- Explain and show an example of expanded Net Present Value method using costs
- Explain and show an example of uncertain cost flows
- Explain and show an example of the Simple Rate of Return method
- Discuss post audit of investment projects


[SLIDE 1]

We have looked at several methods for evaluating a single investment project. Let's expand our discussion of the net present value method to include how management can evaluate two alternative projects.  We will also integrate relevant cost concepts into the discounted cash flow analysis. Managers can use two approaches to compare competing investment projects: the total-cost approach and the incremental-cost approach.  

The total cost approach uses a schedule of all of the costs and cash inflows for each decision alternative.  Management then adjusts each cost or inflow based on the time value of money basis to a present value. Once all of the present value-adjusted costs are combined for each decision alternative, the alternative with the greatest net present value is the most profitable. The drawback to this approach is that it requires management to identify every cost involved in each decision alternative. The total cost method can be complicated and cumbersome.

The incremental cost approach is a simpler variation of the total cost approach. This method uses the same process as the total cost approach, yet instead of examining all costs for the alternatives, management only uses the costs that differ between the alternatives. These costs are known as relevant costs. Management may consider this approach as it can be considerably less cumbersome; however, if more than two decision alternatives are being examined, the total cost method must be used.

Let's consider the following example:

One of the pipe networks for Kana Corporation is in poor condition. Kana requires a return of at least 18% on all investment capital. They are considering the following options:<ol>
<li>This pipe network can be renovated at an immediate cost of $20,000. Further repairs and maintenance will be needed five years from now at a cost of $8,000. In all, this pipe network will be usable for 10 years if this work is done. At the end of 10 years, the pipe network will be scrapped at a salvage value of $6,000. The scrap value now is $7,000. It will cost $30,000 each year to operate the pipe network, and revenues will total $40,000 annually.</li>
<li>Kana can purchase a new pipe network at a cost of $36,000. The new pipe network will have a life of 10 years and will require some repairs at the end of 5 years which will amount to $3,000. At the end of 10 years, it is estimated that the scrap value would be $6,000.  It will cost $21,000 each year to operate the pipe network, and revenues will total $40,000 annually.</li>
</ol>
The Total Cost approach would look like this for the NPV calculation on both projects:

<table border=0 cellpadding=5 cellspacing=0><tr><td colspan=5 style="background-color: #EEEEEE; text-align: center;">Buy the new pipe network</td></tr><tr style="font-weight: bold;"><td>Item</td><td>Year(s)</td><td>Amount of Cash Flows</td><td>18% Factor</td><td>PV of Cash Flows</td></tr><tr><td>Initial investment</td><td>Now</td><td>($36,000)</td><td>1.000</td><td>($36,000)</td></tr><tr><td>Repairs in 5 years</td><td>5</td><td>($3,000)</td><td>0.437</td><td>($1,311)</td></tr><tr><td>Net annual cash inflows</td><td>1-10</td><td>19,000</td><td>4.494</td><td>85,386</td></tr><tr><td>Salvage of the old network</td><td>Now</td><td>7,000</td><td>1.000</td><td>7,000</td></tr><tr><td>Salvage of the new network</td><td>10</td><td>6,000</td><td>0.191</td><td style="border-bottom: 1px solid black;">1,146</td></tr><tr><td><strong>Net present value</strong></td><td></td><td></td><td></td><td style="border-bottom: 2px solid black;">$56,221</td></tr></table>

<table border=0 cellpadding=5 cellspacing=0><tr><td colspan=5 style="background-color: #EEEEEE; text-align: center;">Keep the old pipe network</td></tr><tr style="font-weight: bold;"><td>Item</td><td>Year(s)</td><td>Amount of Cash Flows</td><td>18% Factor</td><td>PV of Cash Flows</td></tr><tr><td>Initial repairs</td><td>Now</td><td>($20,000)</td><td>1.000</td><td>($20,000)</td></tr><tr><td>Repairs in five years</td><td>5</td><td>($8,000)</td><td>0.437</td><td>($3,494)</td></tr><tr><td>Net annual cash inflows</td><td>1-10</td><td>10,000</td><td>4.494</td><td>44,940</td></tr><tr><td>Salvage of the old network</td><td>10</td><td>6,000</td><td>0.191</td><td style="border-bottom: 1px solid black;">1,146</td></tr><tr><td><strong>Net present value</strong></td><td></td><td></td><td></td><td style="border-bottom: 2px solid black;">$22,590</td></tr></table>

