Umedjon HAITMURODOV - FINANCIAL MODELS

Financial Models

   Financial Analysis are another important series of project selection desicions. In this section three common financial models: discounted cash flow analysis, net present value and internal rate of return are going to be examined. These three models are not the only methods of making project decisions, but we can say that these are the most important. 

   In this report Financial Models are going to be discusses and explained both in oral and mathematical ways. Financial Models are one of the important subject to run a business an building financial models can make or even put you in a tower position of your business.

   As we know that time is money, so Financial Models are all predicated on the time value of money principle. This principle suggests us that today’s earned money is worth more than future’s or even tomorrow’s money. For instance, $500 that I receive three years from now is worth significantly less to me than if I were to receive that money today. That is the reason people are putting money  on bank or getting money from bank with interest. If I put $100 in a bank with interest rate of 5%, I will get $105 one year later, or after 10 years I am going to take $150. My interest is going to grow money at a compounded rate each year. In here, the principle also will work in reverse. For calculating the Present value of $100 that I expect to have in the bank in four years’ time I must first discount the amount by the same interest rate.

   There are two reasons why we would expect future money to be worth less:

1.  The impact of inflation

2. The inability to invest the money.

   We know that inflation causes prices to rise and decreases consumers’ spending power. For example, 20-30 years ago the price of houses were a few thousand dollars but now house prices are too high than that years. Also, if I am to receive $100 in four years, its value will have decreased due to the negative effects of inflation. The inability to invest the money means not having that $100 today means that I cannot invest it and earn a return on my money for the next four years. 

Based on the time value of money principle Financial Models divide into five functions. These funcions are:

1. Payback Period
2. Net Present Value 
3. Discounted Payback 
4. Internal Rate of Return 
5. Options Model

     In the coming pages these five functions of Financial Models are going to be explained and discussed. Also, there will be solved questions for all functions to be understood easily.

1.      Payback Period

     The aim of project payback period is to guess the amount of time that will be important the investment in a project. This include the time that project can take to pay back its initial budget and begin to generate positive cash flow for the company. In determining payback period for a project, we must employ a discounted cash flow analysis, based on the principal of the time value of money. The target of the discounted cash flow (DCF) method is to estimate cash outlays and expected cash inflows resulting from investment in a project. All potential costs of development (most of which are contained in the project budget) are assessed and projected prior to the decision to initiate the project. They are then com- pared with all expected sources of revenue from the project.

     We then apply to this calculation a discount rate based on the firm’s cost of capital. The value of that rate is weighted across each source of capital to which the firm has access (typically, debt and equity markets). In this way we weight the cost of capital, which can be calculated as follows:

Kfirm  = (wd)(kd)(1  - t)  + (we)(ke)

     The weighted cost of capital is the percentage of capital derived from either debt (wd) or equity (we) times the percentage costs of debt and equity (kd and ke, respectively). (The value t refers to the company’s marginal tax rate: Because interest payments are tax deductible, we calculate the cost of debt after taxes.)

There is a standard formula for payback calculations:

Payback period  = investment/annual cash savings

Example

     Our company wants to determine which of two project alternatives is the more attractive investment opportunity, using a payback period approach. We have calculated the initial investment cost of the two projects and the expected revenues they should generate for us (see Table 3.5). Which project should we invest in?

Solution

     For our example, the payback for the two projects can be calculated as in Table 3.6. These results suggest that Project A is a superior choice over Project B, based on a shorter projected payback period (2.857 years versus 4.028 years) and a higher rate of return (35% versus 24.8%).

	Revenues	Project A        Outlays	Revenues	Project B         Outlays
Year 0		$500,000		$500,000
Year 1	$ 50,000		$ 75,000
Year 2	150,000		100,000
Year 3	350,000		150,000
Year 4	600,000		150,000
Year 5	500,000		900,000

Project A	Year	Cash Flow	Cum. Cash Flow
	0	($500,000)	($500,000)
	1	50,000	(450,000)
	2	150,000	(300,000)
	3	350,000	50,000
	4	600,000	650,000
	5	500,000	1,150,000
Payback= 2.857 years Rate of Return =35%
Project B	Year	Cash Flow	Cum. Cash Flow
	0	($500,000)	($500,000)
	1	75,000	(425,000)
	2	100,000	(325,000)
	3	150,000	(175,000)
	4	150,000	(25,000)
	5	900,000	875,000
Payback = 4.028years Rate ofReturn=24.8%

2.      Net Present Value

     The most popular financial decision-making approach in project selection, the net present value (NPV) method, projects the change in the firm’s value if a project is undertaken. Thus a positive NPV indicates that the firm will make money and its value will rise as a result of the project. Net present value also employs discounted cash flow analysis, discounting future streams of income to estimate the present value of money. Net present value is one of the most common project selection methods in use today. Its principal advantage is that it allows firms to link project alternatives to financial performance, better ensuring that the projects a company does choose to invest its resources in are likely to generate profit

The simplified formula for NPV is as follows:

NPV(project)  = I0  + g Ft /(1  + r + pt)t

Where,                                                                  

   Ft = the net cash flow for period t

    r = the required rate of return

    I = initial cash investment (cash outlay at time 0)

    pt = inflation rate during period t

     The optimal procedure for developing an NPV calculation consists of several steps, including the con- struction of a table listing the outflows, inflows, discount rate, and discounted cash flows across the relevant time periods.

