PV of Terminal Value – Full Year Discounting vs Mid-Year Discounting

This is the second post in the Mid-Year discounting series. In the first post, I discussed in detail the workings and logic behind the mid-year convention and touched very briefly upon the terminal year calculations as well. It is strongly recommended to read the first post in conjunction with this one.

Now, unlike the free cash flow discounting during the explicit period, wherein the discounting period varies basis if mid-year convention is adopted or not along with taking note of any stubs therein, the Terminal Value discounting only gets affected by the stubs and not the adoption of mid-year convention.

Let me explain the above with an example:

Assume we are valuing the cash flows for Company A that has its FYE in December. For the sake of simplicity lets have explicit forecast period as 5 years. Also, lets assume WACC as 6.25%.

First lets assume simple discounting convention, where we assume cash flows are received at the end of each period. There are further be 2 cases assumed:

1. Analysis is done on January 1: As can be seen below, while assuming no stub period and that cash flows are received at the end of year, we discount the cash flows by full number of years to bring it to the present.

2. Analysis is done on April 30: Here note that, we are still assuming that the cash flows are received at the end of the year but the only difference being that in the current period the company has already finished with one quarter. Thus, we need to adjust the cash flows as well as the discounting period to only account for the remaining 9 months left for the year end and not include the full year financials.

Year 1 discounting above takes the remaining number of days in the year and divided by total number of days (in this case 365). Years 2 onwards its simply the full year + 9 months of current year to bring the cash flows to the present date and so on.

This was simple case where cash flows were assumed at the year end. As noted in previous post, this assumption is not widely used and rather assuming that since cash flows are earned throughout the year, it is reasonable to assume average. That is the cash flows are received at the mid of each valuation period. I will not go into workings again, as it was all explained in the first post, but for comparisons with normal discounting, let me provide you with the screenshots of how the discounting FCF will look like.

1. Analysis is done on January 1:

2. Analysis is done on April 30:

Discounting-cases-examplesDownload

From the above analysis, it should be little clear how both mid-year convention as well as stub period will have impact on cash flows of explicit period.

Lets turn our attention to the Terminal Value.

Earlier, I mentioned that Terminal Value discounting only gets affected by the stubs and not the adoption of mid-year convention. Let us now try to understand, why this is the case with terminal value.

As you will already know, two of the most common ways of getting to the terminal value figure are – Multiple Value Method and Gordon Growth Method

1. Multiple Value Method:

With this approach, we assume an exit multiple and use the corresponding metrics (EBIT / EBITDA) as of the last year of the explicit forecast period to get our terminal value. Now, there are few things to note here.

• Since we use the full year metric, say EBITDA of Year 5 in our example above, the terminal value so obtained is value at the end of the Year 5. To elaborate, it does not matter what convention of discounting for free cash flow we are assuming (normal vs mid-year), since the implied assumption is that the company is sold basis full year EBITDA, this is the value they will receive “at the end” of the explicit period / full year
• The assumption that EBITDA will be “assumed” to have received at the middle of year 5 in case of mid-year convention does not change the fact that it is a full year EBITDA basis which the company is sold at the end of the period

As such, it should be clear as to why the discounting convention does not play a role in the terminal value.

In our example above, if we are using the Multiple Value Method and assume that the company gets sold at 6.5x EBITDA Multiple and assuming EBITDA for Year 5 is say $235 million:

Terminal Value = 235 x 6.5 = $1,527.5 million

To get the PV of this Terminal Value, use the same discount factor as used in the final year if we are using the simple discounting for the other cash flows of the explicit period. So we will refer back to the “Simple Discounting” cases discussed above (since mid-year convention case is not relevant for terminal value) and use discount period as 5 for the January 1 case and 4.671 for the April 30 stub case. (Refer to the tables above).

