Calculation of Net Present Value of the Business


Extremely high wages paid to the chief executive officers of high companies can be explained by successful growth strategies chosen by them that translate into dramatic increases of these companies’ stockholders wealth, overall company earnings and value. The existence of not well-performing companies is due to the failure of their managers to foresee the market movements and adjust the company strategies to them. Thus, when hiring a chief executive officer, the company owners make a very important decision as they put their whole wealth in his/her hands and their income will depend on the cooperation of the management company. The accomplishments will depend on good financial education or extensive positive experience which will be appropriately applied to the operations of this specific company.

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Corporate finance is an extensive field and requires many years of education and background exposure in order to understand it and be able to even anticipate the effects that some financial aspects will have on the corporate performance. But there are some segments of the huge corporate finance knowledge that must be well realized not only by chief executive officers, but by the majority of managers at even operation level because their misperception can lead to fatal for the company mistakes. Thus, financial managerial decision are usually divided into two groups: financing and budgeting decisions, where budgeting refers to choosing the optimal financing source and timing for a business opportunity which will lead to increasing value of the company, and financing refers to singling out of numerous business opportunities those which will provide the biggest financial and social benefits for the company and its’ stockholders. In order to make both decisions, financial analysis of all the alternatives has to be made. In terms of financing decision it implies picking the cheapest source of financing, while when applied to budgeting decision, the best investment opportunity with value gains must be chosen. All the financial analysis decisions are based on comparing the cash flows generated by different business opportunities, or the cash outlays which an investment will require. Thus, the starting point in carrying out a comparison is realizing that cash flows that occur in different times will have different values. This is the ‘time value of money concept’, which means that ‘a dollar today is worth less than a dollar tomorrow’. This is deferred from the fact that even in stable economies inflation exists and the dollar today can buy more goods than a future dollar. The amount of money received in some future point of time is referred to as the ‘future value of money’ and it will grow at the interest rate at which it is invested. For example, $100 invested today for 5% annual interest rate will generate $100*105% = $105. Another thing is how many goods these $105 will be able to buy in one year comparing to the amount of goods that $100 can buy today.

On the contrary, ‘present value’ of a certain amount of money’ refers to the amount that must be invested today to generate at this future date a certain amount of money. Thus, to receive $105 in one year, one must invest $100 today if the interest rate is 5%. The present value of future cash flows is calculated using the discount rate which ‘usually represents the cost of capital for the person or entity calculating the net present value of the stream’. For calculating the present values of further cash streams, the discount factors can be exploited. The discount factor represents how much a future dollar is worth today. For example, the discount rate of 0.95 implies that a future dollar is worth only 0.95 cents today.

The discount factor is derived from the discount rate using the following equation: 1 + (1 + i) n, where I is the rate of interest (discount rate) and n is the number of years. That is why the process of deriving the present value of a future cash flow is knows as discounting. From the formula it is evident that the present value will depend on the year in which the cash flow will be generated and it will be lower, the further the cash flow is received. An important implication is that in order to carry out a precise and accurate estimation of present value of future cash flows or costs, they must be all discounted to a single time period in order to make the proper comparison. As mentioned above, due to the inflation which makes the purchasing power of money different in various points of time, comparing cash flows in nominal terms (the amounts that occur) is misleading. The value of all the future cash flows or outflows for one specific date (discounted nominal cash flows using the discount rate which reflects the accumulated inflation from this specific date till the date when the cash flows occurs) is the sum of present values of all these cash flows. Every project requires certain cash outlays at different spans of the project life, the initial investment, the complementary investments, unpredicted cash spending which occur in the different time. Any business initiative generates capital gains or earnings also in different times. Thus, adding the present values will give the benchmark for estimating the total benefits from the project and the total costs.

Mathematics comes in hand for financial analysts and there are certain shortcuts which make calculating the benefits or costs of the projects much faster. For estimating ‘equally spaced level streams of cash flows’, or ‘annuities’, a level of even cash flows starting immediately (annuities due), or a stream of level cash payments that last perpetually (perpetuity), the formulas are used.

