# Time Value of Money (TVM)

Time value of money is the difference between an amount of money in the present and that same amount of money in the future. Having money now is more valuable than having money later.

The present amount is called the present value, the future amount is called the future value, and the appropriate rate that relates the two amounts is called the discount rate.

Present Value = Future Value / (1 + Discount Rate)

Future Value = Present Value x (1 + Discount Rate)

## Time Value of Money Examples

Now, let’s look at time value of money examples. If you invest \$100 (the present value) for 1 year at a 5% interest rate (the discount rate), then at the end of the year, you would have \$105 (the future value). So, according to this example, \$100 today is worth \$105 a year from today.

\$105 = \$100 x 1.05

\$100 = \$105 / 1.05

Likewise, \$100 a year from today, discounted back at 5%, is worth only \$95.24 today.

\$95.24 = \$100 / 1.05

To calculate the time value of money for a period longer than one year, you simply raise the discount factor by the appropriate number of time periods. For example, to calculate the future value of \$100 at 5% for 5 years:

\$127.63 = \$100 x (1.05)5

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## Profitability Index Method Formula

Profitability Index Method

# Profitability Index Method Formula

Use the following formula where PV = the present value of the future cash flows in question.

Profitability Index = (PV of future cash flows) ÷ Initial investment

Or = (NPV + Initial investment) ÷ Initial Investment: As one would expect, the NPV stands for the Net Present Value of the initial investment.

## Profitability Index Calculation

Example: a company invested \$20,000 for a project and expected NPV of that project is \$5,000.

Profitability Index = (20,000 + 5,000) / 20,000 = 1.25

That means a company should perform the investment project because profitability index is greater than 1.

### Profitability Index Example

Texabonds Inc has decided to consider a project where they predict the annual cash flows to be \$5,000, \$3,000 and \$4,000, respectively for the next three years. At the beginning of the project, the initial investment put into the project is \$10,000. Use the Profitability Index Method and a discount rate of 12% to determine if this is a good project to undertake. In order to solve this problem, it is probably a good idea to make a table so that the numbers can be organized by year.

Using a PI table, the following PVIF’s are found respectively for the 3 years: .893, .797, .712. Once the PVIF’s are determined, simply multiply the cash flows and the PVIF’s together in order to get the PV of cash flows for each respective year (\$4,465, \$2,391, \$2,848). Adding up all the PV’s will get the total present value of the project which is \$9,704. Divide that final number by the original investment \$10,000 and the PI has been determined: .9704. As one can see, the Profitability Index is less than 1 so the project should be scrapped. The NPV can also be determined by subtracting the initial investment (\$10,000) from the total PV of the project (\$9,704) and you are left with -\$296. In this case, because the number is negative, NPV also says that the project should be rejected.