However, in case the previous free cash flows of the explicit period are assumed to be discounted using the mid-year convention, then we need to add 0.5 to the final year discount period to account for the fact that it is a full year EBITDA usage. Hence, in the above example we will take (4.5+0.5)= 5 for the Jan 1 case and (4.171+0.5)=4.671 for Apr 30 case. Notice, this is exactly what the discount rate we are using in the “simple discounting” example above. This is exactly what we should be aware of!

2. Gordon Growth Method:

Under this approach, since we are not assuming an abrupt sale of business at the end of explicit forecast period – as is the case with multiple method – we can safely assume that no matter what the convention used (simple or mid-year), we will continue getting the free cash flows to perpetuity in the year end or mid as the case maybe.

Since the terminal value assumption matches with the assumption so taken for the explicit forecast period, we can use the same discounting period as used for the final year of forecast. So here, for simple discounting it will be 5 for Jan 1 case and 4.671 for the Apr 30 case. And for the mid-year assumption, it would be 4.5 for Jan 1 case and 4.171 for the Apr 30 case.

To get the Terminal Value using this approach, lets continue with above example where final year EBITDA was $235 million. If the WACC was 9.88%, growth rate was 2.5% and last year FCF of forecasted period was $109.98 million, the TV using the Gordon Growth Method is:

TV = (109.98 x (1 + 2.5%)) / (9.88% - 2.50%) = $1,527.5

It is not a surprise that the TV derived from both the methods is exactly the same. This happened as I used the implied growth rate from the Multiple method and applied it here. Though in real life scenarios you will be using either one of the methods, but it is good to understand the relation between the two.

• Formula for getting the implied growth rate from the multiple method is:
  • ( Terminal Value * Discount Rate – Final Year FCF ) / (Terminal Value + Final Year FCF)
• Formula for getting the implied EBITDA multiple is pretty straight forward:
  • Terminal Value from Gordon Method / Final Year EBITDA

• Please keep in mind that in case mid-year convention is used for the explicit period and you wish to compare the terminal value from both the methods (Multiple and Gordon Growth), you would need to multiply the TV from Gordon Growth by (1 + Discount Rate)^0.5, to bring it to the end of the explicit period. This is required since in Multiple Method it is always assumed that the TV is received at the “end” of the year. Note, such comparisons are quite rare in real life scenarios.

Is Setting Depreciation = Capex at Terminal Year A Right Assumption in DCF?

It is a common belief that Capital Expenditure (Capex) and Depreciation must converge over time when looking at the projection window. In this article, we will try to explore the possible reasoning behind this approach and situations this might not necessarily be the right way to go forward.

It is important to note that, D&A and Capex might be higher or lower to the other anytime during the projection period. But what we are trying to understand is their relation to the other right at the terminal year in DCF analysis.

Firstly, let us understand what both the scenarios imply:

1. Capex > D&A: This reflects expansionary scenario, where the company is growing its assets base faster than it is depreciation them
2. Capex < D&A: This reflects the opposite of above scenario, where company’s asset base is declining as it is depreciating faster than it is growing and will eventually become zero

As a refresher, there are broadly 2 types of Capex – Maintenance or replacement and Expansionary. Maintenance Capex is required to maintain or replace the current asset base and expansionary capex is required to grow the company further such as new product line or new capacity for an existing product line. Thus, any outlays that expand the output capabilities of the firm will fall under expansionary Capex umbrella.

Note 1: When a company undertakes a Capex, the assets so generated is capitalized, meaning they are reflected on the balance sheet only and as the assets are used over their useful life, they get expensed in the form of D&A and then move through the income statement.

Note 2: It also essential to always remember that Capex always precedes depreciation. This is intuitive, as one cannot depreciate an asset they don’t own. Hence, it is important to adjust the depreciation to forecasted Capex, instead of doing the reverse.

While trying to ascertain the terminal value, it is important to think of it as – You are trying to project the company’s financial performance forever. Since a perpetual expansionary Capex is not practically viable, it might be prudent to assume that company’s asset base will remain at fairly constant level. This implies that company should invest in maintenance level Capex to maintain the current asset base. Thus, in the terminal year our focus is to determine the “normalized” D&A and Capex.

