Present value factor. Present value of cash flow: what it is, how it is calculated. Net Present Value Calculation

06.03.2024

Both concepts from the title of this section, discounted (present) value, PS (presentvalue, or PV), And net present value, NPV (netpresentvalue, or NPV), denote current the value of expected future cash receipts.

As an example, consider valuing an investment that promises an income of $100 per year at the end of this year and the next four years. We assume that this series of five payments of $100 each is guaranteed and the money will certainly arrive. If a bank were to pay us 10% annual interest on a five-year deposit, then that 10% would be the opportunity cost of the investment—the benchmark rate of return against which we would compare the benefits of our investment.

You can calculate the value of an investment by discounting its cash flows using opportunity cost as the discount rate.

Calculation formula inExceldiscounted (present) value (PV)= NPV(C1,B5:B9)

Present value(PS) in the amount of $379.08 is the current value of the investment.

Suppose this investment were to sell for $400. Obviously, it would not be worth the asking price, since - assuming an opportunity return (discount rate) of 10% - the real value of this investment would be only $379.08. it is appropriate to introduce the concept net present value(NPS). Denoted by the symbol r discount rate for this investment, we get the following NPV formula:

Where CF t is the cash flow from the investment at time t; CF 0 – flow of funds (receipt) at the current moment.

Calculation formula inExcel net present value (NPV)= NPV(C1,B6:B10)+B5

Excel terminology for discounted cash flows differs slightly from standard financial terminology. In Excel, the abbreviation MUR (NPV) denotes present value (not chiI'm standing present value) of a series of cash receipts.

To calculate in Excel net present value series of cash receipts in the usual sense of financial theory, you must first calculate present value future cash flows (using an Excel function such as NPV), and then subtract the initial cash flow from that number. (This value is often the same as the value of the asset in question.)

The Net present value, or NPV, indicator of an investment project allows you to determine what income an investor will receive in monetary terms as a result of his investments. In other words, the NPV of a project shows the amount of financial income as a result of investments in an investment project, taking into account associated costs, that is, net present value. What NPV is in practice and how to calculate net present value will become clear from the NPV formula below and its explanations.

Concept and content of NPV value

Before moving on to the topic of NPV, talking about what it is and how to calculate it, you need to understand the meaning of the phrase that makes up the abbreviation. For the phrase “Net present value” in the domestic economic and mathematical literature you can find several traditional translation options:

In the first version, typical for mathematical textbooks, NPV is defined as net present value (NPV).
The second option - net present value (NPV) - along with the first, is considered the most used.
The third option – net present value – combines elements of the first and second transfers.
The fourth version of the translation of the term NPV, where PV is “current value,” is the least common and is not widely used.

Regardless of the translation, the NPV value remains unchanged, and this term means that

NPV is the net present value of value. That is, cash flow discounting is precisely considered as the process of establishing its (flow) value by bringing the cost of total payments to a certain (current) point in time. Therefore, determining the value of net present value (NPV) becomes, along with IRR, another way to assess the effectiveness of investment projects in advance.

At the level of the general algorithm, in order to determine the prospects of a business project according to this indicator, the following steps need to be taken:

assess cash flows – initial investments and expected receipts,
set the cost of capital - calculate the rate,
discount incoming and outgoing cash flows at an established rate,
sum up all discounted flows, which will give the NPV value.

If the NPV calculation shows values greater than zero, then the investment is profitable. Moreover, the larger the NPV number, the greater, other things being equal, the expected profit value. Given that the lenders' return is usually fixed, anything the project brings in above it belongs to the shareholders - with a positive NPV, the shareholders will earn. The opposite situation with NPV less than zero promises losses for investors.

It is possible that the net present value will be zero. This means that the cash flow is sufficient to replace the invested capital without profit. If a project with an NPV of zero is approved, the size of the company will increase, but the share price will remain unchanged. But investing in such projects may be related to the social or environmental objectives of the initiators of the process, which makes investing in such projects possible.

NPV formula

Net present value is calculated using a calculation formula, which in a simplified form looks like PV - ICo, where PV represents the current cash flow indicators, and ICo is the size of the initial investment. In a more complex form, which shows the discounting mechanism, the formula looks like this:

NPV= - ICo + ∑ n t=1 CF t / (1 + R) t

Here:

NPV– net present value.
CF – Cash Flow is the cash flow (investment payments), and t next to the indicator is the time during which the cash flow occurs (for example, an annual interval).
R – Rate– discount (rate: coefficient that discounts flows).
n– the number of stages of project implementation, which determines the duration of its life cycle (for example, the number of years).
ICo – Invested Capital– initial invested capital.

