Net Present Value (NPV) Analysis of Apple
Posted by Sabrina Warren on Aug012022
1. Introduction
1.1 Time Value of Money
Most people are aware that money in hand is more precious than the money collected in the future. We can utilize it to run a business, buy something now and sell it later for a profit, or just put it in the bank to generate interest. Future currency is also worth less since inflation erodes its purchasing power(Gallo, 2014). This concept is known as the time value of money. But how precisely do we compare the present worth of money to its future value? Herein lies the role of net present value(Dan, 2013).
1.2 Need of NPV
Net present value is the present value of the cash flows of an Apple project at the needed rate of return relative to the initial investment(Gallo, 2014).
It is a method for determining the return on investment, or ROI, for a project or expenditure. Apple can determine whether the project is worthwhile by calculating the investment's expected returns in today's dollars and comparing them to the project's cost(Dan, 2013).
2. Desirability of NPV
Internal rate of return, payback method, and net present value are the three options typically offered to Apple's Company manager when comparing projects and deciding whether to pursue. The majority of financial experts choose to use the net present value, also known as NPV. That is the case for two reasons, which are elucidated in the subsequent paragraphs.
2.1 The advantage over Payback Method
First, NPV examines the time value of money by transforming future cash flows into presentday dollars. Two, it provides a precise figure that Apple may use to compare initial cash spent with the present return value (Dikov, 2020).
According to the cofounder and proprietor of businessliteracy.com, it is vastly superior to the payback approach, which is the most prevalent(Knight, 2014).
The allure of payback is that it is easy to compute and comprehend: when will Apple recoup its initial investment? It does not, however, account for the fact that the purchasing power of money today is larger than that of the same amount of money in the future. According to Knight, this is why NPV is the preferable method (2014).
2.2 Convenience of Use
Thanks to financial calculators and Excel spreadsheets, NPV is now that simple to compute. Apple can also utilize NPV to determine whether or not to make significant acquisitions, such as equipment or software. Apple Companycan also utilize it in mergers and acquisitions, albeit, in this case, it is referred to as the discounted cash flow model. In fact, this is the methodology that Warren Buffet employs when evaluating businesses. NPV is an excellent choice if a corporation uses presentday dollars to estimate future returns(Knight, 2014)
3. Procedure
3.1 Discount Factor
The discount factor formula provides a method for determining the net present value (NPV) for Apple. It is a weighted word used in mathematics and economics to identify the precise factor by which the value is multiplied to get at the net present value as of today.
This is widely used in corporate budgeting to analyze whether a proposal would bring future value.
3.2 Difference between Discount Rate and Discount Factor
Any discount factor equation assumes that money will be worth less in the future owing to causes such as inflation, resulting in a discount factor value between zero and one. The discount factor and discount rate are closely connected; however, whereas the discount rate considers the present value of future cash flows, the discount factor applies to the net present value.
With these numbers, Apple can predict the predicted earnings or losses of an investment and its net future value.
3.3 Formula
The formula Apple can use for the general discount factor is (Thakur, 2018):
Discount Factor= 1/(1*(1+Discount Rate)^(Period Number) )
3.4 Methodology
To utilize this formula, the periodic interest rate or discount rate must be determined by Apple. This is simply calculated by dividing the yearly discount factor interest rate by the number of annual payments.
Additionally, Apple will want the total number of payments that will be paid. To perform these computations, Apple can generate a discount factor template or table in Excel by inserting the aforementioned formula with our own values. Applewill compute it the following way:
Period 
1  2  3  4 
Cash Flow 
£100,000 
£100,000 
£100,000 
£100,000 
=1/1*(1+£C£4)^C2) 
=1/1*(1+£C£4)^D2) 
=1/1*(1+£C£4)^E2) 
=1/1*(1+£C£4)^F2) 

Discount Factor 
0.93 
0.86 
0.79 
0.74 
This demonstrates the diminishing discount factor with time, whether it is an annual discount factor or a shorter
time frame to match our accounting period. This applies whether the time range reflects an annual discount factor or a
shorter time frame.
