Start-up Valuation : Pre-Money and Post-Money Valuation

Readers,

I am quickly jotting down a note on Pre-Money and Post-Money Valuation.

It is defined that

  • The premoney valuation is the value of the existing venture and its business plan without the proceeds from the contemplated new equity issue.
  • The post-money valuation is the pre-money valuation plus the proceeds from the contemplated new equity issue.
One thing that I am trying to understand as to why the Post-Money Valuation is just as simple as adding the new investment Dollar onto the Pre-Money Valuation.

There are two points I would like to note down:

(i) As Pre-Money valuation is the valuation of the assets-in-place, then by injecting the new investment, the business might use that new injection to scale up its existing business even more, higher than the initial projected cash flows. The venture could invest that new injection to buy more stock, hire more qualified engineers and resources, etc. Then where will all this higher positive cash flows be reflected into the Post-Money Valuation?

(ii) if all those higher positive cash flows generated by investment funded by the new injection (assuming the money from the new Venture Capital (VC) flowing into the company or business and not to the existing founders), is not factored into the Post-Money valuation, then there is an assumption that the NPV from the perspective of the Venture Capital from investment in that new venture is ZERO.

NPV (Buy security) = PV (All cash flows paid by the security) – Price (Security) = ZERO.

This assumption that NPV of buying security in the new venture is ZERO might make sense, since if the NPV of buying a security were positive, then this would present an arbitrage opportunity, since positive NPV will mean that the VC is to receive a cash today (at the time of the injection being made to the new venture). Since this arbitrage opportunities theoretically do not exist in the normal markets, then the NPV of buying a security in the new venture is ZERO, meaning the trading securities should not create or destroy the value  (note : financing or financial transactions should be neutral in this case, and its presence is just to adjust the timing and risk of the cash flows to best suit the needs of the firm or investors). The real value should come from the real investment being engaged by the company (Modigliani-Miller proposition, which is pretty much about the conservation of value, or separating investment and funding activities).

If the (ii) sounds OK, then my next question, if the NPV of buying security is ZERO, then why the VC wants to inject the money to the new venture in the first place?

My initial argument is, VC could see that somehow though NPV of buying a security is ZERO, yet, the business might have upside potential in the future that could produce more income (or cash) than initially forecasted. Meaning with VC required rate of return (in the book’s example, using 50%  compound annual rate of return), the actual return could turn out to be much higher rate of return (as a footnote, VC requires really high rate of return as the potential for realizing that expected return from all its portfolio might be only 10% success rate, and the rest is a fall-out).

Prof. PDM to Karnen:

It is just definitional.  Pre-money includes the value generated by the new investments as well, but which goes to the existing investors.

Karnen to Prof. PDM:

I agree with you, the money flowing to the Venture should somehow play a role in having the venture to execute positive NPV projects, otherwise, the VC will not be willing to invest.

Respondent 1 to Karnen:

Note: the respondent’s response is in italics.

Responding to this :  the  definition of:

  • The premoney valuation is the value of the existing venture and its business plan without the proceeds from the contemplated new equity issue.
  • The post-money valuation is the pre-money valuation plus the proceeds from the contemplated new equity issue.

One thing that I am trying to understand as to why the Post-Money Valuation is just as simple as adding the new investment Dollar onto the Pre-Money Valuation.

The main reason that we can usually just add the proceeds to the Pre-Money to get the Post-Money is due to the assumption made regarding the return to new investors. As the deal is “priced” using a required return, providing that return is NPV=0.  Therefore, the equity issue neither adds nor subtracts anything in terms of NPV (dollar value above required return), but adds the proceeds to the total post-offering PV.

There are two points I would like to raise up:

(i) As Pre-Money valuation is the valuation of the assets-in-place, then by injecting the new investment, the business might use that new injection to scale up its existing business even more, higher than the initial projected cash flows. The venture could invest that new injection to buy more stock, hire more qualified engineers and resources, etc. Then where all this higher positive cash flows be reflected into the Post-Money Valuation?

The Pre-Money value is the value of the existing assets/operations in place and the value of all options to expand. New investors are paid required returns (not NPV), leaving any return above the required (any NPV) to the existing Pre-Money owners.  This Pre-Money value of the PV of existing operations and any NPV from intended expansion-option projects (after raising the money and paying a required return (NPV-0 to new investors) includes the NPV of the type of projects you suggest.  Put differently, the “N” part belongs to existing owners; the “PV” part belongs to the investors providing the new capital as their investment is priced at the required rate of return for NPV=0 on their injection.

(ii) if all those higher positive cash flows generated by investment funded by the new injection (assuming the money from the new VC flowing into the company or business and not to the existing founders), is not factored into the Post-Money valuation, then there is an assumption that the NPV from the perspective of the Venture Capital from investment in that new venture is ZERO.