Thus, NPV is calculated as the difference between the total cash flows updated at a certain point in time by risk factors and the initial investment, that is, investor profit is considered as the added value of the project.

Since it is important for an investor not only to make a profitable investment, but also to competently manage capital over a long period of time, this formula can be further expanded to include not one-time, but additional periodic investments and an inflation rate (i)

NPV= ∑ n t=1 CF t / (1 + R) t - ∑ m j =1 IC j / (1 + i) j

Example of NPV calculation

An example calculation for three conditional projects allows you to both calculate NPV and determine which of the projects will be more attractive for investment.

According to the example conditions:

initial investments - ICo - in each of the three projects are equal to 400 USD,
the rate of return - the discount rate - is 13%,
the profits that projects can bring (by year) are listed in the table for a 5-year period.

Let's calculate net present value to choose the most profitable project for investment. The discount factor 1/(1 + R) t for an interval of one year will be t = 1: 1/(1+0.13)1 = 0.885. If we recalculate the NPV of each scenario by year with the substitution of the defining values into the formula, it turns out that for the first project NPV = 0.39, for the second – 10.41, for the third – 7.18.

According to this formula, the second project has the highest net present value, therefore, if we are based only on the NPV parameter, then it will be the most attractive for investment in terms of profit.

However, the projects being compared may have different durations (life cycles). Therefore, there are often situations when, for example, when comparing three-year and five-year projects, the NPV will be higher for the five-year one, and the average value over the years will be higher for the three-year one. To avoid any contradictions, the average annual rate of return (IRR) must also be calculated in such situations.

In addition, the volume of initial investment and the expected profit are not always known, which creates difficulties in applying the calculations.

Difficulties in applying calculations

As a rule, in reality, the variables read (substituted into the formula) are rarely accurate. The main difficulty is determining two parameters: the assessment of all cash flows associated with the project and the discount rate.

Cash flows are:

initial investment – initial outflow of funds,
annual inflows and outflows of funds expected in subsequent periods.

Taken together, the amount of flow indicates the amount of cash that an enterprise or company has at its disposal at the current moment in time. It is also an indicator of the financial stability of the company. To calculate its values, you need to subtract Cash Outflows (CO), the outflow, from the Cash Inflows (CI) value - the inflow of funds:

When forecasting potential revenues, it is necessary to determine the nature and degree of dependence between the influence of factors that form cash flows and the cash flow itself. The procedural complexity of a large complex project also lies in the amount of information that needs to be taken into account. So, in a project related to the release of a new product, it will be necessary to predict the volume of expected sales in units, while simultaneously determining the price of each unit sold. And in the long term, in order to take this into account, it may be necessary to base forecasts on the general state of the economy, the mobility of demand depending on the development potential of competitors, the effectiveness of advertising campaigns and a host of other factors.

In terms of operational processes, it is necessary to predict expenses (payments), which, in turn, will require an assessment of prices for raw materials, rental rates, utilities, salaries, exchange rate changes in the foreign exchange market and other factors. Moreover, if a multi-year project is planned, then estimates should be made for the corresponding number of years in advance.

If we are talking about a venture project that does not yet have statistical data on production, sales and costs, then forecasting cash income is carried out on the basis of an expert approach. It is expected that experts should compare a growing project with its industry counterparts and, together with the development potential, assess the possibilities of cash flows.

R – discount rate

The discount rate is a kind of alternative return that an investor could potentially earn. By determining the discount rate, the value of the company is assessed, which is one of the most common purposes for establishing this parameter.

The assessment is made based on a number of methods, each of which has its own advantages and initial data used in the calculation:

CAPM model. The technique allows you to take into account the impact of market risks on the discount rate. The assessment is made on the basis of trading on the MICEX exchange, which determines the quotations of ordinary shares. In its advantages and choice of initial data, the method is similar to the Fama and French model.
WACC model. The advantage of the model is the ability to take into account the degree of efficiency of both equity and borrowed capital. In addition to the quotations of ordinary shares, interest rates on borrowed capital are taken into account.
Ross model. Makes it possible to take into account macro- and microfactors of the market, industry characteristics that determine the discount rate. Rosstat statistics on macroindicators are used as initial data.
Methods based on return on equity, which are based on balance sheet data.
Gordon model. Using it, an investor can calculate dividend yield, also based on quotes of ordinary shares, and also other models.