For instance, to determine the discount factor for a cash flow that will occur one year from now, all that needs to be done by Apple is divide one by the interest rate plus one. If the interest rate was 5%, the discount factor would be calculated as 1 less than 1.05, which is equivalent to 95%.
3.5 Usage in NPV Analysis
After Applehas computed their discount factor and discount rate, they will be able to apply these two factors to the problem of determining the net present value of an investment. The total present value of all positive cash flows should be added together, and the total present value of all negative cash flows should be subtracted.
After making the appropriate calculations using the interest rate, Apple will arrive at the net present value. Many discount factor calculators available online will apply these formulas; alternatively, Apple may perform an analysis using Excel.
4. Net Present Value
4.1 Case 1: Variable Cash Flow
Calculating both the expenses (which result in negative cash flows) and the benefits allow Appleto arrive at the Net Present Value of a series of cash flows (positive cash flows).This is accomplished by the utilization of the following formula(Indeed Editorial Team, 2021):
NPV= ∑_(t=0)^n▒〖CF〗_t/〖(1+i)〗^t
Where CFt denotes the cash flow during the period, n is the total number of periods, t denotes the currently active period, and I represent the discount rate of Apple(Dikov, 2020).
4.2 Case 2: Constant Cash Flow
The following is an example of a basic finite geometric series that may be used to express the formula if Apple projects a consistent cash flow year after year(Indeed Editorial Team, 2021):
NPV= CF*((1(1/(1+i))^(n+1))/(1 (1/(1+i)) ))
Where CF represents the continuous cash flow throughout each period, n represents the total number of periods, and I is the discount rate for Apple(Dikov, 2020).
5. NPV in Capital Budgeting
5.1 Nature of the Project
Before Apple can use net present value to evaluate a capital investment project, we will first need to determine if the project in question is independent or part of a chain of mutually exclusive projects (Taylor, 2017).
5.1.1 Independent
It refers to endeavors that are not influenced by the revenue flows generated by other initiatives.
5.1.2 Mutually Exclusive
If two projects are mutually exclusive, it indicates that there are two approaches to achieve the same outcome and cannot be done simultaneously. For example, it's possible that Apple may request bids on a certain project and that they've gotten several of those bids.
Apple should avoid the temptation to take two different bids for the same project. That illustrates a project that cannot coexist with another(Carlson, 2021).
5.2 Decision Rules
Every approach to budgeting capital expenses includes a list of decision rules. For instance, the decision rule for the payback period approach states that Apple must agree to move forward with the project if it is able to earn back its initial investment in a predetermined amount of time(Luehrman, 2016).
The same decision rule should be used when applying the discounted payback time technique. The concept of net present value comes with its own set of decision criteria, which are as follows:
5.2.1 Case 1: Independent Project
Apple should accept the proposal if the NPV is larger than zero.
5.2.2 Case 2: Mutually Exclusive Projects
If the net present value (NPV) of one project is larger than the NPV of the other project, then Apple will accept the project with the higher NPV. If both initiatives' net present value (NPV)s negative, then neither project should be pursued(Tamplin, 2021).
Consider the following scenario as we go through the process:
5.3 An Example
Let's say that the Apple is thinking about two different initiatives: A and B. Apple’sCompanycost of capital for each individual project is ten percent, and the initial investment is ten thousand dollars.
Apple is interested in determining and analyzing the difference in the net present value of these cash flows between the two projects. Every project has a different pattern of incoming funding. To put it another way, the cash flows do not constitute annuities.
5.3.1 Cash Flows
Apple wishes to compute the NPV for each project. The cash flows in each of the four years of Project A are as follows: $5,000, $4,000, $3,000, and $1,000, respectively. Project A is a fouryear endeavor. The cash flows in each of the four years of Project B are as follows: $1,000, $3,000, $4,000, and $6,750, respectively. Project B is also a fouryear Endeavor.