(This is the assumption since we’re using a required return for competing investors considering this type of investment and risk.)

NPV (Buy security) = PV (All cash flows paid by the security) – Price (Security) = ZERO.

This assumption that NPV of buying security in the new venture is ZERO might make sense, since if the NPV of buying a security were positive, then this would present an arbitrage opportunity, since positive NPV will mean that the VC is to receive a cash today (at the time of the injection being made to the new venture). Since this arbitrage opportunities theoretically do not exist in the normal markets, then the NPV of buying a security in the new venture is ZERO, meaning the trading securities should not create or destroy the value  (note : financing or financial transactions should be neutral in this case, and its presence is just to adjust the timing and risk of the cash flows to best suit the needs of the firm or investors). The real value should come from the real investment being engaged by the company (MM proposition, which is pretty much about the conservation of value, or separating investment and funding activities).

If the (ii) sounds OK, then my next question, if the NPV of buying security is ZERO, then why the VC wants to inject the money to the new venture in the first place?

(To make the required return they have calibrated and a competitive market agrees is the “going rate” for that type of investment and risk. The key here is that when we use a discount rate like 50%, we have assumed that such a rate is competitively available to the venture to move money across time. Otherwise the discounting to get value doesn’t make sense. All monies (from existing and new investors) moves across time at that same rate (assuming they have the same claim and risk). This is embedded in the notion that we are allowed to make the time-value adjustments using a single discount rate at each point in time.)

My initial argument is, VC could see that somehow though NPV of buying a security is ZERO, yet, the business might have upside potential in the future that could produce more income (or cash) than initially forecasted. Meaning with VC required rate of return (in the book’s example, using 50%  compound annual rate of return), the actual return could turn out to be much higher rate of return (as a footnote, VC requires really high rate of return as the potential for realizing that expected return from all its portfolio might be only 10% success rate, and the rest is a fall-out).

(It appears that you have worked through the rationale. I think your concern is more fundamental than our textbook application, however.  That is, the concern is not just about discounting in the venture investing context. The same concern would apply to the use of a required discount rate for project financing in a mature company. When we use a required discount rate to impose the new investors’ claims on the cash flow stream (taking the rate to be the competitively offered rate that is appropriate for the investment and risk), we have assumed that all NPV from the funded project goes to existing investors.  This is the same as saying the present value of the new money is equal to the discounted value of future cash flows at the required return. If we have to give some NPV to the new investors, then the “required” return is higher than the return we’re asserting is the “required” return.  Again, this is a fundamental assumption involved in discounting using “required” returns – there is a competitive fringe of investors that can only successfully demand the market-determined required rate of return. You don’t have to pay them above that amount. You cannot get their money for less. This means that the NPV goes to existing owners of the right to take the new capital and create something beyond the required return on that new capital. Existing investors get the NPV in such a context. Perhaps it would help to think of the expansion rights as something like a patent that can only be used by its owners.)

Karnen to Respondent 1:

From reading your comments, it sounds to me that the first investor and second investor will be compensated with MAX the required rate of return. If this is the case, then the investor’s money in nature is similar to DEBT, which means they will only get what is PROMISED to them from investing their money into the venture. Then all NPV, or any ACTUAL return from the venture above the required rate of return, then this will go to the founder(s). If this is correct, then the first and second round will only have downside risk, but can’t enjoy the upside potential of the venture.

The reference to the Exit Value at Period_t-1 (fifth year in the case being shown). This “Exit value” could mean anything, I gather, not necessarily, the venture will really free-flow the money to the investors and founders.

Yes, the exit value is just an imposed horizon value that could be from a conjectured IPO, acquisition or private equity buyout of one’s investment.  For example, if one considers the IPO the event for that horizon, it is not (in the U.S.) typically a liquidity event given that insiders typically are locked up for 6 more months. Nonetheless, we can think of the IPO price as some type of valuation to “mark to market” the locked-up investors’ investments. Their eventual realized proceeds could be more or less than the IPO price.

In many books I read about the Silicon Valley success stories, the Exit here will mean the successful IPO, for example, eBay, Netscape, Google, Facebook, Twitter, etc. So in the case of IPO, since there is no money free-flowing to the investors (both first round and second round) from the venture, but the 1st and 2nd investors if they want, they could sell their shares to the public as well (or offer their shares to other private investors), then the ACTUAL rate of return to the 1st and 2nd round investor, will not be limited to the required rate of return they put in the first place. If this is correct, then this is not in line with what I understand from the one I explained above which 1st and 2nd round investor return profile will be similar to DEBT, in other words, their return will be MAX to the required rate of return..