#### Profitability Index Formula Table

A table for the problem is shown below:

```YearCash FlowPVIF at 12%PV of Cash Flow
1\$5,000.893\$4,465
2 3,000.797 2,391
3 4,000.712       __2,848__```

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# Profitability Index Definition

Profitability index method measures the present value of benefits for every dollar investment. In other words, it involves the ratio that is created by comparing the ratio of the present value of future cash flows from a project to the initial investment in the project. The Profitability Index Method is often times compared similarly to the Net Present Value Method for their close proximity. One should use caution when utilizing both the NPV and profitability index methods in tandem. Often times, it has been found that both methods can rank projects in a different way. One project could possibly be ranked number 1 for one of the methods while it ranks dead last in the other. Use digression when using both in tandem.

## Application

Profitability index is primarily used as a tool to rank projects. The higher the value of profitability index, the more attractiveness of a proposed project is. For a single project, profitability index value of 1 or greater is acceptable. If a project has profitability index (>1), then a company should perform the project. However if a project has profitability index (<1), a company should reject the project.

There is relationship between profitability index and net present value method. If profitability index >1, the NPV is positive. If profitability index <1, NPV is negative. The profitability index is a relative measure of an investment’s value while NPV is an absolute measure. The profitability index method can be a useful substitute for NPV method when presenting a project’s benefits per dollar of investment. It makes the most sense to look at the concept from a project-by-project basis. The profitability index gives a company the opportunity to determine whether a project should be pursued or not. If the profitability index is above one, then a company can execute and pursue the project. If the profitability index is below one, then the project should be scrapped for the detrimental cash flow problems

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# Present Value (PV) Definition

The present value is simply the value of future dollars or currency in present day terms. The present value is simply answering the question how much a dollar in the future is worth today.

## Present Value (PV) Explanation

The present value is often used in valuation to discount projections that companies make about themselves so they can figure out how much the company stock price is or maybe its equity value. The present value becomes useful because of inflation. If inflation were to increase at an increasing rate then the company would see the present day dollar as less valuable to them.

### Present Value (PV) Formula

The present value formula is as follows:
PV = FV/((1 + i)n)

Where:
PV = Present Value
FV = Future Value
i = rate
n = number of years or periods

### Present Value (PV) Example

Jim Bob has just won the lottery. He has the choice of accepting the \$2 million now, or he can accept \$1 million now and another \$2 million 5 years from now. Which of the choices should Jim Bob take? Assume a rate of 8%.

Option #1 PV = \$2 million

Option #2 PV = \$500,000 + \$1,361,166 = 1,861,166

PV calculation:
PV = 2 million/((1+.08)5) = \$1,361,166

Option #1 is better because it is worth more to you today than the present payment plus the payment at the end. Strategic CFO Lab Member Extra

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# Adjusted Present Value (APV) Method of Valuation Definition

Adjusted Present Value (APV) Method of Valuation is the net present value of a project if financed solely by equity (present value of un-leveraged cash flows) plus the present value of all the benefits of financing. Use this method for a highly leveraged project.

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## Adjusted Present Value Method Calculation

1. Calculate the value of un-leveraged project by discounting the expected free cash flow to the firm at the un-leveraged cost of equity.

2. Then, calculate the expected tax benefit from a given level of debt by discounting the expected tax saving at the cost of debt to reflect the riskiness of this cash flow.

3. Finally, evaluate the effect of a given level of debt on the default risk of a company and expected bankruptcy costs.

Thus, the APV calculation is as follows:

Value of the operating assets = Un-levered firm value + PV of tax benefits – Expected Bankruptcy Costs

Adjusted present value = value of the operating assets + value of cash and marketable securities.

APV method is very similar to traditional discounted cash flow (DCF) model. However, instead of weighted average cost of capital(WACC), cash flows would be discounted at the cost of assets, and tax shields at the cost of debt. Technically, an APV valuation model combined impact of both growth and the tax shield of debt on the cost of capital, the cost of equity, and systematic risk. Thus it is a more flexible way of approaching valuation than other method. However, APV method has some flaws. Company value will be overstated when adding the tax benefits to un-levered company value to get the levered company value, especially for some companies with high debt ratios.

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# Net Present Value Definition

Net Present Value (NPV) is defined as the present value of the future net cash flows from an investment project. NPV is one of the main ways to evaluate an investment. The net present value method is one of the most used techniques; therefore, it is a common term in the mind of any experienced business person.

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## Net Present Value Method Explanation