The change in the discount rate and the amount of net present value are related to each other by a nonlinear relationship, which can simply be reflected on a graph. Hence the rule for the investor follows: when choosing a project - an investment object - you need to compare not only the NPV values, but also the nature of their change depending on the rate values. The variability of scenarios allows an investor to choose a less risky project for investment.

Since 2012, at the instigation of UNIDO, the calculation of NPV has been included as an element in the calculation of the index of the rate of specific increase in value, which is considered the optimal approach when choosing the best investment decision. The assessment method was proposed by a group of economists headed by A.B. Kogan, in 2009. It allows you to effectively compare alternatives in situations where it is not possible to compare using a single criterion, and therefore the comparison is based on different parameters. Such situations arise when the analysis of investment attractiveness using traditional NPV and IRR methods does not lead to clear results or when the results of the methods contradict each other.

One of the key and most used, especially in international practice, methods for assessing the quality of investment projects is the method net present value (NPV), based on the calculation of the possible increase in the value of the company as a result of the implementation of the corresponding investment project. The formula for calculating net present value is

where – cash receipts (cash flow) for the period V, r – the desired rate of profitability (profitability), i.e. the level of return on invested funds that can be ensured when they are placed in publicly accessible financial institutions and instruments. In other words, r – opportunity costs (opportunity cost) of capital raised for investment in the project under consideration; – initial investment of funds, or the amount of initial investment.

In reality, however, an investor may be faced with a situation where the project does not involve one-time capital expenditures, but multiple ones, when investments are carried out over several time increments. In this case, the formula for calculating net present value takes a slightly different form:

where – investment costs for the period t.

Obviously, if the present value of the cash inflow from a project exceeds the present value of the sum of all capital investments, the project in question will have a positive net present value. Positive value NPV for the project means that investment costs generate net cash flows with a return greater than alternative options in the market with the same level of risk, i.e. the project's profitability exceeds the required return of capital owners. In this case, the project can be accepted for implementation, since the costs of it will be reimbursed and, in addition, its implementation will provide some income that increases the value of the company and the welfare of its shareholders.

Obviously, in the case of analyzing several alternative projects, the project with a higher value should be accepted NPV Projects with NPV = 0 do not change the position of capital owners, since the company’s valuation in this case does not change and the share price remains unchanged. But the adoption of such projects increases the company’s assets by the amount of investment, which may be of interest to management (increasing prestige, power, etc.).

Negative value NPV shows that the desired rate of profitability is not achieved and the project is unprofitable; it is usually rejected. Among several alternative projects, the one with the higher value should be accepted NPV

When calculating NPV Discount rates that vary from year to year may be used. If the value of r is not constant and will change from period to period, then it is necessary to apply individual discount factors to each cash flow that will correspond to a given calculation step. In this case NPV It is recommended to calculate using the formula

Where .

At the same time, it is quite possible that a project that is acceptable at a constant discount rate may become unacceptable at a variable one.

It is also important to note that net present value is an additive criterion in the spatiotemporal aspect, i.e. . Consequently, the net present value of a set of projects, for example an entire company, is equal to the sum of the present values of the projects that make it up. This important property makes it possible to use this criterion when analyzing the optimality of an investment portfolio of projects. Besides, in NPV both the lifespan of the project and all income (expenses) at all its stages are taken into account.

When using the method in practice NPV The choice (justification) of the discount rate remains a rather difficult problem.

Since a company may have a large number of shareholders, the discount rate must satisfy the minimum return on capital requirements of most of these individuals. Moreover, in companies with some degree of leverage, the discount rate must represent a return that satisfies all types of investors (shareholders and creditors) of the company. Therefore, for such a company, an acceptable discount rate would be the weighted average cost of capital

where is the price of the company’s source of funds; – the share of the th source in their total amount.

It should be noted that the validity of using this indicator in analytical calculations is associated with some reservations and conventions. In particular, its value is influenced not only by the internal conditions of the company’s activities, but also by the external conditions of the financial market. Thus, when interest rates change, the rate of return required by shareholders on invested capital also changes, which affects the value WACC.

For completeness of presentation of information necessary for calculation NPV Let's look at typical cash flows at an enterprise.

Typical input cash flows:

additional sales volume and increase in product price;
reduction of average gross costs (reduction of production costs);
the residual value of the equipment at the end of the last year of the investment project (since the equipment can be sold or used for another project);
release of working capital at the end of the last year of the investment project (closing accounts receivable, selling remaining inventory, selling shares and bonds of other enterprises).