Stressing again the importance of adjusting all the future cash flows for inflation and risk, the concepts of nominal cash flows, or payments in current dollars, or real cash flows, or payments equal in constant dollars (one benchmark date for all future cash flows) are used. Usually, the business projects can be rather long-lived, and using effective interest rate (rate of interest per period compounded for the number of periods in a year) to bring all the cash flows to a single date, or using the annual percentage rate (annualized using simple interest rate) can generate different results. Thus, the present value of a future cash flow discounted using the effective interest rate will be smaller, but when the cash flows are large and projects lives are long, the difference can be very significant.

Inflation is not the only determinant which makes the future benefits from accepting a business initiative look less attractive today. Any business idea is risky due to the volatility of the overall economy, volatility of the unique market segment where the project will operate, uncertainty about the demand for the products or services produces by the products due to possible technological innovations and creation of substitutes, the risk of the default of the company and many others. Thus, the risk must be taken into consideration when estimating the relative attractiveness of the project. The riskier the project, the less is the certainty that the initial investment in this opportunity will be recovered. This uncertainties makes investors want to know the rates of returns that the project will generate and how much wealthier it will make them, and they demand higher rates of returns for riskier projects in order to initiate it. The return on the investment opportunity relates to the predicted payoff over the initial outlay and compensation for the investors for both waiting for the profits (time value of money) and worrying whether the profits will be received or not (risk of investing in a specific asset). The risk of the project or an asset, or of the portfolio which consists of several projects or assets is looked upon in terms of volatility of returns (how the assumed returns deviate from the predicted expected average return) and is measured as standard deviation and variance of the expected returns. Initiating every project bears both market risk, or risk that the overall economy/market segment where the project competes will turn down, and the unique risk, or the risk of not receiving payoffs from this very project due to bad management or other circumstances. Diversifying the assets in a portfolio, thus choosing assets that depend on different fundamentals in the market movements, reduces the overall portfolio risk and risk on some projects which may not seem appealing due to high risk can be ‘diversified away’ when putting these assets together in a portfolio with other low-risk assets, or assets for which performance depends on different fundamentals. The implication is that the big investors, or the smart investors, who hold carefully diversified portfolios, should worry only about the overall market risk (that overall economy will go bad), because with such a portfolio, the loss on holding one asset will be compensated by the gain from another asset, as diversification by mixing assets that move in different directions, will imply that.

This sounds very reasonable and if these techniques are known, why then defaults exist? The answer is that precise and reliable estimation of risks and returns on the investment opportunity are very hard to make due to certain obstacles. Furthermore, the assumed ‘cooperation’ of these assets when put in portfolio maybe perceived differently by the manager than the reality will be which can lead to losses.

On the difficulties side, first of all, the opportunity cost of capital is the hardest assumption to be drawn. Opportunity cost of capital is the expected rated of return which could be achieved from investing in a business endeavor with the same risk. It can be looked upon as the ‘depreciation rate’ of the future earnings for the investor. The opportunity cost of capital thus reflects the inflation rate and the risk of the project. For example, one can invest $1,000 today in project a and generate $1,100 in a year. This will give the expected rate of return of 10%. Also, another business idea with the same risk level exists, which will yield $1,200. As the risk for the project B. is the same, we can find the present value of this income gain, using 10% as the opportunity return that could be achieved from investing in project a. Discounting the future $1,200 at 10% discount rate, the present value of this cash flow is $1,090, which means that with the same risk for both opportunities, opportunity B. is worth more today.