So, the question is – “Is the simplifying normalization assumption of setting depreciation equal to Capex in the terminal year right assumption?”

This assumption is typically appropriate in zero-growth/inflation scenarios. If growth is projected in the cash flow forecast, capex should typically exceed depreciation in the terminal period. The reason for the same is quite straightforward. Capex has a direct correlation to both growth and depreciation expense.

Increased levels of Capex should in turn lead to increased future growth. Likewise, increased Capex will raise future levels of depreciation expense. As long as a company earns a positive return on its capital investment, then capital Capex in excess of maintenance capital requirements should result in some level of future growth.

Please note, some models might assume that Capex drives revenue, but this is not necessarily true. Capex grows as revenue grows, but it doesn’t always drive revenue. Eg: Software companies are far less dependent on Capex to boost its revenue.

Let’s discuss this further to get a better understanding:

Projected capital expenditures should always reflect the expected long term growth rate assumed (LTG Rate), or conversely, a selected LTG rate should be supported by a certain level of Capex and an assumed rate of return on that investment (ROI). If growth expectations are increased or decreased, then either Capex need to be adjusted accordingly or new assumptions needs to be established regarding return on invested capital. Assuming the rate of return on invested capital is held constant, then any change to the LTG rate assumption should require the adjustments to the assumptions for both Capex and depreciation.

Note: Formula for calculating the sustainable long term growth rate for a company is,
g = b x ROE,
where, g = LTG Rate, b = Reinvestment Rate or plowback ratio and ROE = Return on Equity

This formula also illustrates the connected relationship between Capex and the LTG rate (i.e., that the two variables increase or decrease in tandem).

Nearly all company projections and discount rate data are presented in nominal terms. Thus, the LTG rates is based on nominal LTG rates that is including the impacts of both inflation and real returns.

Now consider a scenario where expected inflation of Country A is say 4%,

1. LTG Rate = 4%; inherent assumption of 0% real growth rate
2. LTG Rate = 3%; implies negative real growth rate
3. LTG Rate = 5%; implies 1% real growth rate

Thus, for normalized cash flow projections that include an assumption of a positive nominal LTG rate, equating Capex and depreciation expense may be flawed. When the estimated LTG rate is positive (i.e., any selected LTG rate greater than 0%, even if that growth rate results in negative or zero expected real growth) Capex may exceed depreciation expense.

Deep Dive Into Anti-Dilution …

Earnings per common share (EPS) is computed by dividing net income by the weighted average number of common shares outstanding during the period on a basic and diluted basis.

• Public companies with simple capital structure are required to report only Basic EPS, however the ones with complex capital structure (with potential dilutive securities), are required to report both basic and diluted EPS in their financial reports

Analysts give precedence to Diluted EPS in their financial analysis as against the Basic EPS. The essence of Diluted EPS is to consider all the securities (options, convertible instruments such as convertible bond, convertible preferred stocks etc.), that have a potential to be converted (basis in-the-money conversion test) into common stock and add that to the total common shares outstanding. Thus, allocating the net income to all the shareholders expected to have a claim on the bottom line.

Below is the snapshot from the latest 10-K of Starbucks as of October 03, 2021:

As can be seen in the example above, dilution usually results in a lower EPS as compared to the Basic EPS

However, as the name suggests, there are certain cases where the convertible securities have an anti-dilutive effect on EPS instead of dilutive impact. Meaning, they result in higher post conversion EPS instead of lower. I will explain such one of such cases with an excel example towards the end.

Companies exclude such securities from their Diluted EPS calculation, thereby following the principal of prudence and conservatism. Below is an excerpt from financial statement of a public company highlighting this fact.

Thus, to summarize:

• Dilution results in reduction in EPS or an increase in loss per share resulting from the assumption that convertible instruments are converted and / or options are exercised, resulting in issuance of common ordinary shares
• Antidilution results in an increase in EPS or a reduction in loss per share resulting from the assumption that convertible instruments are converted and / or options are exercised, resulting in issuance of common ordinary shares

So, How Does Anti-Dilution Exactly Happen?