When we use a discount rate on expected cash flows to get a value today that is paid by an investor that investor owns a security with those expected cash flows. When actual cash flows are realized, then the rules of the security (the security’s position in the waterfall) determines the actual/realized cash flows which can be more or less than those that were “expected” when the security was purchased. It is true that some securities will have levels where additional cash flows “knock in” or “knock out.” That is, the security’s legal structure can allow for acceleration or deceleration of participation in cash flows at various levels.  Whether the participation level starts, stops, accelerates or decelerates is part of the negotiation when the security is created/purchased. Traditional debt knocks out its participation in cash flow above the level of its principal and accrued interest. Traditional equity knocks in when debt claims have been serviced. Hybrid securities can have both debt-like and equity-like claims. If those are to have max and min characteristics (usually referred to as “participation” in VC investments) they should be specified in the legal documents defining the securities at the time of purchase. 

The valuation approaches treat the securities as they would produce flows in “upside scenarios,”  i.e., as if converted to equity.  If one wanted to base the valuation on a larger (broader than the three we consider) scenarios where detailed treatment of “downside scenarios” and liquidation preferencing, etc. is taken into account, then one would need to have a mathematical description of the waterfall specification and then proceed to consider more scenarios and their likelihoods.  Our observation of much of the early-stage venture financing is that such detailed inclusion is seldom considered to be a significant component of the price to which venture investors agree.  More often, the value appears to be based on some “upside scenario” and the associated realized returns in those scenarios (X% per year or 3X, 5X or 10X on investment, etc.). Perhaps this is a concession to the large amount of complete write-offs for failed ventures (where even the debt-like preferencing doesn’t provide much in the way of cash flow). Of course, 50-100% is clearly not an “expected” return. It is a “utopian” return targeted for successful investments so that overall portfolio returns will be reasonable (given that many of the investments are 100% losses).

Debt Cost of Capital : Which to Use?

Readers,

Another question that is frequently being asked is about Debt Cost of Capital.

Though in practice, analysts and finance books and papers spend more time in discussing the EQUITY cost of capital, yet most of the corporation issues more DEBT than EQUITY.

Looking into the size of the world’s capital markets, both in total or for each country, the size of the debt markets in 2011 was much higher compared to equity market.

IMF 2011 the size of the World’s Capital Markets

source:
https://www.imf.org/external/pubs/ft/gfsr/2012/02/sa/satable1.pdf (accessed on 20 June 2020)

If we look the Capital Markets size in year 2018, Bonds Market capitalization still surpassed the capitalization value in the Equity Market, as displayed below.

Source:
https://www.sifma.org/wp-content/uploads/2019/09/2019-Capital-Markets-Fact-Book-SIFMA.pdf (accessed on 20 June 2020)

When it comes to determine Debt Cost of Capital, using the survey shows the following findings (see the answer to Point No. 5, which gave us that in estimating the before-tax cost of debt:

(i) the surveyed corporations 26% uses U.S. Treasury Yield + Spread, 21% marginal YTM outstanding debt and 21% weighted average outstanding issues

(ii) the surveyed financial advisors: 55% current yield to maturity and 45% new debt yield to maturity

(iii) the surveyed textbook or trade books : 83% yield to maturity and 17% marginal cost of new debt


Source: “Best Practices” in Estimating the Cost of Capital: An Update by W. Todd Brotherson, Kenneth M. Eades, Robert S. Harris, and Robert C. Higgins (2011). Accessed from
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2686738 on 20 June 2020).

While in 2011 Survey conducted by the AFP Association for Financial Professionals, in its report : 2011 AFP Current Trends in Estimating and Applying the Cost of Capital Report of Survey Results, reported that

(i) Thirty-seven percent of organizations simply use the current rate on the debt that they have outstanding, while a third forecast the rate for new debt issuance.
(ii) Twenty-two percent use the average rate on outstanding debt over a defined period of time, and

(iii) seven percent consider the historical rate on outstanding debt.

(iv) A plurality of smaller organizations use the current rate on outstanding debt while the most widely cited method for large organizations and publicly traded organizations is the forecasted rate for newly issued debt.

AFP 2011 report were accessed from
http://business.baylor.edu/don_cunningham/How_Firms_Estimate_Cost_of_Capital_(2011).pdf on 20 June 2020.

We could see from the above that there were no consistency among corporations and finance advisors, with what is suggested to be used by many finance textbooks.

There are two points I would like to discuss related to cost of debt:

(i) Knowing the difference between PROMISED RETURN vs EXPECTED RETURN with regards to the interest rates on corporate debt or bonds

(ii) Using DEBT YIELD TO MATURITY as the Debt Cost of Capital and the mistake that we could fall into.

Let’s start this fun journey!