This simple example exploits calculation of Net Present Value of the business opportunity in order to see how much it is worth today. Net Present Value refers to the present value of all the earnings generating from accepting the project deducted for the initial outlays necessary for starting this project. This investment assessment tool estimates by how much in today’s dollars the wealth of investor will increase if he pursues this initiative. As the perceptions of benefits from the projects are different for different investors, as well as valuation needs vary, other techniques are used to estimate whether the deal is worthy. The Internal Rate of Return rule states that the affair is worthy if the rate of return that it provides is higher than the opportunity cost of capital, or the return that could have been achieved from investing in the project with the same risk. The Internal Rate of Return is simply the discount rate at which the Net Present Value of the activity equals zero. The uses estimation of the time period which it will take for the initial spending on the investment activity to recover. Different investors require different payback periods, and if the estimated payback period meets this requirement (is shorter), then the affair is worthy. Having stressed the importance of considering the time value of money, it is clear that the Payback Period Rule is faulty as it does not account for this fundamental, and also this rule does not add to the overall project value the benefits generated by the project after the cutoff date. Managers as well employ the Book Rate of Return or Average Accounting Return (accounting income divided by book value) to set the benchmark for estimating the worthiness of the opportunity. Remembering the fact that accountants are rewarded to reflect the accounting profits in ways favorable for the taxation of the company, and that in the majority of cases the market value of a company or a project differs from the accounting numbers, this method cannot lead to proper conclusions. The Profitability Index Tool, can favor projects with high rates of return but low value added to the company value, as it measures the ratio of present value to initial investment. Recapitulating, NPV rule is the superior in making investment pursuing decisions and leads to most accurate calculations, thus I chose considering it in more details as the core for my work.

The NPV canon declares that the financial managers increase the wealth of the stockholders and the value of the company by singling out and accepting the projects that are worth more today than they cost, therefore, they have positive Net Present Values. The equation for estimating the activity’s NPV is as follows:

NPV = -C0 + C1 / (1 + r) + C2 / (1 + r) 2 +…+ Cn / (1 + r) n,

Where -C0 is the initial outlay necessary for taking on the project, and thus it is negative, and C1, C2, Cn are the earnings from the project and r is the discount rate to bring the future incomes to one date and it is the opportunity cost of capital.

The opportunity cost of capital will not only depend on the risk of the project, but all will be impacted by the financial structure of the company and the financing of the project. Finding the correct discount rate is the crucial task for the manager. The work by Colin Drury and Mike Tayles reveals that the most frequently used investment assessment technique is unadjusted payback period rule which is exploited by 63% of managers, followed by the IRR method used by 57% of managers, and then 43% use NPV technique. Another empirical finding by the authors is that bigger companies that can afford to higher managers with better education employ the NPV and IRR rules more often to estimate the attractiveness of the business ideas. The research work by Graham and Campbell suggest that 74,9% of the surveyed CFOs always or almost always work with Net Present Value method as the capital budgeting decision benchmark, while 75,7%n of the CFOs always or almost always work with the Internal Rate of Return tool.

Even though these techniques are most currently used, C. Drury and M. Tayles proved that several mistakes are commonly made when employing these methods. These mistakes lead to underinvestment, or lower level of accepting investment proposals that rationality based on careful financial analysis will advise. The first common mistake is the incorrect treatment of inflation. Often, managers do not fully understand the time value of money conception and the nominal and real interest rates. Thus, they discounted the future cash flows in nominal prices by real discount rates, or the cash flows in real terms (current prices) by nominal interest rates. The second will lead to underestimating the net present value of the project and means that many good business opportunities were missed because of this misperception. Another mistake was traced when managers used cash flows in real terms to calculate the internal rat of return of the project, but then compared this rate of return with the nominal discount rate on the project with the same risk. As the authors pointed out, if the rate of inflation is 3% annually, discounting the real cash flows at nominal discount rate but not adjusting them for this level of inflation, will underestimate the NPV y 14% if the project lives 5 years. This can be a great deal of money for a company lost due to such managerial imperfections.

Furthermore, the companies tend to be more risk-averse, thus using higher discount rates to find the value that the activity will add to their company, than the real cost of capital for this company is. A good benchmark estimated by the authors, that can be used by financial managers, is the fact that a project with average risk, all equity-financed, which lives from five to fifteen years, should be given the discount rate of 11% in real terms and 15% in nominal terms. For the project with the same life and financing, but high risk, the discount rates should be 20% nominal and 23% real terms. If the company is partially debt financed and the cost of the debt (the percent paid on the loan) is 9% (assuming 2% premium for risk of default over return on government bonds), taking corporation tax of 35%, the project with the same risk as the whole stock market risk, should be assigned the nominal discount rate of 13% and 9-10% real discount rate. For the same debt-holding company, but a project with high risk, the discount rates must be set at a level of 19% in nominal terms and 15-16% in real terms.