5.3.2 Calculation
To calculate the NPV of the project, Applestarts by adding the cash flow from Year 0, which represents the initial investment in the project, to the cash flows from the remaining years of the project.
The original investment results in a negative cash flow and is therefore expressed as a negative figure. In this illustration, the cash flows for each project for years 1 through 4 are all exemplified by positive numbers.
To get the NPV for Project A, Applefollows these steps:
NPV(A) = ($10,000) + $5,000/(1.10)1 + $4,000/(1.10)2 + $3,000/(1.10)3 + $1,000/(1.10)4
10%  0  1  2  3  4 
CFs  10,000  5,000  4,000  3,000  1,000 
NPV  716.54 
The NPV of Project A is $716.54, which indicates that investing in the project increases the firm's value by $716.54.
For Project B:
NPV(B) = ($10,000) + $1,000/(1.10)1 + $3,000/(1.10)2 + $4,000/(1.10)3 + $6,750/(1.10)4
10%  0  1  2  3  4 
CFs  10,000  1,000  3,000  4,000  6,750 
NPV  912.75 
Since Project B has a higher NPV than A, Applecan safely choose Project B instead of A based on our analysis.
6. NPV in Stock Valuation
The most popular approach for evaluating the value of Apple shares is the Discounted Cash Flow (DCF) model, which employs Net Present Value (NPV) in its calculation. The DCF model methodology is explained below.
6.1 Initial Steps
Beginning with the revenue statement of Apple, we project future (typically five) years' income and expenses(Probasco, 2021). Then, projections are made for fixed assets and changes in the working capital of Apple
. The second level is capital structure projection. Depending on the type of DCF model being constructed, the most frequent strategy is to maintain the Applecurrent capital structure, assuming no major changes other than those that are known, such as debt maturity(CFI, 2022).
6.2 Terminal Value
The terminal value, a crucial component of a DCF model, is then calculated. It frequently accounts for more than 50 percent of the Applenet present value, especially if the forecast term is five years or less. There are two methods for calculating the terminal value: the perpetual growth rate method and the exit multiple methods (Matthiessen, 2019).
6.2.1 Perpetual Growth Rate Method
The perpetual growth rate method assumes that the cash flow created at the end of the projected period rises at a constant rate in perpetuity. Consider that another company is looking to acquire
Company Apple, whose cash is $10 million, grows at a rate of 2% indefinitely, with a cost of capital of 15%. $10 million / (15 percent  2 percent) = $77 million is the terminal value.
6.2.2 Exit Multiple Method
Using the exit multiple method, it is assumed that Applewas sold for the price that a reasonable buyer would pay. This often entails an EV/EBITDA multiple equal to or close to the current market values of comparable companies. As seen in the following example, if Apple has $6.3 million in EBITDA and comparable businesses are trading at 8x, then the terminal value is $6.3 million x 8 = $50 million.
Entry 
2018 
2019 
2020 
2021 
2022 
Exit 

Date 
31/12/17 
30/06/18 
30/06/19 
30/06/20 
30/06/21 
30/06/22 
30/06/22 
Time Periods  0  1  2  3  4  
Year Fraction  0.5  1  1  1  1  
EBIT  47,814  51,095  55,861  58,693  63,039  
Less: Cash Taxes  11,954  12,774  13,965  14,673  15,760  
Plus: D&A  15,008  15,005  15,003  15,002  15,001  
Less: Capex  15,000  15,000  15,000  15,000  15,000  
Less: Cgs NWC  375  611  398  511  272  
Unlevered FCF  35,494  37,715  41,501  43,510  47,008  
(Entry)/Exit  290,450  542,129  
Transaction CF    17,747  37,715  41,501  43,510  47,008  542,129 
Transaction CF  290,450  17,747  37,715  41,501  43,510  47,008  542,129 
Intrinsic Value 

Enterprise Value  462,983 
Plus: Cash  239,550 
Less: Debt  30,000 
Equity Value  672,532 
Equity Value/Share  33.63 
Terminal Value 

Perpetual Growth  537,981 
EV/EBITDA  546,278 
Average  542,129 
6.2.3 Decision
If we want to determine the equity value of Apple, we must adjust the net present value (NPV) of the unlevered free cash flow for cash and equivalents, debt, and any minority stake(Ahern, 2022). This yields the equity value, which may then be divided by the number of shares to obtain the share price. Then, we may determine whether the stock of Appleis overvalued or undervalued and decide whether to purchase or sell it.