Typical weekend cash flows:

initial investment in the first year(s) of the investment project;
increase in working capital needs in the first year(s) of the investment project (increase in accounts receivable to attract new customers, purchase of raw materials and components to start production);
equipment repair and maintenance costs;
additional non-production costs (social, environmental, etc.).

Previously, we noted that the resulting net cash flows are designed to ensure the return of the invested amount of funds and obtain the maximum (if possible) income for investors. Let's consider how cash flows are divided into input (output) by estimating using the method NPV specific investment project.

Example. The Multihvat company needs to make a choice between two models of new equipment, which it plans to use to increase its own production volumes in order to enter the world market. Investments in equipment of the type A amount to 30 thousand dollars, for equipment of the type IN - 45 thousand dollars with the same period of operation of 5 years.

Let's calculate (Table 6.3) the net present value for both models of equipment for the discount rate r= 20%.

Table 6.3

Cash flows, dollars
Cash flows, dollars
Fixed Assets

Payments for business activities

Depreciation deductions
Taxable result
Income tax
Net result
Depreciation deductions
Net cash flow
Discount coefficient					1,2-*

The same on a cumulative basis

According to the calculation results presented in table. 6.3, for equipment model A net present value will be

Similar calculations for the equipment of the model IN are presented in table. 6.4.

Table 6.4

Net present value of the modelIN

Cash flows, dollars
Cash flows, dollars
Fixed Assets
Income from economic activities
for economic activities
Cash flow before taxes
Depreciation deductions
Taxable result
Income tax
Net result
Depreciation deductions
Net cash flow
Coefficient discounting
Discounted Cash Flow
The same on a cumulative basis

Net present value for model equipment IN

A comparison of the net present values for both models shows that the model IN – preferable (47,895 > 28,620).

To take inflation into account when assessing the effectiveness of investments, the discount rate (yield) must be adjusted to the inflation rate i in accordance with the conclusions from the famous Fisher effect:

Example. The Default company plans to purchase new equipment at a price of $40,000, which, according to the company's administration, will provide $20,000 in cost savings (in the form of input cash flow over the next three years). During this period, the equipment will be completely worn out. The company's cost of capital is the expected rate of inflation per year.

Let us first evaluate the project without taking into account inflation (Table 6.5).

Now let’s take into account the effect of inflation in the calculation scheme (Table 6.6).

Table 6.5

CalculationNPV excluding inflation

Cash flows, dollars
Cash flows, dollars
Fixed Assets
Annual fund inflow
Net cash flow
Discount coefficient
Discounted Cash Flow
The same on a cumulative basis

Table 6.6

CalculationNPV taking into account inflation

Cash flows, dollars
Cash flows, dollars
Fixed Assets
Annual real inflow of funds
Inflation index
Indexed (nominal) inflow of funds
Net cash flow

Discounted Cash Flow
The same on a cumulative basis

The answers for both options are exactly the same, which is completely natural in the case of the same inflation rate for all components of expenses and income. For this reason, and also taking into account the relatively low level of inflation in developed countries, most companies in Western countries, as a rule, do not take inflation into account when calculating the effectiveness of investment projects.

Criterion NPV has, as follows from the above, both advantages and disadvantages. The obvious advantage of this approach is that this criterion is absolute, and therefore takes into account the scale of investment. This allows you to calculate the increase in the value of the company, which is its main goal. However, advantages also come with disadvantages. The first is that the magnitude NPV difficult, and in some cases impossible, to standardize. For example, NPV of some project is 200 thousand dollars. Is this a lot or a little? It is very difficult to answer this question, especially if a non-alternative project is being considered.

The second disadvantage is due to the fact that NPV does not explicitly show by what investment efforts a particular result is achieved. Although in calculation NPV The size of the investment is taken into account; a relative comparison of investment costs with the results obtained is not carried out. And finally, the third drawback of the criterion NPV This is explained by the fact that for the investor (and, of course, not only for him), it is important to have information about the payback period for the investment costs made.

Considering the above, criteria calculated as relative values, in particular such as the profitability index and internal rate of return, are widely used in financial management.

NPV (abbreviation in English - Net Present Value), in Russian this indicator has several variations of the name, among them:

net present value (abbreviated NPV) is the most common name and abbreviation, even the formula in Excel is called exactly that;
net present value (abbreviated NPV) - the name is due to the fact that cash flows are discounted and only then summed up;
net present value (abbreviated NPV) - the name is due to the fact that all income and losses from activities due to discounting are, as it were, reduced to the current value of money (after all, from the point of view of economics, if we earn 1,000 rubles and then actually receive less than if we received the same amount, but now).