A. PROMISED RETURN vs EXPECTED RETURN OF CORPORATE DEBT RETURN

I gather, we are all clear that in doing the corporate valuation, we need to DISCOUNT:

(i) PROMISED [forecasted] CASH FLOWS with the PROMISED rate of return; or

(ii) EXPECTED [forecasted] CASH FLOWS with the EXPECTED rate of return.

However, when we are talking about Net Present Value, this will be about discounting the EXPECTED CASH FLOWS with the EXPECTED rate of return.

Now we have PROMISED vs EXPECTED rate of return, and what makes them different?

I am tying to sketch quickly the components of the corporate bonds interest as displayed below:

Expected rate of return is distinguished from promised rate of return for corporate bond, since unlike that of government bonds, for corporate bonds, there is a probability (read: risk) that the promised principal and coupon will not be repaid or serviced.

So, return on default-free [government] bonds + RISK premium = this will be EXPECTED RETURN. Adding the [expected] default risk premium onto EXPECTED RETURN, then it is PROMISED RETURN.

When I put here PROMISED, it means that the company put its promise to the lender that it will pay FIXED future payments. However, bear in mind that though the company promised to pay the lender FIXED future payments, yet it doesn’t mean that there is a guarantee a FIXED RATE OF RETURN over horizons shorter than the bonds’ maturities, and the longer the bonds will mature, generally speaking, it will be riskier investments compared to shorter maturities. This will be applicable even for the government-issued bonds.

Remember : FIXED INCOME is not the same with FIXED RATE OF RETURN!

Something that I would like you to bring home that, except for 100% default free bonds, the PROMISED rate of return will be HIGHER than the EXPECTED rate of return. If you’ve ever found the Rate of Return published in the financial information, then that is QUOTED rate of return and QUOTED rate of return = PROMISED rate of return.

I need to go back a bit. Above I am saying that the EXPECTED rate of return will consist of :

(i) Default risk-free rate of return

(ii) PLUS RISK PREMIUM. This risk premium could include, among others, the liquidity premium, maturity risk premium, and tax premium, foreign exchange rate risk premium and other risk to compensate the lender for his/her willingness to take on risk, which risk is systematic and non-diversifiable.

Tax premium is present since the interest from the government bonds might be taxed at rate lower than that of corporate bonds.

Liquidity risk premium is present coming from the fact that there may not be always a ready buyer for the corporate bonds. Generally speaking, there will be always buyers for government-issued bonds or treasury bills or notes.

Maturity risk premium is added since there is a chance that the default risk-free rate will change over time. The longer the maturity will come, the higher the maturity risk premium will be added on. However, this maturity risk premium will be applicable not only for corporate bonds, but also for government bonds. Since government bonds/bills/notes have zero default risk premium and zero liquidity premium then, we could say, that the difference of rate of return of shorter government bills and longer government bonds or notes, should come largely from the maturity risk premium, which will factor into it, the risk of future inflation.

So to recap the components of the required rate of return being asked by the investors for any debt instrument or bond will include the following elements as depicted below.

In calculating the cost of debt, Prof. Aswath Damodaran put that :

In general terms, it is determined by the following variables:

  • The riskless rate. As the riskless rate increases, the cost of debt for firms will also increase.
  • The default risk (and associated default spread) of the company. As the default risk of a firm increases, the cost of borrowing money will also increase.
  • The tax advantage associated with debt. Since interest is tax deductible, the after-tax cost of debt is a function of the tax rate. The tax benefit that accrues from paying interest makes the after-tax cost of debt lower than the pretax cost. Furthermore, this benefit increases as the tax rate increases.

Source: Aswath Damodaran. Investment Valuation : Tools and Techniques for Determining the Value of any Asset. Third Edition. 2012. John Wiley & Sons, Inc., Hoboken, New Jersey. Page 211.

So we see that at least in the general terms, in determining the cost of debt, there are two elements, (i) the risk-less rate and (ii) the default risk. Any investment instrument that is to be considered purely risk-free will require two basic conditions to be satisfied:

  • no default risk. This element will make the debt instrument issued by private sector not considered, since it might have some measures of default risk, even for those debt instruments falling under AAA (or Aaa) rating.
  • no reinvestment risk. This has a painful implication to the valuation since essentially, we need to use the different risk-free rates for each period, and different expected returns in determining the cost of debt. For example,
    • the risk-free rate for a one-year time horizon has to be the expected return on a default-free government one-year zero coupon bond,
    • the risk-free rate for a two-year time horizon is the expected return on a default-free government two-year zero coupon bond, and so on.

To be said that a debt is RISK-FREE, then the the actual returns on debt (or any investment) should be equal to its expected returns. And as far as it relates to debt, again this is only possible if there is no default risk and no reinvestment risk.