The empirical evidence shows that more than half of the firms use larger numbers as discount rates which leads to lower NPVs of the projects and thus less projects are desirable as investment opportunities. The explanation to this phenomenon can be the fact that sometimes financial middle managers tend to overestimate the earnings generated by the project due to their irrational positive expectations. By setting higher discount rates, top management tries to eliminate this effect. Higher rates of return are also required from separate projects which do not diversify the activities of the company (cannot thus reduce the risk of the portfolio of company activities).

Liquidity constraints experienced by some companies lead to acceptance of short-lived projects with . Employing this technique means that many projects that generate bigger earnings later on will be omitted. Another mistake done often by managers is the inability to trace all the indirect affects from accepting the project, which can add to its’ value or, on the contrary, be a negative side of it. The advice drawn is that using Discounted Cash Flow method to calculate Net Present Value of an endeavor, one must be precise and make all the projections carefully. A good corporate governance idea is for headquarters to precisely estimate discount rates for different departments and use the portfolio theory when estimating attractiveness of the projects, which implies that the risk of the project is lower as the company is diversified by carrying different tasks.

To further deepen the application of the NPV rule, Graham and Campbell surveyed 392 chief financial officers to trace how the practice of government finance corresponds with the theory. An interesting finding is that when setting the discount rates, managers also take into consideration together with market risks, interest rate risk, size of the company and the project, inflation risk and foreign exchange risk. When projecting the future incomes, firms take into account the impacts of the commodity prices, GDP trends, inflation and foreign exchange risk. But very few firms paid attention to adjusting discount rate of future cash flows to high or and financial distress costs. Large firms also include in their estimations business cycle trend change risk, commodity price risk, interest rate risk. For large firms exchange rate risk matters more, while for smaller firms which have higher debt to value ratio the interest rate is a more important determinant. Due to the increasing globalization trends and the fact that many companies compete not only in local, but global markets, thus diversifying their activities, many firms use average cost capital for their companies to estimate the foreign projects. But very few firms employ different discount rates for different cash flows within one project, thus forgetting the differences in volatility and probabilities.

Russell Thomas argues and finds reasonable proves that discounted cash flow analysis and NPV rule are outdated and are misleading. The author claims that ‘it is wise to use DCF when the decision involves a relatively simple business structure, uncomplicated projects, and a stable environment that enables reliable forecasts, and when buy-in of other stakeholders is not dependent on the value they receive’. Taking into consideration the increased efficiency of project management during the project lifecycle on one hand and increased market volatility on the other, it becomes more and more difficult to make reliable projections of the incomes generated by the project. The cash flows from the project may also affect one another which is not traced in NPV rule, and the changes within the company performance and structure can affect the cash flows and thus the project value also. Furthermore, David Brookfield states that NPV is a rather passive investment estimation technique and does not place value on real options incurred by accepting the project which add value to it or deduct. Such options include the option of deferring investment which increases the project worthiness, flexibility in changing the project trends during its’ life are a positive value-adder, interest rates changes option and others.

Trying to understand deeper why NPV is still the best criteria, the pitfalls of the main competitor to NPV, or the IRR rule must be drawn. In general, the IRR rule will lead to the same conclusions as the NPV rule if project’s cash flows are conventional implying that the project refers to first outlaying funds and then only receiving. The second condition for the IRR rule to hold is the fact that the project must not interact, thus the decision to go on with one project must not eliminate the choice of accepting the other project. These rules are derived from several problems within IRR, first, the multiple returns problems which occurs when sometimes cash flows from the business are not only positive, but additional cash outlays during the project life are necessary. The IRR will be misleading in this situation. Secondly, if the project is about not receiving income, but the profitability of borrowing at a given rate must be considered, then IRR must be used in reverse. Borrowing should be accepted if the IRR of this deal (first money in and then future cash outlays) is lower than the opportunity cost of capital (borrowing from the alternative source of funding). With mutually exclusive projects, a simple example can be exploited. Project a requires initial $100 investment and will provide $150 payment in one year, which means the IRR is 50% for this deal. Project B. requires initial $1,000 outlay and will generate only $1,200 in one year, which makes it a project with 20% IRR. The rule leads to the decision to accept project a which provides higher return of 50% over 20% return. But Project B. generates much larger NPV of $90 real dollars if the discount rate of 10% is used, while project a provides net present gain of $36 with the same discount rate. Obviously, employing just IRR maybe misleading, thus, many other factors, as liquidity constraints, scope of initial outlays and others must be considered when making investment analysis. I believe that other rules that should be followed when conducting NPV method require also very deep consideration and are a matter of another work, thus I will concentrate on the basic ideas and the importance of setting the correct discount rate.