It is true that when potentially dilutive securities get converted, it results in a higher common stock outstanding. This thereby has a denominator effect. However, such securities might also have a numerator effect. Let’s see how.

While looking into dilution, we mostly focus on the denominator, i.e., number of new shares created, thereby increasing the total share count (denominator effect). While most often we tend to overlook the adjustments required to be made to the Net Income due to the conversion of securities or as we call – the numerator effect.

When a bond or preferred shares are issued, it promises the investors a fixed return in the form of coupon rate or dividend which are deducted from the numerator (Net Income), before using it for the EPS calculation. However, if we assume that these securities are no longer interest or dividend bearing securities and are common shares instead, we need to add back the interest / dividend so deducted from the numerator to make apples to apples adjustments.

If the numerator effect is larger than the denominator effect, it results in higher EPS and hence is anti-dilutive.

Some security instruments have provisions or ownership rights that allow the owners to purchase additional shares when another security mechanism would otherwise dilute their ownership interests. These are often called anti-dilution provisions.

Guidance on Calculating Dilution Impact

Compare the Basic EPS with the Diluted EPS (basis the detailed adjustments scenarios provided below.

• If Basic EPS > Diluted EPS >> Dilutive Impact (Include)
• If Basic EPS < Diluted EPS >> Anti-Dilutive Impact (Do not include)

Case 1: Options and Warrants: Always results in dilution if the securities are in-the-money

• Numerator: No Impact
• Denominator: Check for in-the-money test and apply treasury stock method to calculate the total dilution impact

Case 2: Convertible Debt: Can be dilutive or anti-dilutive depending upon the numerator vs denominator effect

• Numerator: Adjusted for the after-tax effect of interest charged
• Denominator: Includes shares that would be issued on the conversion of debt

Case 3: Convertible Preferred Shares: Can be dilutive or anti-dilutive depending upon the numerator vs denominator effect

• Numerator: Adjusted for the dividend charged
• Denominator: Include shares that would be issued on the conversion of preferred stock

Case 4: Convertible Preferred Shares: Can be dilutive or anti-dilutive depending upon the numerator vs denominator effect

• Numerator: Adjusted for the dividend charged and after-tax effect of interest charged
• Denominator: Include shares that would be issued on the conversion of preferred stock and convertible debt

Quick Test : Dilutive vs Anti-Dilutive

Calculate the Basic Shares and Compare with the Conversion ratio of each security. Where, conversion ratio is incremental change in numerator / incremental change in denominator

• Preferred Stock: If Increase in Numerator (Preferred Dividend) / Increase in Denominator (New Shares Issued) is < Basic EPS >>> Dilutive, else anti-dilutive
• Convertible Debt: If Increase in Numerator (Interest Expense * (1-Tax Rate)) / Increase in Denominator (New Shares Issued) is < Basic EPS >>> Dilutive, else anti-dilutive

Note: If there are multiple convertibles, then rank all the convertible securities by the conversion ratio and select only the ones which have the conversion ratio less than Basic EPS. For example, if Basic EPS is 3.2 and post-tax interest expense for a convertible bond is 60 and resulting increase in number of shares is 25, then conversion ratio is 60 / 25 = 2.4, which is < Basic EPS, hence the impact of such security will be dilutive.

If there are multiple securities, with conversion ratios as 2.4, 2.8, 3.6 and 4.2, the only first two are dilutive and remaining are anti-dilutive.

Practice Questions: (Solutions are in the attached excel)

Ques 1. Company A has a Net Income of $275,000 and 65,000 shares outstanding. Company also has 150 convertible debentures of $750 par value with a coupon rate of 6%. Each debenture can be converted to 20 shares. Company has a marginal tax rate of 25%. What is the company’s basic and diluted EPS.

Ques 2. What would be the new EPS, if in addition to this company also had $150,000 non-convertible preferred shares with 12% dividend.