NPV is an indicator of the profit that participants in an investment project will receive. Mathematically, this indicator is found by discounting the values of net cash flow (regardless of whether it is negative or positive).

Net present value can be found for any period of time of the project since its beginning (for 5 years, for 7 years, for 10 years, and so on) depending on the need for calculation.

What is it needed for

NPV is one of the indicators of project efficiency, along with IRR, simple and discounted payback period. It is needed to:

understand what kind of income the project will bring, whether it will pay off in principle or is it unprofitable, when it will be able to pay off and how much money it will bring at a particular point in time;
to compare investment projects (if there are a number of projects, but there is not enough money for everyone, then projects with the greatest opportunity to earn money, i.e. the highest NPV, are taken).

Calculation formula

To calculate the indicator, the following formula is used:

CF - the amount of net cash flow over a period of time (month, quarter, year, etc.);
t is the period of time for which the net cash flow is taken;
N is the number of periods for which the investment project is calculated;
i is the discount rate taken into account in this project.

Calculation example

To consider an example of calculating the NPV indicator, let's take a simplified project for the construction of a small office building. According to the investment project, the following cash flows are planned (thousand rubles):

Article	1 year	2 year	3 year	4 year	5 year
Investments in the project	100 000
Operating income		35 000	37 000	38 000	40 000
Operating expenses		4 000	4 500	5 000	5 500
Net cash flow	- 100 000	31 000	32 500	33 000	34 500

The project discount rate is 10%.

Substituting into the formula the values of net cash flow for each period (where negative cash flow is obtained, we put it with a minus sign) and adjusting them taking into account the discount rate, we get the following result:

NPV = - 100,000 / 1.1 + 31,000 / 1.1 2 + 32,500 / 1.1 3 + 33,000 / 1.1 4 + 34,500 / 1.1 5 = 3,089.70

To illustrate how NPV is calculated in Excel, let's look at the previous example by entering it into tables. The calculation can be done in two ways

Excel has an NPV formula that calculates the net present value, to do this you need to specify the discount rate (without the percent sign) and highlight the range of the net cash flow. The formula looks like this: = NPV (percent; range of net cash flow).
You can create an additional table yourself where you can discount the cash flow and sum it up.

Below in the figure we have shown both calculations (the first shows the formulas, the second the calculation results):

As you can see, both calculation methods lead to the same result, which means that depending on what you are more comfortable using, you can use any of the presented calculation options.

Net present value is the sum of the current values of all predicted cash flows, taking into account the discount rate.

The net present value (NPV) method is as follows.
1. The current cost of costs (Io) is determined, i.e. The question of how much investment needs to be reserved for the project is decided.
2. The current value of future cash receipts from the project is calculated, for which the income for each year CF (cash flow) is reduced to the current date.

The calculation results show how much money would need to be invested now to receive the planned income if the income rate were equal to the barrier rate (for an investor, the interest rate in a bank, in a mutual fund, etc., for an enterprise, the price of total capital or through risks). Summing up the current value of income for all years, we obtain the total current value of income from the project (PV):

3. The present value of investment costs (Io) is compared with the present value of income (PV). The difference between them is the net present value of income (NPV):

NPV shows the investor's net gains or net losses from investing money in a project compared to keeping the money in a bank. If NPV > 0, then we can assume that the investment will increase the wealth of the enterprise and the investment should be made. At NPV

Net present value (NPV) is one of the main indicators used in investment analysis, but it has several disadvantages and cannot be the only means of evaluating an investment. NPV measures the absolute value of the return on an investment, and it is likely that the larger the investment, the greater the net present value. Hence, it is not possible to compare multiple investments of different sizes using this indicator. In addition, NPV does not determine the period over which the investment will pay off.

If capital investments associated with the upcoming implementation of the project are carried out in several stages (intervals), then the NPV indicator is calculated using the following formula:

, Where

CFt - cash inflow in period t;

r - barrier rate (discount rate);
n is the total number of periods (intervals, steps) t = 1, 2, ..., n (or the duration of the investment).

Typically for CFt the t value ranges from 1 to n; in the case where CФо > 0 is considered a costly investment (example: funds allocated for an environmental program).

Defined by: as the sum of the current values of all predicted, taking into account the barrier rate (discount rate), cash flows.

Characterizes: investment efficiency in absolute terms, in current value.