In order to apply the theory in practice, I did a simple analysis of investment opportunity. The sample investment analysis is the chance of purchasing income-generating property which consists of three floors and different contracts with tenants that use the property in different ways are signed. Thus, the present value of the property will equal to the sum of present values of incomes generated from the rents received from the tenants. The market value of the property was estimated at $700,000 million and thus the owner of the property demands this price. The total leasable area of the building is 2,200 square meters. The first contract was signed for ten years with a firm that leases 800 square meters on the first floor and the base rent for the lease is $250. The rent is adjust on annual basis according to the inflation rate, thus, the annual increase is averaged to 3% in nominal terms. The second commercial use is by the firm that has a 5-year contract for 600 square meters on the second floor with the base rent of $200 per square meter. The current rent level is agreed to increase at 2% in real terms. In year six, the company will reconsider the lease agreement. The company estimates the probability of continuing the lease for another 5 years as 0,5. Then, the second firm would like the rent to be decreasing by 1% in real terms from the rent in nominal terms in year 5. The third floor is for residential use and comprises of 4 residential units, all occupied with the contracts signed for 10 years. The base rent for square meter for residential use is $100 and the agreed upon increase is the inflation rate.

Also, the owner is negotiating the probability of putting the advertisements board on the building in the next year, or year 2 of the project, which will give the additional cash flow of $4,000 in nominal terms.

It is important to include in the calculation of the property value the exit value of the building, or the salvage value, referring to the price that can be received if the building is sold at the end of the project. The salvage value is calculated using Income Capitalization method, where it equals the Net Operating Income in year 10(all receipts minus all expenditures) divided by (capitalized at) the average exit yield for this type of property. The assumed exit yield is 8% which is the average long-term proved exit yield for this type of property with mixed uses in this market area.

The maintenance costs are on average $100 for commercial use, the first and the second floor use in our case, and $120 for residential use due to higher utilization by the residents. Due to the inflation and depreciation of the building, the operating costs are assumed to increase by 2% annually in real terms for commercial space and 1% in real terms for residential space.

The property land is leased and the yearly land lease payments must be made which account to 6% of the assessed by tax authorities land value, which is $350,000. The next land value reassessment will be made in four years, but the lease payments are agreed upon to be hold constant for the next 10 years. Due to the depreciation of the building and the needs to update it to the new changing demands from the tenants, cash outlay in year three of the project is needed estimated of $40,000 in nominal terms. The tax rate on the income from property and capital gains is 30%.

The property costs $700,000 million and the purchase deal will be financed by a loan of $400,000 at the initiation of the project and the $600,000 will be equity financed. The loan conditions are rather favorable and it is 6% of yearly interest payments with the maturity of 20 years. The loan is amortized with equal amounts yearly.

The project maybe a worthy investment opportunity and generate wealth for the investor or can be a loss. In order to evaluate the value of the project, the cash flows, or the incomes generating from holding it are calculated in present terms and added. I shall transfer all the inflows and payments to nominal terms to make the calculations accurate. The results of the calculations are presented in Appendix 1. The rent for each firm is calculated by multiplying the leasable area by the base rent for square meter and by the inflation rate, which is coumpounded for future periods. The rent for the second firm increases in real terms, and thus the leasable area is multiplied by the base rent and then adjusted for both the real increase plus the inflation increase. There is a 0,5 chance that the second firm will sign a new contract, and thus we multiply the possible rents from this contract by 0,5. Thus, the expected cash flow in year six from the second firm, for example, equals =0,5*Leasable area*Rent for firm2 in Year 5. The rent in year 7 from the second firm will equal Rent in year 6 multiplied by 0,99, thus deducting the agreed upon rental increase of 1% in real terms.