<table border=0 cellpadding=5 cellspacing=0><tr><td>NPV of the New Pipe Network</td><td>$56,221</td></tr><tr><td>NPV of the Old Pipe Network</td><td style="border-bottom: 1px solid black;">$22,590</td></tr><tr><td>NPV in favor of buying the New Network</td><td style="border-bottom: 2px solid black;">$33,631</td></tr> </table>

The incremental-cost approach would look like this for the NPV calculation:

<table border=0 cellpadding=5 cellspacing=0><tr style="font-weight: bold;"><td>Item</td><td>Year(s)</td><td>Amount of Cash Flows</td><td>18% Factor</td><td>PV of Cash Flows</td></tr><tr><td>Incremental investment required<br />to purchase the new pipe network</td><td>Now</td><td>($16,000)</td><td>1.000</td><td>($16,000)</td></tr><tr><td>Repairs in five years avoided</td><td>5</td><td>$5,000</td><td>0.437</td><td>$2,185</td></tr><tr><td>Increased net annual cash inflows</td><td>1-10</td><td>$9,000</td><td>4.494</td><td>$40,000</td></tr><tr><td>Salvage of the old network</td><td>Now</td><td>7,000</td><td>1.000</td><td>7,000</td></tr><tr><td>Difference in salvage value in 10 years</td><td>10</td><td>-0-</td><td>-</td><td style="border-bottom: 1px solid black;">-0-</td></tr><tr><td><strong>NPV in favor of buying the new Network</strong></td><td></td><td></td><td></td><td style="border-bottom: 2px solid black;">33,631</td></tr></table>

As you can see, the incremental approach is simpler to use and you get the same NPV using either approach.  


[SLIDE 2]

Not all capital decisions involve revenue.  Some decisions may only involve costs, such as whether to lease or buy, and the decision is made on the basis of which alternative would be least costly.  In situations where no revenue is involved, the most desirable alternative is the one with the least total cost from a present value perspective, also known as a least-cost decision.

Let's consider the following example:

Carmen Furniture Company is trying to decide whether to overhaul an old delivery truck or purchase a new one.  The company uses a discount rate of 10 percent.  The information pertaining to the alternatives is shown below:<ul>
<li>The old truck has the following costs:  Overhaul cost now is $4,500, Annual operating costs are $10,000, Salvage value in 5 years is $250, and Salvage value now is $9,000</li>
<li>The new truck costs include:  Purchase price is $21,000, Annual operating costs are $6,000, and Salvage value in 5 years is $3,000</li>
</ul>
The least cost approach would look like this for the NPV calculation on both projects:

<table border=0 cellpadding=5 cellspacing=0><tr><td colspan=5 style="background-color: #EEEEEE;">Purchase New Truck</td></tr><tr style="font-weight: bold;"><td>Item</td><td>Year(s)</td><td>Cash Flows</td><td>10% Factor</td><td>Present Value</td></tr><tr><td>Purchase Price</td><td>Now</td><td>($21,000)</td><td>1.000</td><td>($21,000)</td></tr><tr><td>Annual operating costs</td><td>1-5</td><td>($6,000)</td><td>3.791</td><td>($22,746)</td></tr><tr><td>Salvage value of Old Truck</td><td>Now</td><td>9,000</td><td>1.000</td><td>9,000</td></tr><tr><td>Salvage of the new network</td><td>5</td><td>3,000</td><td>0.621</td><td>1,863</td></tr><tr><td>Net present value</td><td></td><td></td><td></td><td>($32,883)</td></tr></table>

<table border=0 cellpadding=5 cellspacing=0><tr><td colspan=5 style="background-color: #EEEEEE;">Keep Old Truck</td></tr><tr style="font-weight: bold;"><td>Item</td><td>Year(s)</td><td>Cash Flows</td><td>10% Factor</td><td>Present Value</td></tr><tr><td>Overhaul cost</td><td>Now</td><td>($4,500)</td><td>1.000</td><td>($4,500)</td></tr><tr><td>Annual operating costs</td><td>1-5</td><td>($10,000)</td><td>3.791</td><td>($37,910)</td></tr><tr><td>Salvage value of old truck</td><td>5</td><td>250</td><td>0.621</td><td>155</td></tr><tr><td>Net present value</td><td></td><td></td><td></td><td>($42,255)</td></tr></table>