In similar vein of discussion, then there are two sources of risk:

  • interest rate risk, which is about the general changes in the long-term rates (this is somehow also about the expected inflation and expected LONG-TERM real growth rate)
  • credit or default risk

Here, then we have long-term vs short-term debt. In general,

  • When interest rates go up, bond prices fall (and vice-versa), with longer-maturity bonds will be more sensitive to long-term rate changes. This is because longer-term bonds have a greater duration than near-term bonds that are closer to maturity and have less coupon payments remaining, which means that longer-term bonds are also exposed to a greater probability that interest rates will change (up or down) over its remaining duration.
  • The above fact lies in the very nature of the fixed-income (periodic fixed coupon payment) nature of bonds, meaning when the investor purchases a bonds, then the investor will be stuck to that PROMISED fixed coupon payment. Whatever happens to the market interest rate, the investor can’t not ask the issuer to change its coupon payment.

So first, there is an Inverse relationship between bonds yield (or market interest rate) and bonds price.

Second, we need to differentiate short-term and long-term debt. Longer-term is more exposed to the changes in the interest rate, and this relationship between price and interest will be INVERSE. This inverse relationship will exist even if the debt is default-risk free.

Third, long-term debt then tends to have a beta higher than 0, or positive beta, though the figure might be small, 0.2. However, with short-term default-free debt, then the beta tends to have a near-zero beta, as its value will not be altered by changes in the expected long-term interest rate. This will bring us that when we refer to risk-free debt (no reinvestment risk and no default rate risk), this should necessarily be short-term. This is why we found the finance textbooks or any finance websites suggested that risk-free rate of return can be estimated by using the interest rate on a short-term government-issued debt instrument, such as one-year US Treasury bill.

From the above, we could then need to be able to distinguish now the RISK-FREE DEBT from DEFAULT-RISK DEBT. RISK-FREE DEBT will include the DEFAULT-FREE DEBT, but DEFAULT-FREE DEBT is NOT necessarily RISK-FREE DEBT.

Then how to reconcile the whole discussion above?

  • First, I need to bring you to EXPECTED and PROMISED rate of return again. EXPECTED Rate of Return will include the risk-free rate (this will again necessarily mean SHORT-TERM) plus all kinds of RISK PREMIUM mentioned above, including the Maturity risk premium, with longer-term debt. We could use the government zero-coupon bonds with matching duration, to take out the reinvestment rate risk, which will give us the risk-free debt with longer period.
  • ADDING ON the EXPECTED rate with the DEFAULT RISK premium, then we will have PROMISED rate of return.

Before we move to next discussion, there are one point worthy noting that we don’t need to use the year-to-year specific risk-free rates, as a practical compromise, the present value effect of using year-specific risk-free rates tends to be small for most well-behaved term structures. Well-behaved term structures would include a upward-sloping yield curve, where long-term rates are at most 2 to 3 percent higher than short-term rates (as said by Prof. Damodaran, page 155 of the same source textbook above.)

First we will see how the bank or lender viewed this

Second, the components of the expected rate of return, time premium etc (continued)

Discussion

Cost of debt should always refer to the current and expected market rate, meaning that historical rate is supposed to not be used. Some I noted, the analysts will use the expected incremental borrowing rate and YTM (with or without default be factored into).


When we value existing business or value new business (or expansion of the existing business), using market rate of debt will be more relevant as the discount rate instead of going back to calculate the Interest paid_t/D_t-1.

Respondent 1 to Discussion:

Strictly the cost of debt is what the market says. That’s ok.

However, if you look around, MOST (MOST is most!) firms don’t have traded debt. Not even all the firms in the stock market have public debt (say publicly traded bonds).

In our real life, in everyday life, what we find is non-traded debt and its cost is just KdD_t-1 where Kd is the contractual or stipulated value of Kd.

Let’s see some statistics:

In the US you have this number of traded firms, according to Damodaran website.

Total Market7053
Total Market (without financials)5878

These firms are traded, agree? According to 2015 Statistics of U.S. Businesses, of the 5.9M firms in the U.S., 3,643,737 have fewer than 5 employees. Their total employment is 5,877,075. Let’s say, 6 millions and 94 industries. From these industries, Damodaran shows industries with 94 to 611 firms. Adding ALL emerging markets together he adds to

Total Market22402
Total Market (without financials)20162

These numbers of firms include firms from China and India. Just imagine the hodgepodge of data we have. Well, you could say, don’t use Damodaran’s data. OK.

Where do we have a slightly better idea of what beta for a given firm should be? Where do we get a better estimate of Kd the firm pays and TS that the firm gets for those items? Perhaps we should develop an idea about a subjective estimate of Ke done by the owner. (Remember that the great idea of CAPM is to be able to estimate the Ke for an unknown inaccessible owner).