Ques 3. How would the impact change if the preferred shares were convertible, with each preferred share being converted to 5 ordinary shares. Face value of preferred shares is $10 each.

eps-dilution-impactDownload

Excelling Excel Chart Series 1 – Waterfall Charts

Chances are that since you are looking for step-by-step guide to create a waterfall chart, you already know the usefulness of it and what it helps in achieving. But, to give a very short introduction into it – “Waterfall charts are few of the common charts used to provide a comprehensive view on the cumulative effects of various variables / data items on the overall value. It helps to view the sequential effect from the initial value to the final value.“

Let dig right into the steps to create a Waterfall Chart.

If you are using the latest version of MS Excel, then excel has made our life easy by providing a direct option to create a waterfall chart, similar to how we create pie charts or bar charts. However, in case you are using previous version, then be rest assured, this blog will help you with detailed instructions for earlier versions of Excel as well. Hence, I will divide the steps into 2 segments: One for the most updated version and one for the earlier version. I will also attach the corresponding excel file with charts made basis both the version here for your ready reference and template.

In both of these cases, we will use the following data set to build our chart. The data set simply represents what components went into growth of Sales from 2020 to 2021. As we can se Acquisitions and Price Inflation contributed to increased sales, however closed location and organic sales decline resulted in a decrease of sales in 2021. Below is the table with the raw data:

Steps to Create A Waterfall Chart in Office 2016, 2019 and 365:

• Select the data set from 2020 Sales to $972.6
• Press ( ALT + N + I1) or Go to Insert –> Charts –> Select Waterfall Charts (as shown in picture below)

• You will get a chart similar to below:

• Before moving ahead, it is important to make the chart little cleaner. To do that clear our the gridlines, chart title (if not needed) and legends

• Next (note this is very important step to ensure the ending value is correctly reflected in the chart) – Right click on the last bar (2021 Sales) and select the second last option (Set as Total)

• Change the Vertical axis basis the data range (in our case can be $900 – $1,010) and recolor the bars by fill option – with positive values shown as Green and negative values as red (as shown below)

• For the final step, we can hide the vertical axis and also remove the connector lines between bars by selecting the connector lines and pressing delete
  • Alternatively, right click inside the chart and go to format plot area. In the panel on right, select “Series Option” and untick the “Show connector lines” radio button

• Final chart will look as below:

Steps to Create A Waterfall Chart in Earlier Office Versions:

Unlike the above steps, where excel did all the work for us and left the formatting part to the user. There are more steps required to be performed in cases where the pre-existing charting tool for waterfall chart is not available. The manner in which the raw data needs to be organized is also very specific, without which we will not able to achieve the required results.

• As noted, since the excel cannot itself recognize the data for waterfall chart, we need to alter the raw data in various columns for easier chart construction
• Whenever one creates the waterfall chart, they will need to organize the data into 5 columns namely – Label, Base, Rise, Fall and Value
  • Label: It just represents the label of the data set that will be shown on our Y-axis. In the example we have have been using, the label column will show 2020 Sales, Acquisitions, Price Inflation, Closed Locations, Other Organic and 2021 Sales
  • Rise: Represents the column for positive values
  • Fall: Represents the column for negative values
  • Value: Represents the column that we will finally use to label the data points
• Base
  • First row will be linked to the starting value. In our example Base column first row will be linked to 2020 Sales data
  • From second row onwards base column will have the following formula:
    • Base ₂ = Base ₁ + Rise ₁ – Fall ₂ ; meaning base row 2 will be equal to base value in row above (row 1 here) + rise value in row above – fall value in same row (row 2)
    • Base ₃ = Base ₂ + Rise ₂ – Fall ₃ and so on
• Rise
  • Since there will be no rise value in starting figure, as this is our base value, we will not put any formula there (2020 Sales row in our case)
  • For each subsequent label (acquisitions etc), we will put either of the below formula in the respective rise column
    • Max (Value of respective label, 0)
    • If(Value of Label<0,0,Value)
• Fall
  • Again, since there will be no fall value in starting figure as it is our base value, we will keep this row under fall column as blank
  • For each subsequent label (acquisitions etc), we will put either of the below formula in the respective rise column
    • – Min (Value of respective label, 0)
    • If(Value of Label>0,0,-Value)