Synonyms: net present effect, net present value, Net Present Value.

Acronym: NPV

Flaws: does not take into account the size of the investment, the level of reinvestment is not taken into account.

Eligibility Criteria: NPV >= 0 (the more the better)

Comparison conditions: To correctly compare two investments, they must have the same investment costs.

Example No. 1. Calculation of net present value.
The investment amount is $115,000.
Investment income in the first year: $32,000;
in the second year: $41,000;
in the third year: $43,750;
in the fourth year: $38,250.
The size of the barrier rate is 9.2%

Let's recalculate cash flows in the form of current values:
PV 1 = 32000 / (1 + 0.092) = $29304.03
PV 2 = 41000 / (1 + 0.092) 2 = $34382.59
PV 3 = 43750 / (1 + 0.092) 3 = $33597.75
PV 4 = 38250 / (1 + 0.092) 4 = $26899.29

NPV = (29304.03 + 34382.59 + 33597.75 + 26899.29) - 115000 = $9183.66

Answer: The net present value is $9,183.66.

The formula for calculating the NPV (net present value) indicator taking into account the variable barrier rate:

NPV - net present value;
CFt - inflow (or outflow) of funds in period t;
It is the amount of investments (costs) in the t-th period;
ri - barrier rate (discount rate), fractions of a unit (in practical calculations, instead of (1+r) t, (1+r 0)*(1+r 1)*...*(1+r t) is used, because . the barrier rate can vary greatly due to inflation and other components);

N is the total number of periods (intervals, steps) t = 1, 2, ..., n (usually the zero period implies the costs incurred to implement the investment and the number of periods does not increase).

Example No. 2. NPV with a variable barrier rate.
Investment size - $12800.

in the second year: $5185;
in the third year: $6270.

10.7% in the second year;
9.5% in the third year.
Determine the net present value for the investment project.

n =3.
Let's recalculate cash flows in the form of current values:
PV 1 = 7360 / (1 + 0.114) = $6066.82
PV 2 = 5185 / (1 + 0.114)/(1 + 0.107) = $4204.52
PV 3 = 6270 / (1 + 0.114)/(1 + 0.107)/(1 + 0.095) = $4643.23

NPV = (6066.82 + 4204.52 + 4643.23) - 12800 = $2654.57

Answer: The net present value is $2,654.57.

The rule according to which, from two projects with the same costs, the project with a large NPV is selected does not always apply. A project with a lower NPV but a short payback period may be more profitable than a project with a higher NPV.

Example No. 3. Comparison of two projects.
The cost of investment for both projects is 100 rubles.
The first project generates a profit equal to 130 rubles at the end of 1 year, and the second 140 rubles after 5 years.
For simplicity of calculations, we assume that barrier rates are equal to zero.
NPV 1 = 130 - 100 = 30 rub.
NPV 2 = 140 - 100 = 40 rub.

But at the same time, the annual profitability calculated using the IRR model will be 30% for the first project, and 6.970% for the second. It is clear that the first investment project will be accepted, despite the lower NPV.

To more accurately determine the net present value of cash flows, the modified net present value (MNPV) indicator is used.

Example No. 4. Sensitivity analysis.
The investment amount is $12,800.
Investment income in the first year: $7360;
in the second year: $5185;
in the third year: $6270.
The size of the barrier rate is 11.4% in the first year;
10.7% in the second year;
9.5% in the third year.
Calculate how the net present value would be affected by a 30% increase in investment income?

The initial value of the net present value was calculated in example No. 2 and is equal to NPV ex = 2654.57.

Let's recalculate cash flows in the form of current values, taking into account sensitivity analysis data:
PV 1 ah = (1 + 0.3) * 7360 / (1 + 0.114) = 1.3 * 6066.82 = $7886.866
PV 2 ah = (1 + 0.3) * 5185 / (1 + 0.114)/(1 + 0.107) = 1.3 * 4204.52 = $5465.876
PV 3 ah = (1 + 0.3) * 6270 / (1 + 0.114)/(1 + 0.107)/(1 + 0.095) = 1.3 * 4643.23 = $6036.199

Let's determine the change in net present value: (NPV ach - NPV out) / NPV out * 100% =
= (6036,199 - 2654,57) / 2654,57 * 100% = 127,39%.
Answer. A 30% increase in investment income resulted in a 127.39% increase in net present value.

Note. Discounting cash flows with a time-varying barrier rate (discount rate) corresponds to “Methodological guidelines No. VK 477...” clause 6.11 (p. 140).