Example

     Assume that you are considering whether or not to invest in a project that will cost $100,000 in initial invest- ment. Your company requires a rate of return of 10%, and you expect inflation to remain relatively constant at 4%. You anticipate a useful life of four years for the project and have projected future cash flows as follows:

Solution

Year 1:	$20,000
Year 2:	$50,000
Year 3:	$50,000
Year 4:	$25,000

We know the formula for determining NPV:

NPV = I0  + g Ft /(1  + r + p)t

                            Net flows:    just the difference between inflows and outflows

                       Discount factor:    simply the reciprocal of the discount rate (1/(1 + k + p)t)

Year	Inflows	Outflows	Net Flow	Discount Factor	NPV
0		100,000	(100,000)	1.000
1	20,000		20,000	0.8772
2	50,000		50,000	0.7695
3	50,000		50,000	0.6749
4	25,000		25,000	0.5921

Year	Inflows	Outflows	Net Flow	Discount Factor	NPV
0		100,000	(100,000)	1.000	(100,000)
1	20,000		20,000	0.8772	17,544
2	50,000		50,000	0.7695	38,475
3	50,000		50,000	0.6749	33,745
4	25,000		25,000	0.5921	14,803
Total					$4,567

How did we arrive at the Discount Factor for Year 3? Using the formula we set above, calculate the appropriate data:

                                          Discount factor = (1/(1  + .10 + .04)3) = .6749

3.      Discount Payback

     Now that we have considered the time value of money, as shown in the NPV method, we can apply this logic to the simple payback model to create a screening and selection model with a bit more power. Remember that with NPV we use discounted cash flow as our means to decide whether or not to invest in a project opportunity. Now, let’s apply that same principle to the discounted payback method. Under the discounted payback method, the time period we are interested in is the length of time until the sum of the discounted cash flows is equal to the initial investment.

   Let’s try a simple example to illustrate the difference between straight payback and discounted payback methods. Suppose we require a 12.5% return on new investments and we have a project opportunity that will cost an initial investment of $30,000 with a promised return per year of $10,000. Under the simple payback model, it should only take three years to pay off the initial investment. However, as Table 3.9 demonstrates, when we discount our cash flows at 12.5 percent and start adding them, it actually takes four years to pay back the initial project investment.

   The advantage of the discounted payback method is that it allows us to make a more “intelligent” determination of the length of time needed to satisfy the initial project investment. That is, while simple payback is useful for accounting purposes, discounted payback is actually more representative of financial realities that all organizations must consider when pursuing projects. The effects of inflation and future investment opportunities do matter with individual investment decisions and so, should also matter when evaluating project opportunities.

4.      Internal Rate of Return

    Internal rate of return (IRR) is an alternative method for evaluating the expected outlays and income associ- ated with a new project investment opportunity. If the IRR is greater than or equal to the company’s required rate of return, the project is worth funding. In the example above, we found that the IRR is 15% for the project, making it higher than the hurdle rate of 10% and a good candidate for investment. The advantage of using IRR analysis lies in its ability to compare alter- native projects from the perspective of expected return on investment (ROI). Projects having higher IRR are generally superior to those having lower IRR.

Example

    Let’s take a simple example. Suppose that a project required an initial cash investment of $5,000 and was expected to generate inflows of $2,500, $2,000, and $2,000 for the next three years. Further, assume that our company’s required rate of return for new projects is 10%. The question is: Is this project worth funding?

Solution

Cash investment = $5,000

                                 Year 1 inflow = $2,500

                                  Year 2 inflow = $2,000

                                 Year 3 inflow = $2,000

                   Required rate of return = 10%

Step One: Try 12%.

Year	Inflows	at 12%	NPV
1	2,500	.893	2,232.50
2	2,000	.797	1,594
3	2,000	.712	1,424
Present value of inflows			5,250.50
Cash investment			- 5,000
Difference			$ 250.50

Step Two: Try 15%.

		Discount Factor
Year	Inflows	at 15%	NPV
1	2,500	.870	2,175
2	2,000	.756	1,512
3	2,000	.658	1,316
Present value of inflows			5,003
Cash investment			5,000
Difference			$3

5.      Options Model

   Let’s say that a firm has an opportunity to build a power plant in a developing nation. The investment is particularly risky: The company may ultimately fail to make a positive return on its investment and may fail to find a buyer for the plant if it chooses to abandon the project. Both the NPV and IRR methods fail to account for this very real possibility—namely, that a firm may not recover the money that it invests in a project. Clearly, however, many firms must consider this option when making investment decisions.

1.        Whether it has the flexibility to postpone the project

2.      Whether future information will help it make its decision

Example

   A construction firm is considering whether or not to upgrade an existing chemical plant. The initial cost of the upgrade is $5,000,000, and the company requires a 10% return on its investment. The plant can be upgraded in one year and start earning revenue the following year. The best forecast promises cash flows of $1 million per year, but should adverse economic and political conditions prevail, the probability of realizing this amount drops to 40%, with a 60% probability that the investment will yield only $200,000 per year.

Solution

We can first calculate the NPV of the proposed investment as follows:

Cash Flows = .4($1 million)  + .6($200,000) =  $520,000

NPV =  - $5,000,000 +  g $520,000/(1.1)t

=  - $5,000,000 + ($520,000/.1)

=  - $5,000,000 +  $5,200,000

=  $200,000

    Because the $520,000 is a perpetuity that begins in Year 1, we divide it by the discount rate of 10% to determine the value of the perpetuity. According to this calculation, the company should undertake the project. This recommendation, however, ignores the possibility that by waiting a year, the firm may gain a better sense of the political/economic climate in the host country. Thus the firm is neglecting important information that could be useful in making its decision. Suppose, for example, that by waiting a year, the company determines that its investment will have a 50% likelihood (up from the original projection of 40%) of paying off at the higher value of $1 million per year.

   The following link contains a video in which Financial Models are going to be explained by excel in a very simple way.

https://www.youtube.com/watch?v=Xs3MCM0dXW0