Once organized as above, our data set should look like this:

To build the chart select data from 2020 Sales to Fall column of 2021 Sales and follow the steps below:

• Go to Insert >> Charts >> 2D Stacked Column Chart

• Clean up the chart by removing the background grid lines (select the gridlines and press delete), delete the legend, chart title (if not required) and remove the vertical axis by unchecking the Primary Vertical option under Chart elements (as shown below)

• Select the “Base” columns (blue bars) and select no fill color option
• Recolor the starting (2020 Sales) and ending (2021 Sales) bar with one color
• Recolor the rise bars with Green and Fall bars with Red color
• Finally add data labels, but please note you will have to manually link each label to the Value column (this step is little tedious!)
• Finally, you have your finished chart as below

Below is the file that contains chart using both the methods.

excel-bridgeDownload

Mid-Year Discounting With Stubs – Straight & Simple Explanation !!

You will find many resources explaining the concept of mid-year discounting. But just like conventional discounting method, which takes overly simplistic view of real life problems, knowing basic mid-year convention too will not suffice. What you need is to understand how to apply this mid-year convention when you are sitting in say Q2 or Q3 of fiscal year and not the beginning of year (as most will explain). This article will help you in exactly that!

Why Mid-Year Discounting (and what’s with STUBS !?!) ?

If you are here understanding mid-year conventions, chances are you already know why we would use mid-year convention, over traditional text-book taught end-of-year discounting. But a quick refresher doesn’t hurt anybody, no ?

So to answer the question of why we would prefer to use mid-year convention to discount the cash flows, let us understand what really is our objective when we are discounting these cash flows. In the most basic sense, we are trying to determine what will be the today’s value of say $100 received at the end of the year. So we have 2 time periods here: Day we expect to receive the amount and the present day – the day on which the value is ascertained.

Conventional method assumes these time period to be the beginning and end of the year. Thus, there is an implicit assumption in end-of-year discounting that entire cash flows for the year are received at the end of the year. Does this really happen in real world? Answer is simple NO! Companies earn such cash flows on daily basis, but since it will be too tedious to calculate each penny earned basis the timings, we arrive at a compromise – we take an average. This is where the mid-year convention comes into the picture.

We use mid-year convention to represent the fact that company’s cash flows do not come all at once ie., at the end of each year, rather it comes evenly throughout the year

Example: End-of-year vs Mid-Year

Example 1: Assume the company expects $100 cash flow for four years with 12% discount rate.

	Year 1	Year 2	Year 3	Year 4
Cash Flow	$100	$100	$100	$100
Discount Period – Conventional Method	1	2	3	4
PV of Cash Flow – Conventional Method	$89	$80	$71	$64
Discount Period – Mid-Year	0.5	1.5	2.5	3.5
PV of Cash Flow – Mid-Year	$94	$84	$75	$67

Click on the link below to download the excel file for the workings of above table

Example-Mid-Year-ConventionDownload

Explanation: Few things that are important to repeat before explaining the calculations above:

• Conventional method assumes that cash flows are received at the last day of each year, hence the discounting by full year
• Mid-year convention assumes that the cash flows are received in the middle of the year

Conventional Method:

Year 1: Since the method assumes that $100 is received at the period end, the first year cash flows are discounted for full year to get the present value. Thus, ($100)/(1+12%)^1 gives us $89

Year 2: Again, for next year’s $100, the assumption is same that it arrives at the end of year 2. Thus, we need to discount it by full 2 years to get the present value. Thus, ($100)/(1+12%)^2 gives us $80 and so on for other years

Mid-Year Method:

Year 1: Now, this method assumes that the $100 in year 1 is received at the mid-year. Thus, to get the present value of this $100 we need to discount only by half a year. ($100)/(1+12%)^0.5 gives us $94