From these industries, Damodaran shows industries with 9 to 907 firms.

From Damodaran tables you can “obtain” the betas (levered and unlevered) for each industry.

Now you can tell yourself how good are our estimates of betas and hence our Ku and Ke. 

Going back to Kd, who has a better estimate of Kd for most firms in our countries? In the same US for the enormous number of firms that don’t trade? What I am trying to call your attention is that recognizing that Kd SHOULD be the market Kd rate and not the contractual cost of debt is irrelevant. YES! In the VERY FEW cases we deal with large firms and not all of them issue public bonds.

In short, if we become very picky, we will conclude we can’t make a reasonable estimate of cost of capital for firms and owners!

Karnen’s comments to Respondent 1:

I guess, differentiating whether the debt is publicly traded or not, is not a crucial point to me. Debt is debt….meaning that it will be foolish for lenders to extend their money to the company without really looking into the market (or at least what the market is expecting).

Kd and Ke (or Ku) is different stuff, and Kd should be relatively much easier (I don’t say it is easy) to calculate.

I always remember that that it is necessary to “asking the people that give you the money, how much return they want it back”. Again this philosophy could go to Kd. Debt is different from Ke, since we don’t need to estimate it, we just have to look at the going market rate for debt, or asking the lenders (or banker, bonds trader, etc.). Even if the debt is not publicly traded, however, plenty of information is up there in the market. Big banks usually post their prime lending rate. or we have LIBOR (which many banks are still anchoring their ask rate started from LIBOR), etc. The interesting part of Kd, the historical cost of debt is not relevant anymore. So in my personal opinion, estimating Kd is not like taking something from the thin air.

Other point about Kd is most of it is about PROMISED rate of return (though if the default rate is high, we need to factor it to get the EXPECTED rate of return, the one that we will use into the Cost of Capital). Since it is a PROMISED coupon rate, then we could see into the market, how much big COUPON RATE that have been published in the market.

Prof. Damodaran in many of his valuation textbooks suggested to calculate Kd by using Risk-free rate + default spread to come up with the [promised] cost of debt (see page 211 of 3rd Edition of Investment Valuation, which uses synthetic rating). I don’t say that I totally agree with Prof. Damodaran’s approach, yet, it means we could use the information from the market for the Kd.

For Ke (or Ku), using data from market is a lot problematic, we could either go straight to estimate the expected returns (i) directly from the historical average return (with its all troubling big standard error of expected return) or (ii) infer beta from historical data, and use CAPM. But this is a whole different discussion.

I go even further, stating that even that the debt is whether publicly or not publicly traded is irrelevant at all.

Just to put the debt on the public exchange or not, this will not change the nature of the expected return on debt. Other than transparency (institutional issue) and liquidity that the exchange could provide in order to match the consumption-savings profile of the investors, then expected returns on a debt should likely reflect the company-specific DEFAULT risk of the debt issuer. This should not come as a surprise in view of its very nature of the debt instrument, promising the FIXED rate of return (=coupon rate being fixed during the term of the debt) to the lenders.

Accordingly, we see that the debt beta is mostly approaching to zero, meaning that its expected return could be said uncorrelated with the market volatility. In other words, the famous mean-variance rationale cannot be applied to debt instruments that have limited upside gain and much greater downside potential coming from the company-specific events.

Karnen:

Now we moved to why it is important to know the difference between PROMISED Yield-to-Maturity (YTM) and EXPECTED YTM.

Quoted BONDS YTM is a promised YTM, since the repayment of bonds principal and the service of bonds interest are as promised by the bonds issuer to the bondsholder.

If the default rate is relatively small, then we could use the quoted YTM as the reasonable proxy for the expected Cost of Debt.

Let’s check using Moody’s data.

Source: Moody’s Investors Service. Annual Default Study: Corporate Default and Recovery Rates, 1920 – 2017. Data Report 15 February 2018

Note: IG = Investment Grade; SG = Speculative Grade

From the above Exhibit, we could see that there is a huge gap for the default rate between those bonds in the Investment Grade vs Speculative Grade.

For Investment-grade bonds, with 20 years of data, the default rate maxed at 5.33%. However, for those Speculative-grade bonds, the second year has reached 8.51% default rate and peaked at 40.75% at 20th year.

With such high default rate for speculative grade bonds, then quoted YTM which calculation is based on PROMISED cash flows, then if we use that quoted YTM as the expected cost of debt, then we have overstated the expected YTM.

So for the speculative-grade bonds, we need use the following formula:

Kd is the Expected YTM.

Alternatively,

Expected YTM = Kd = (1 – pb) [Interest + Principal] + pb ( [Interest + Principal] – Expected Loss), or
= promised Yield to Maturity – Prob(default) * Expected Loss Rate

Pb here is the probability of default.