7. Assumptions
Even though the discounted value of future cash flows is not a statement that nonfinancial individuals easily utter still, it is worthwhile to explain and present NPV due to its superiority, as any investment that passes the net present value test will improve shareholder value. In contrast, any project that fails would actually harm the company and its shareholders if carried out anyhow(Entras, 2016).
There are three potential estimation errors that will have a significant impact on the final outcomes of our calculation.
7.1 Initial Expenditure
First, there is the initial expenditure(Kristiani, 2022). Does Apple know how much the project or expense will cost? There is no risk when purchasing a piece of equipment with a visible price tag. But if Apple is modernizing its IT system and estimating staff time and resources, the project timetable, and how much it will pay external vendors, the numbers can vary significantly(Jones & Smith, 1982).
7.2 Discount Rate
There are further dangers associated with the discount rate. Apple is applying today's rate to future returns, so there is a potential that, for example, in Year Three of the project, interest rates will skyrocket, and the cost of their money will increase(Ionos, 2019).
This would imply that Apple’sreturns for that year will be lower than anticipated.
7.3 Anticipated Returns
Third, Apple must be confident in the anticipated returns of the project(Mendell, 2020). These forecasts are typically optimistic since people want to complete the project or purchase the equipment(Bey, Doersch, & Patterson, 1981). This, however, can lead to erroneous NPV calculations.
8. Sensitivity Analysis
Given that the computation is based on a number of assumptions and approximations, there is a considerable possibility of a mistake. After our initial computation, Apple can mitigate the risks by doublechecking our calculations and conducting sensitivity(Borgonovo & Peccati, 2004). The following is one illustration:
8.1 An Example
Cash Flow projections for the following 12 years are offered for Company Apple(see below). Capital cost is eight percent. Assuming the variables remain constant, we calculate the Apple’s Net Present Value (NPV).
Sensitivity Analysis 

Year 0 
Years 1  12 

Investment  ($5,400.00) ”  
Sales  $16,000.00  
Variable Costs  $13,000.00  
Fixed Costs  $2,000.00  
Depreciation  $450.00  
Pretax Profit  $550.00  
Taxes (40%)  $220.00  
Profit After Tax  $330.00  
Operating Cash flow  $780.00  
Net Cash Flow  ($5,400.00) ”  $780.00 
NPV  $470.25 
Possible Outcomes 

Variable 
Pessimistic 
Expected 
Optimistic 
Investment  5800  5400  5000 
Sales  14000  16000  18000 
Variable Costs  11620 which is 83% of Sales  13000 which is 80.25% of Sales  14400 which is 80% of Sales 
Fixed Costs  2100  2000  1900 
NPV  ($121.00) ”  $470.25  $778.00 
9. Conclusion
NPV's significance in predicting the future of Apple and its projects is undeniable and an indispensable tool within the field of Financial Analysis. However, it must be remembered that it is expressed in absolute rather than relative terms and hence does not account for the magnitude of the investment, Apple opportunity costs, or the project's duration. In light of the limitations and benefits of NPV, it is imperative for Apple not to rely solely on it and to undertake assessments using alternative approaches, such as IRR, to be certain.