Year 2: This is where the calculations and discount period gets interesting! The second year $100 is again assumed to be received in the middle of that year. However, be little mindful of howto arrive at the discount period for year 2:-

– Let’s divide the time period into 2 parts, year 1 and year 2. Now the cash flow comes in the middle of year 2. Thus when we discount the same by 0.5, we will arrive at the beginning of year 2 or the end of year 1

– To come to present value, we need to discount the above cash flow further so as to know the value today. Since the above cash flow is one year forward, we will discount it by one more year. Hence, the total years by which $100 of Year 2 gets discounted is (0.5 + 1 = 1.5)

Year 3: Let us do another year, $100 received in the mid of Year 3, needs to get discounted by 0.5 to come at the beginning of year 2. But to know its value today, we need to discount it further by 2 years. Thus discount period is (0.5 + 2 = 2.5)

Let us bring in “Stubs” now …

Ok, so what are stubs and why we have been emphasizing on it since the beginning ? In the real world, it is highly unlikely that the company valuations are done right at the start of the year only. Until now, all our examples have been with the assumption that there is a full one year between the cash flow receipt and valuation date. What if we are already a quarter down and now are being asked for this valuation. The remaining period between now and year end is what we call as stub. Thus in this case, we have a stub of 9 months or 0.75 years.

Example 2: Company A has a year end on December 31st of each year. You have been asked to determine the discount periods for cash flows coming at the end of current period and next 3 years into the future.

	Stub (Q2 – Q4)	Year 1	Year 3	Year 3
Discount Period – Conventional Method	0.75	1.75	2.75	3.75
Discount Period – Mid-Year	0.375	1.25	2.25	3.25

Explanation:

Do not let the above numbers confuse you. If you understood the concept of mid-year convention above, this is just a simple add-on to that. Let’s discuss it step-by-step.

Conventional Method:

– Stub: The approach here is pretty straightforward. There is 9 months between end of the year (when cash flows are received) and today, hence first year cash flow (i.e., stub period) is discounted by 9 months or 0.75 years

– Year 1: This build on one year out. Hence, second cash flow is received after 1 year and 9 months. This translates to 1.75 years for discounting and so on

Mid-Year Convention:

– Stub: Use similar logic as above. If there are 9 months between today and end of period and we are using mid-year convention, then by the very assumption of mid-year rule, the cash flows are received mid of this 9 months period. Thus, the stub cash flows are discounted by (0.75/2 = 0.375 year)

– Year 1: Again, lets divide this into 2 parts – Stub + 1 Year. We are receiving cash flow in the middle of Year 1, thus we discount the cash flow for that year by 0.5. But on doing just 0.5 years, we have brought this cash flow to the end of stub period. Thus, we need to discount further by 9 months to bring that cash flow to today. Thus, for Year 1 we get (0.5 + 0.75 = 1.25 yrs)

Key Note: Mid-Year discounting is about when you receive cash in the year. In Year 1, the stub of 9 months is not halved i.e., we did not do 0.5 + (0.75/2), because we do not receive any Year 1 cash flow in this stub. The stub discounting is purely to get the mid-year discounted cash flow which represents the value at the start of that year to the present day.

Terminal Value With Mid-Year

I will very briefly touch upon the terminal value concept when using mid-year convention. Discounting changes basis the method used:

1. Multiple Method: Here add 0.5 to the final year discount number to reflect that you are assuming that the company gets sold at the end of the year (not mid)
2. Gordon Method: Use the final year discount number as is since you are assuming that the cash flows grow into perpetuity and are still received throughout the year rather than just at the end

Key Takeaways

• With same cash flows and discount rate, mid-year convention results in higher present value due to lower discount period
  • Higher the discount rate, more pronounced the difference between the end-of-year present value and that from mid-year convention
  • Longer the period more larger the difference between end-of-year and mid-year present value

Russian Financial Crisis 2014 !!

