, $1,000 and $2,000, you would not be able to use the annuity table because the cash flows are not exactly equal. You would use the PV $1 table and calculate the present value of each cash flow separately, and then add them up.

3. Net Present Value Method

Let us return now to the topic of Net Present Value. Here is a step by step procedure:

  1. Sketch out the cash flows for the investment, including cash inflows and outflows, from period 0 (today) to the end of the project.

  2. Use the present value of $1 for lump sums or PV annuity table to calculate the present value of each cash flow, discounted at the given rate of interest.

  3. Subtract the cost of the project in time period 0 from the sum of the future cash flows. If the result is positive or zero, the investment is acceptable; if the result is negative, the investment is unacceptable.

Note that the NPV gives you a dollar figure as the answer. Some companies comparing several investments may choose the one with the highest NPV, although there may be other factors to consider.

NPV Example

Johnson Company is considering purchase of a piece of equipment that will cost $10,000. The new equipment will save the company $3,000 per year for 5 years. A tune-up will be necessary in year 3, costing $500. The equipment will have a salvage value of $300 at the end of the five year period. The company's cost of capital is 8%. Compute the NPV of this investment. Is the investment acceptable?
 
Year
0
1
2
3
4
5
Cost ($10,000)          
Savings  
$3,000
$3,000
$3,000
$3,000
$3,000
Tune-up      
($500)
   
Salvage          
$500
Total Cash  
$3,000
$3,000
$2,500
$3,000
$3,500
             
PV Factor  
.92593
.85734
.79383
.73503
.68058
PVs $11,922
$2,778
$2572
$1985
$2,205
$2382
NPV $1,922          

In the table above, I have sketched out the cash flows each year. Negative cash flows, such as the initial investment and the tune up are shown in parentheses. The Total Cash line shows the sum of the cash flows each year. You will note that the cash flows are not exactly equal each year, so you will have to use the PV of $1 table. The PV Factors for an 8% cost of capital are inserted under the appropriate year and multiplied times the cash flow to derive the PVs. These amounts are added up (the amount is $11,922) and this amount is placed under the original investment amount of $10,000. Subtract the cost of the investment from the savings to arrive at the NPV figure of $1,922. Because the NPV is greater than or equal to zero, the investment is considered acceptable.

Notice that the acceptance criterion is NPV greater than or equal to zero. If the NPV is exactly equal to zero, the investment is earning the rate of interest used in the discounting. In the example above, if the PVs of the cash flows had been equal to $10,000, the NPV would equal zero, and the investment would have generated a rate of return of exactly 8%. This leads us to the definition of the Internal Rate of Return.

Reviewing the problem above, the cash flows in that example were unequal. Looking at the "Total Cash" line, the cash flows in years 1-5 were $3,000, $3,000, $2500, $3,000, and $3500. The fact that the cash flows were unequal required the discounting to be separate for each year. If the cash flows are exactly equal each year, your NPV calculation is simplified--multiply the cash flow amount times the appropriate factor in your annuity table and compare it with the investment.

4a. Internal Rate of Return (Equal Cash Flows)

The Internal Rate of Return is that rate of return which makes the NPV exactly equal to zero. Here's an example. Suppose that a certain investment costs $2577 and generates savings of $1,000 per year for three years. What is the internal rate of return?

Here is a picture of the investment:
 
Year
0
1
2
3
Investment
($2,577)
     
Cash Flows
?
$1,000
$1,000
$1,000
NPV
0
     

The investment cost is $2,577. The savings are $1,000 per year for three years--an annuity. If the annuity is discounted back to the present, the present value would have to be $2,577 in order to arrive at an NPV of 0. Another way of saying this is that there must be an interest factor in the annuity table such that the interest factor times $1,000 is equal to $2,577. Solve for the interest factor. F*1000=2577; F must be 2.577. Look for 2.577 along the "3-year" row of table C-2. The internal rate of return is 8%.

4b. Internal Rate of Return (Unequal Cash Flows)

Determining the Internal Rate of Return becomes more difficult if the cash flows are unequal. Suppose an investment costs $5,535 and generates cash flows of $3,000, $2,000, and $1,000 over a three year period. What is the internal rate of return? Here's the picture:
 
Year
0
1
2
3
Investment
($5,535)
     
Cash Flows
PV=?
$3,000
$2,000
$1,000
NPV
0
     
         
IRR = 6%?
$5,449
.94340
.89000
.83962
IRR = 4%?
$5,623
.96154
.92456
.88900
IRR = 5%?        

This is not an annuity, so the PV of $1 table must be used. You must experiment with each interest rate until you find one that comes closest. I tried a discount rate of 6% first, which produced a present value of $5449--too low. I next tried a discount rate of 4% which produced a present value of $5,623--too high. (Notice that the lower the discount rate, the higher the present value!) I have left the 5% row for your calculation--which should produce a present value of $5,535 and thus an NPV of 0. Conclusion: the internal rate of return in this example is 5%.

Once the Internal Rate of Return has been determined, a company must compare it with the company's hurdle rate. The hurdle rate is the minimum acceptable rate of return for a company's investments. So if the hurdle rate is 4% and this investment earns 5%, this investment would be considered acceptable.

In practice, the analysis of investments using either NPV or IRR would be approached using a spreadsheet program such as Excel or Google Spreadsheet.