Prof. Sheridan Titman and Prof. John D. Martin gave a good illustration using Moody’s data on default and recovery rate about how to come up with promised YTM and expected YTM, as illustrated in their well-written Valuation book.

Source : Valuation, The Art and Science of Corporate Investment Decisions. Third Edition. Page 149. Pearson Education, Inc.

Upon factoring the default and recovery rate, we could see that there is a meaningful gap between promised YTM vs expected YTM, in this example, 17.76% vs 11.87%, or 589 basis point difference.

So, using promised YTM instead of expected YTM, we have over-estimate the cost of debt, resulting in overstated cost of capital. However, this is not necessarily bringing the valuation being overstated or understated, since it will depend whether this overstated cost of debt (and cost of capital) be offset partially by the overstated/over-optimistic scenario being built into the expected future cash flows, the ones that are being discounted. It means that it is common to see that the analysts inadvertently introduce too-hope-for (technically speaking, forecasting errors) into the estimates of the cash flows.

Personally, my suggestion, is reality check is critical in the cost of debt and valuation, and in this case, the selection of peers becomes parallel-wise important to do.

Financial Model + RISK

Readers,

It is said that “the search for value” is what drives a huge amount of efforts over a long period of time in the financial markets and among finance scholars.

However, this is not wholly correct or half the story. The other half story and more imposing is “the search for [understanding] the risk”.

A bit historical background on this:

  • Markowitz Modern Portfolio Theory is about giving equal weight to RISK as well as return (1952).
  • Sharpe CAPM shows us that the expected return on risky assets is a function of its RISK (1964).
  • 2M’s (Modigliani-Miller) 2 propositions (1958) said that the value of a company is a function of its business’s RISK and changing the capital structure or its financing side just will change how that risk is parceled up among the debt and share-holders.
  • Fama’s Efficient Market Hypothesis explains the market that gave the mantle to CAPM, that is there is no free lunch as far as it relates to RISK (1970)
  • Black-Scholes-Merton (1976)’s option pricing is coming from the needs to hedge the RISK.

So it all those 5 monumental points in finance history..all is about the RISK.

So, when we are building the financial models, the model should center on the risk. The models built are not about just looking at the resulting parameters, such as ROI, IRR, NPV, Equity Value, EPS, etc. but the risk measurement should be there and shown. A good financial model is providing us the insight into the risk.

Some models has managed to incorporate some modeling methods to deal with the uncertainty in the modelling, such as factoring the probability, sensitivity analysis, scenario analysis, simulation, break-event point analysis, stress-testing, VAR, Monte Carlo analysis, etc.

However, the risk should be understood not just as the NUMBER as there is no simple mechanical way to depict this. Logic and theory should be the foundation to grasp the RISK.

The complication with RISK is the inter [cross]-interaction among so many factors and elements of responses from the decisions being made in the financial markets, including factors that are coming from non-financial markets, such as politics, consumers behaviour and demand, technology, production and supply chain, innovation — in other words – EVERYTHING that HUMAN could make the decisions [betting and responding to] over it.

(continued)

#StayatHome Financial Modeling : Discount Rate or Opportunity Cost of Capital

Talking about Discount Rate makes me remember the song by Bruce Springsteen…Dancing in the Dark

Even if we’re just dancin’ in the dark
Even if we’re just dancin’ in the dark
Even if we’re just dancin’ in the dark
Even if we’re just dancin’ in the dark

Readers,

Many times, participants asked me about what discount rate that we need to discount the expected cash flows in your financial model? They mostly understand that WACC (Weighted Average Cost of Capital) should be there. But I don’t want to discuss WACC, too boring.

Humming…

I get up in the evenin’
And I ain’t got nothin’ to say
I come home in the mornin’
I go to bed feelin’ the same way
I ain’t nothin’ but tired
Man, I’m just tired and bored with myself
Hey there, baby, I could use just a little help

just a little help, yeah…

Instead of answering, like many finance professors, they will answer back with question..there are no hard and fast rules.

Let’s say, you have a business that runs well. You want to expand this business with another project requiring US$ 1 million, and as usual, you go to your banker. Your banker using 5 Cs’ analysis will look into your business, and come up with the conclusion, this is creditworthy, and the bank will charge with 8% interest per year.

Question: Is the project’s cost of capital 8%?

This might sound quite logical, I got the funding bearing interest of 8% per year, and that money all being used to fund the project’s investment?

“Sound” logical, but is it true? You are in hesitation, and coming to my class asking about this?

The confusion comes from the reality that project’s cost of capital is UNOBSERVABLE. There is no way for us to go to the market and find it or any paper or publication will tell us how much in % the cost of capital for our project will be.