While we in India, like all other net oil importing nations, are celebrating the fall in the crude oil prices; the sentiment is quite the reverse for the net oil exporting nations. It is rightly said that for someone to win, someone has to lose. The prime example of this and of yet another country, after US and Europe, finding itself at the brink of an economic meltdown is – Russia.

Vladimir Putin today finds himself fighting two battles. He is not only at war with Ukraine, but also internally fighting hard to keep Russian economy at bay from slipping into a stagflation, which is seeming inevitable. The Russian ruble has plummeted against the US dollar, the reserves are falling, interest rates are rising and the inflation is soaring. The country is facing one of its worst financial crisis since 1998, the time when the government defaulted on its debt.

So, what is causing all these problems for Russia ?

Root cause can be pinned down to two primary factors:

1. The falling global crude oil prices.

2. The sanctions imposed by the western countries on Russia.

 

 Oil is the backbone of the Russian economy. Almost 50% of the state’s revenue is derived from oil and gas exports and about a quarter of the country’s GDP is linked to energy industry. Thus, a free-fall of the oil prices is bound to hurt the economy. The 40% drop in oil prices from over $100 US Dollar/barrel in June, 2014 to under $60 USD/ barrel in December, 2014, is estimated to have resulted in $100 billion loss of revenue to Russia (CNN estimates).

The other prime reason is the economic sanctions imposed by the west, as a result of Russia’s incursions into Ukraine and Crimea. Economic Sanctions are the domestic penalties applied by one country on another country. Economic sanctions may include various forms of trade barriers and restrictions on financial transactions (source: Wikipedia).

The result of this is that the ruble has lost about 45% of its value against the US dollar so far this year. It even hit an unprecedented low of 80 ruble to the US Dollar.

Enter the Government:

The falling ruble saw the Russian Central Bank pressing the panic button and increasing the interest rate by 6.5 percentage points, the single largest interest rate increase since the 1998 crisis. As a result, the interest rate moved from 10.5% to 17%.

The idea behind increasing the interest rate was to discourage the wave of Russians swapping the rubles for dollars and other less volatile assets. In theory, higher interest rate makes the currency an attractive investment and thus encourages people to keep money as deposit in the bank.

In addition to the emergency rate hike, the government is also estimated to have spent around $87 Bn of its foreign exchange reserves in open market. The action was aimed at preventing the collapse in the ruble and to stabilize the exchange rate. The total international currency reserves now stands at $416 billion.

Unfortunately, both the measures have failed to produce the desired result and the confidence of the people in the ruble and the economy is declining by the day.

The problem doesn’t stop here for Mr. Putin. Lets have a look at how deep in trouble the Russian economy really is.

1. Inflation: The inflation target of the central bank was 5% and currently it stands close to 9.5%. Food price inflation touched 12.6% in November, 2014. This is fueled further by Russian ban on food imports in retaliation to western sanctions.

2. Capital Flight: According to the central bank, the net capital outflows is estimated at $130 Bn for this year and another $120 Bn by the next year.

3. Fall in GDP: A year ago, Russian economy was growing by about 1.5%. Its central bank is now forecasting a 4.5% drop in GDP in 2015, if the price of oil stays at $60/barrel.

4. Debt Burden: The Russian government, bank  and companies have a combined foreign currency debt of around $678 billion. Out of that, $130 billion will have to be repaid this year. The total corporate debt, which is falling due next year, is about $76 billion. The corporates’ foreign currency debts are quickly becoming unsustainable with falling ruble. Companies have already started approaching the central bank for bail-outs. In times to come, more corporate defaults are likely.

All these factors have crippled the Russian economy and are forcing it into stagflation [contracting economy (due to falling oil prices and rising interest rate) + high inflation].

In the light of all these, the downgrade to junk status by S&P seems like a distinct possibility. This will further add to the woes of Mr. Putin who is facing an uphill climb. Before yet another domino is set into motion, sending shock waves to other economies of world, one can only hope that Kremlin gets its acts together and does it fast. But one thing is for sure, New Year 2015 doesn’t seem very happy for the people of Russia at the moment.