Net present value can be explained quite simply, though the process of applying NPV may be considerably more difficult. Net present value analysis eliminates the time element in comparing alternative investments. Furthermore, the NPV method usually provides better decisions than other methods when making capital investments. Consequently, it is the more popular evaluation method of capital budgeting projects.

When choosing between competing investments using the net present value calculation you should select the one with the highest present value.

If:

NPV > 0, accept the investment.
NPV < 0, reject the investment.
NPV = 0, the investment is marginal

### Net Present Value Discount Rate

The most critical decision variable in applying the net present value method is the selection of an appropriate discount rate. Typically you should use either the weighted average cost of capital for the company or the rate of return on alternative investments. As a rule the higher the discount rate the lower the net present value with everything else being equal. In addition, you should apply a risk element in establishing the discount rate. Riskier investments should have a higher discount rate than a safe investment. Longer investments should use a higher discount rate than short time projects. Similar to the rates on the yield curve for treasury bills.

Other net present value discount rate factors include: Should you use before tax or after tax discount rates? AS a general rule if you are using before tax net cash flows then use before tax discount rates. After tax net cash flow should use after tax discount rate.

### Net Present Value Formula

The Net Present Value Formula for a single investment is: NPV = PV less I

Where:

PV = Present Value
I = Investment
NPV = Net Present Value

The Net Present Value Formula for multiple investments is:

The sum of all terms of:

CF (Cash flow)/ (1 + r)t

Where:

CF = A one-time cash flow
r = the Discount Rate
t = the time of the cash flow

### Net Present Value Calculation

For a single investment:

\$120,000 – \$5,000 = \$115,000

Where:

PV = \$120,000
I = \$5,000
NPV = \$115,000

For multiple investments:

\$120,000 / (1 + 10%)1 = \$109,091

Where:

CF = \$120,000
r = 10%
t = Year 1
NPV = \$109,091

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Net present value benefits include the following:

### Net Present Value Limitations

Net present value disadvantages include the following:

### Net Present Value Example

For example, Jody is the owner of a debt collections firm called Collectco. Jody has been working on his company for several years. As the years have piled up on Jody, so has the urge to retire and live a simpler life. Finally reaching the end of his rope, Jody is ready to move on and spend more time with his children. In order to do this, Jody must sell his company. Adding to this, Jody must first make sure his company is up to date with industry standards. If Jody’s company is not performing to the same efficiency as the industry standard, then he will loose some of it’s value in negotiations with a buyer.

Jody begins by hiring an expert consultant in the industry to conduct an audit on the company. The audit turned out to be much better than Jody expected. But despite this, Jody must update his collections software as it is no longer supported by technical assistance from the creator. Jody performs the net present value calculation to evaluate this investment.

\$120,000 – \$5,000 = \$115,000

Where:

PV = The yearly income of Collectco = \$120,000
I = The cost of the new collections software = \$5,000
NPV = \$115,000

Now, Jody can begin the process of finding a buyer for his company. His consultant, an expert in the business dealings of collections firms, tells him that it is in his best interest to know the Net Present Value of his company before he begins negotiations. So, Jody starts this process by attempting to find the easiest way to perform this calculation. After finding few relevant online results for the search “net present value calculator”, Jody happens to find the NPV formula. Jody then performs the following calculation:

\$120,000 / (1 + 10%)1 = \$109,091

Where:

CF = Collectco yearly cash flow = \$120,000
r = 10%
t = Year 1
NPV = \$109,091

With this investment and information, Jody can begin to achieve what he has always dreamed of: a comfortable retirement which allows him to spend time with the people he cares about most. Jody is pleased because all of his efforts are resulting in the life he has worked to gain.

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# NPV vs Payback Method

NPV (Net Present Value) is calculated in terms of currency while Payback method refers to the period of time required for the return on an investment to repay the total initial investment. Payback, NPV and many other measurements form a number of solutions to evaluate project value.

Payback method, vs NPV method, has limitations for its use because it does not properly account for the time value of money, inflation, risk, financing or other important considerations. While NPV method considers time value and it gives a direct measure of the dollar benefit on a present value basis of the project to the firm’s shareholders. NPV is the best single measure of profitability.

Payback vs NPV ignores any benefits that occur after the payback period. It also does not measure total incomes. An implicit assumption in the use of payback period is that returns to the investment continue after payback period. Payback method does not specify any required comparison to other investments or investment decision making. It indicates the maximum acceptable period for the investment. While NPV measures the total dollar value of project benefits. NPV, payback period fully considered, is the better way to compare with different investment projects. If you’re looking to sell your company in the near future, download the free Top 10 Destroyers of Value whitepaper to learn how to maximize your value. Strategic CFO Lab Member Extra

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