The additional cash flow is given in nominal terms and thus does not need to be converted. Operating costs are calculated by multiplying the occupied area by the costs incurred from managing one square meter by (1+0,02+0,03)^Year, which reflects the 0,02 yearly increase in real terms for commercial space plus 0,03 adjusting for inflation because we are making all the calculations in nominal terms.

Land lease payments are constant and just account to 5% of the land value in all the years. The renovating costs are in nominal terms and thus are just assumed at $40,000 level. The loan payments are calculated using the annuity formula, thus, the yearly equal payments on the loan of $400,000 with yearly interest of 6% and 20 years to maturity will equal = $400,000/(1/0,06-1/(0,06*(1+0,06)^20)), and are $34,873.

From all the receipts received from all the tenants and the occasional cash flows we subtract the outlays, which are the maintenance costs, lease payments, loan payments and interest payments, taxes and investments to renovate the building. Investments are not treated as tax deductible in this case. I subtracted also the amortization of the loans and this will be the After to Equity. Salvage value is estimated by dividing the Net Operating Income in year ten by the assumed exit yield.

After having made the projections of the possible cash inflows and outflows, the next step in the investment analysis procedure is to estimate the opportunity cost of capital, or the discount rate which will be applied for these cash flows. Using the advice stated before that for average risk projects all equity financed the nominal discount rate of 15% should be applied, I readjusted it to the fact that the project is partially debt financed.

The return on equity equals re = r + D/E (r – rd), and r represents the return on the project of this risk if it is all equity-financed, as advised, 15% is taken, D/E is the debt to value ratio for this project and rd is the cost of debt or the interest on the loan. The formula shows that the higher is the debt to value ratio in the project, the higher return will be demanded from it due to the default risk. The calculation lead to conclusion that stock holders will demand 21% of return on equity from the project which is of average risk and is 40% debt financed. Then, taking into consideration the tax, Weighted Average Cost of Capital is estimated to be used as the discount rate for the project.

WACC = rd (1-T)*D/V + re * E/V, and it is equal to 0,06*(1-0,3)*0,4 + 0,21*0,6= 0,0168 + 0,1254 = 0,1422 or 14,22%. The cash flows to equity are discounted by this discount rate. The Salvage Value equals $498,924 and has the present value of $115,576. The Present value of all cash flows plus the present value of the salvage value is $464,238 which leads to the Net Present Value of the project of $-235,561 and thus the project should be rejected as it generates less income than it costs. The internal rate of return of this project is -14%.

To conclude, though it has several pitfalls, careful and proper usage of NPV rule will lead to best decisions on investment opportunities which will translate into increasing well-being of the company. NPV method includes projecting the possible cash flows that the investment will generate, choosing proper discount rate to bring them to one date, summing the present values of the cash flows and calculating the net present value, or the value in present money that acceptance of the project will add to the company.

Fundamentals of Corporate Finance, Brealey and Myers, McGraw-Hill, page 38.

Belli, Pedro (Author). Economic Analysis of Investment Operations: Analytical Tools.

Washington, DC, USA: World Bank, 2001,-page 17.

Fundamentals of Corporate Finance, Brealey and Myers, McGraw-Hill, page 318.

C. Drury, M. Tayles, the Misapplication of Capital Investment Appraisal Techniques, Management Decision, 35/2, 1997: 86-93.

Graham J., Campbell J.R., the Theory and Practice of Corporate Finance: Evidence from the Field, Journal of Financial Economics, 60, 2001: 187-243.

Russell Thomas, Business Value Analysis: Coping with Unruly Uncertainty, Strategic Leadership, 29/2, 2001, p. 16-23.

David Brookfield, Risk and Capital Budgeting: avoiding the pitfalls in using NPV when risk arises, Management Decision, Vol. 33, No. 8, 1995: 56-59.

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