10. Works Cited
Ahern, D. (2022, June 15). Explaining the DCF Model. Retrieved from eB: https://einvestingforbeginners.com/dcfvaluation/
Bey, R. B., Doersch, R. H., & Patterson, J. H. (1981). The Net Present Value Criterion. Project Management Quarterly, 12(2), 3545.
Borgonovo, E., & Peccati, L. (2004). Sensitivity Analysis In Investment Project Evaluation. International Journal of Production Economics, 90(1), 1725.
Carlson, R. (2021, February 8). NPV as a Capital Budgeting Method. Retrieved from The Balance: Small Business: https://www.thebalancesmb.com/netpresentvaluenpvasacapitalbudgetingmethod392915
CFI. (2022, June 2). DCF Model Training. Retrieved from Corporate Finance Institute: https://corporatefinanceinstitute.com/resources/knowledge/modeling/dcfmodeltrainingfreeguide/
Dan. (2013, July 24). Time Value of Money. Retrieved from The Strategic CFO: https://strategiccfo.com/articles/accounting/timevalueofmoney/
Dikov, D. (2020, March 13). NPV in Financial Analysis. Retrieved from Magnimetrics: https://magnimetrics.com/netpresentvaluenpvinfinancialanalysis/
Entras. (2016, April 1). NPV of a Business Case: Common Pitfalls. Retrieved from Entras: https://www.entras.be/news/npvofabusinesscasecommonpitfalls/
Gallo, A. (2014, November 1). A Refresher on Net Present Value. Retrieved from Harvard Business Review: https://hbr.org/2014/11/arefresheronnetpresentvalue
Indeed Editorial Team. (2021, December 9). How To Calculate Net Present Value. Retrieved from Indeed: https://www.indeed.com/careeradvice/careerdevelopment/calculatenpv
Ionos. (2019, April 19). What is Net Present Value. Retrieved from Ionos: https://www.ionos.com/startupguide/growourbusiness/whatisnetpresentvalue/
Jones, T. W., & Smith, J. D. (1982). A Historical Perspective Of Net Present Value And Equivalent Annual Cost. The Accounting Historians Journal, 9, 103110.
Juhász, L. (2011). Net Present Value Versus Internal Rate Of Return. Economics Sociology, 4(1), 4653.
Knight, J. (2014, August 1). Financial Intelligence. (A. Gallo, Interviewer)
Kristiani, V. M. (2022, March 5). Net Present Value. Retrieved from Hashmicro: https://www.hashmicro.com/blog/netpresentvaluenpv/
Luehrman, T. A. (2016, June 10). NPV and Capital Budgeting. Retrieved from Harvard Business Publishing: https://hbsp.harvard.edu/product/5176PDFENG
Matthiessen, A. (2019, March 20). Startup valuation. Retrieved from EY: https://www.ey.com/en_nl/financenavigator/startupvaluationapplyingthediscountedcashflowmethodinsixeasysteps
Mendell, B. (2020, May 31). Pros and Cons of Using NPV. Retrieved from Forisk: https://forisk.com/blog/2020/05/31/prosandconsofusingnetpresentvaluenpv/
Probasco, J. (2021, October 20). Net present value: One way to determine the viability of an investment. Retrieved from Business Insider: https://www.businessinsider.com/personalfinance/npv
QS Study. (2018, May 10). Limitations of NPV. Retrieved from QS Study: https://qsstudy.com/limitationsnetpresentvaluenpv/
Tamplin, T. (2021, September 21). Capital Budgeting: Important Problems and Solutions. Retrieved from Finance Strategists: https://learn.financestrategists.com/explanation/managementaccounting/capitalbudgetingimportantproblemsandsolutions/
Taylor, P. (2017, May 13). NPV Analysis. Retrieved from Stantec: https://www.stantec.com/content/dam/stantec/files/PDFAssets/UK/uknetpresentvaluebrochure.pdf
Thakur, M. (2018, February 7). Discount Factor Formula. Retrieved from Educba: https://www.educba.com/discountfactorformula/
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