<table border=0 cellpadding=5 cellspacing=0><tr><td>NPV of the New Truck Purchase</td><td>($32,883) </td></tr>
<tr><td>NPV of Overhauling existing Truck</td><td>($42,255)</td></tr><tr><td>NPV in favor of Purchasing the new truck</td><td>$9,372</td></tr></table>

Notice that both NPV numbers are negative because there is no revenue involved. This makes it a least cost decision. The purchase of a new truck shows the least total cost of the two alternatives and therefore, the net present value in favor of purchasing the new truck is $9,372.


[SLIDE 3]

So far, we have assumed that all future cash flows are know with certainty.  Sometimes, future cash flows are uncertain or difficult to estimate.  Without getting too technical, here is some useful information managers can use to evaluate alternatives with uncertain cash flows. 

The best way to understand how to evaluate projects with uncertain cash flows is to look at an example.  We will assume that all of the cash flows related to an investment in a supertanker have been estimated, except for its salvage value in 20 years.  Management is using a discount rate of 12% and has determined that the net present value of all the cash flows, except the salvage value is a negative $1.04 million.  This negative net present value will be offset by the salvage value of the supertanker.  The question is: How large would the salvage value need to be to make this investment attractive for consideration?   Let's view the calculation.

The equation that can used to determine what the salvage value of the supertanker is:  
<span style="color: red;">
Net Present value to be offset / Present Value Factor</span>

Using this formula, we would take the net present value of $1.04 million divided by present value factor for 12% of 0.104 and we get $10 million for the salvage value.  Therefore, if the salvage value of the supertanker is at least $10 million, then the net present value of the investment would be positive and therefore acceptable for consideration. While the salvage value is not known with certainty, the calculation offers a useful reference point for making a decision on the investment.


[SLIDE 4]

Remember that when managers are considering investment opportunities, they must make two types of decisions.<ol>
<li>Screening decisions, which pertain to whether or not a proposed investment is acceptable.</li>
<li>Preference decisions, which occur after screening decisions and attempt to rank selected project in terms of preference.</li>
</ol>
Preference decisions are made because the number of acceptable investment alternatives usually exceeds the amount of available funds.  When manager use the internal rate of return method to rank competing investment projects, the preference rule is: the higher the internal rate of return, the more desirable the project. For example, an investment project with an IRR of 18% would be preferred to another project that promises a return of only 15%.

When managers use the net present value method, the NPV of one project cannot be compared directly to the NPV of another project unless the investments in the projects are of equal size.

In looking at an example of a ranking of Investment using the NPV method, we show two alternatives.  One investment requires $80,000 for an initial cash outflow with the other investment requires $5,000 for the initial cash outflow.

<table border=0 cellpadding=5 cellspacing=0><tr style="font-weight: bold;"><td></td><td>Investment A</td><td>Investment B</td></tr><tr><td>Investment required</td><td>($80,000)</td><td>($5,000)</td></tr>
<tr><td>Present value of cash inflows</td><td>81,000</td><td>6,000</td></tr><tr><td>Net present value</td><td>$1,000</td><td>$1,000</td></tr></table>

Each project has a net present value of $1,000, but they are not equally desirable. The project requiring an investment of only $5,000 is much more desirable (especially when funds are limited) than the project requiring $80.000. However, there is a way to compare the two projects on a valid basis using a Profitability Index.  Profitability index is the present value of cash inflows divided by the investment required. The formula for profitability index is:
<span style="color: red;">
Profitability index = Present value of cash inflows / Investment required</span>

<table border=0 cellpadding=5 cellspacing=0><tr style="font-weight: bold;"><td></td><td>Investment A</td><td>Investment B</td></tr><tr><td>Investment required</td><td>($80,000)</td><td>($5,000)</td></tr><tr><td>Present value of cash inflows</td><td>81,000</td><td>6,000</td></tr><tr><td>Profitability Index</td><td>1.01</td><td>1.20</td></tr></table>

When using the project profitability index to rank competing investments projects, the preference rule is: The higher the project profitability index, the more desirable the project.  Applying this rule to the two investments above, investment B should be chosen over investment A. 

A few details should be clarified with respect to the computation of the project profitability index. The "Investment required" refers to any cash outflows that occur at the beginning of the project, reduced by any salvage value recovered from the sale of old equipment. The "Investment required" also includes any investment in working capital that the project may need. 


[SLIDE 5]

The final capital budgeting technique we will review is the Simple Rate of Return method. The simple rate of return is the incremental amount of net income expected from a prospective investment opportunity, divided by the investment in it. The simple rate of return is an imprecise but easy way to measure the estimated performance of a capital investment, since it uses financial statement information. This method does not use an investment's cash flows but considers the financial reporting effects of the investment instead. The simple rate of return method measures expected performance using two variables:<ol>
<li>Annual incremental net operating income</li>
<li>Initial investment</li>
</ol>
The basic equation is as follows:
<span style="color: red;">
Simple Rate of Return = Annual incremental net operating income / Initial  Investment</span>

As an example, we assume there is an opportunity under which a business can earn an incremental increase in its net income of $8,000 in exchange for an initial investment of $100,000, then the project has a simple rate of return of 8% (calculated as $8,000 incremental net income / $100,000 investment).  If the business has a minimum rate of return on projects of 8% then the company would accept the project.  Similarly, if a prospective project could result in a cost reduction (rather than incremental net income), then one would substitute the amount of cost savings for incremental net income in the calculation.

While this method has the advantage of being simple and easy to calculate, it also suffers from several problems, which are:<ul>
<li><strong>Time value of money</strong>- The method does not use discounting to reduce the incremental amount of net income to its present value. Instead, it assumes that any net income earned during the measurement period is the same as its present value. This failing overstates the rate of return, especially for income that may be many periods in the future. Thus, the method assumes that net income earned several years from now has the same value as net income earned in the present.</li>
<li><strong>Cash Flow</strong>- The method uses net income in the numerator of the calculation, rather than cash flows. Cash flows are considered the best method of judging the return on an investment, whereas a variety of adjusting entries and non-cash transactions could alter the amount of net income to be a figure substantially different from cash flows. Examples of non-cash items that impact net income are depreciation and amortization which are not included in a cash flow analysis.</li>
<li><strong>Constant profit stream</strong>- The method assumes that a business earns the same amount of incremental net income in period after period when in reality, this amount will probably change over time.</li>
<li><strong>Constraint Analysis</strong>- The method does not factor in whether or not the capital project under consideration has any impact on the throughput of a company's operations, or on the constrained resource within the organization.</li>
</ul>
The problems enumerated here indicate that the simple rate of return is an excessively simplistic method to use for judging a capital budgeting request. Instead, consider other techniques such as net present value analysis and throughput analysis.


[SLIDE 6]

A final important step in the capital budgeting process is the review of investment projects after they have been implemented. This can provide useful information on the effectiveness of the company's selection process. Post audit refers to an analysis of the outcome of a capital budgeting investment. The post audit procedure consists of comparing <strong><i>actual</i></strong> cash flows from an accepted project with <strong><i>projected</i></strong> cash flows that were estimated when the project was adopted. The same capital budgeting method should be used in the post audit as was used in the original approval process. That is, if a project was approved on the basis of a net present value analysis, then the same procedure should be used in performing the post audit.

Because projected cash flows contain an element of uncertainty, actual values would not be expected to match estimated values exactly.  Instead, a project review should be concerned with identifying systematic biases or errors in cash flow estimation on the part of individuals, departments, plants, or divisions and attempting to determine why these biases or errors exist. This type of analysis, when properly performed, can help a company's decision makers better evaluate investment proposals submitted in the future.  This analysis is conducted to see if the assumptions incorporated into the original capital proposal turned out to be accurate, and whether the project outcome was as expected. The results of this audit are then incorporated into future capital budgeting decisions, thereby improving the decision-making process.  

Another objective of the project review process involves determining whether a project that has not lived up to expectations should be continued or abandoned. The decision to abandon a project requires the company to compare the cost of abandonment with any future cash flows that are expected over the project's remaining life. These estimates of future cash flows will usually be more accurate after the project has been in service for a period of time.