However, interest rate on debt is REAL, and OBSERVABLE. Even your banker could tell you straight how much interest the bank will give you the credit.

Again, you need to put your feet on the ground…time for REALITY CHECK.

The loan interest rate might be related to project cash flows, since the project investment will be financed by the loan and the project cash flows will be used as well to service the debt repayment and the yearly interest rate. Though it is RELATED, but here we are talking about the COST OF CAPITAL to discount the PROJECT’S EXPECTED CASH FLOWS. So in this case, we are talking about the RISK OF THE PROJECT. The loan interest rate then is NOTHING TO DO with the RISK OF THE PROJECT.

When the Banker does the assessment of your business expansion business, and comes up with the annual interest rate, that will say about the soundness of the business, and that includes the already-existing business. Which means that the Bank looks into the current cash flows produced by the already-existing business, plus the new incremental cash flows that will be generated by the business expansion project. If the business expansion project’s cash flows and assets were not sufficient to repay the loan principal and service the interest charge, then the Bank has another door to go, that is the bank could demand repayment from the cash flows generated by already-existing business.

Don’t you think the Banker is the smartest people in the world? Don’t forget to remember: Money attracts Brain! Some people trades products but some people trades money.

Hopefully you are still with me.

The loan then is nothing to do with the project’s risk.

The key words every time we are discussing the cost of capital is THE OPPORTUNITY cost of capital. I guess, we need to keep this OPPORTUNITY word in all textbooks, to remind the readers, and reduce any confusion about the cost of capital. Since it is the opportunity that is the key word, then it will implicate something, we need to compare between two investments, in this instance:

(i) Either the money going to finance the project. Let’s say, the project will only come back with the expected rate of return of 12%; OR

(ii) the money be invested to other investment option, let’s say, other stock in the capital market, with equally risk level, which will return the expected rate of 20%.

So taking the loan or not, IT IS NOT RELEVANT TO THE PROJECT’S DISCOUNT RATE OR COST OF CAPITAL.

I don’t think it will make finance sense at all, if the management decide to:

(i) take the loan with interest rate of 8% per year, and then invest the money to the project with the expected rate of return of 12%, if at the same time…

(ii) the company’s shareholder could pick up the loan with 8% annual interest rate and invest the money to capital market which its expected return of 20%.

I hope Readers will see that when it is the OPPORTUNITY cost of capital, then we need to see everything from the SHAREHOLDERS’ EYES.

Don’t ever forget your SHAREHOLDERS!

Comparing the above two ALTERNATIVES or OPTIONS, then we could say that the Project’s OPPORTUNITY cost of capital should be 20% instead of 8%!!!!!!!!!

You will judge the project’s soundness using the cost of capital of 202% and not 8% (interest rate on loan) or 120% (your expected rate), but 20%, since this is the return that you could get from equally risky investment.

If the money from bank could be used to gain 20% return in the capital market, then it will be easily challenged as to why you put the bank loan money into the project that will give back lower rate, that is 12%.

There is something that I said above that you might not really notice. I refer to the capital or stock market when I said that we need to look to the capital/stock market for finding alternative equally risky investment.

Of course we can’t leave the bonds market away.

To find the OPPORTUNITY COST OF CAPITAL, then we need to look to the Bonds Market and Stock Market. As ever I put before in my another writing “Government Bonds with Negative Yield?”, Bonds Market will always be the anchor for all your investment decisions, either you want to put your money in the bank, real estate, stock, you need to check on the Bonds Market, as interest as the Mother of Economics, is formed through demand and supply forces in that market. Even the expected return rate on common equity will somehow factor into it, the bonds yield. This is why sometimes we find that analysts will use bonds-yield-plus-[subjective]risk-premium approach to estimate a company’s cost of common equity. It is logical to think that companies with risky, low-rated, and consequently high-interest-rate debt (which is readily observable in the market) will also have risky, high-cost equity.

I got a question instantly, then what happens to all those WACC concepts that I got from my finance class?

I don’t say WACC is wrong or correct to be used, yet, probably what we learnt so far is just half the story.

I am trying to depict the WACC discussion into what I call Traditional View and Expanded View.

As you can see, and know very well, under Traditional View, with money flowing from Debt-holders and Equity-holders, WACC to fund a project then will be the weighted average of cost of debt and cost of equity proportional to the market value of each fund.
Well, I guess, nobody from finance schools will challenge the above.

However, I am a bit piqued by knowing that the interest rate on loan/debt (how we get the interest rate, that’s different story, some analysts, just use bonds yield, stated interest rate, etc.) is nothing to do with the project risk. The interest rate being requested by the debt-holder will only reflect the soundness or good health of the Company overall, including its existing business. In the case, the new expansion project can’t repay or service the loan, the bank could come to company to demand repayment from the cash flowing from its existing business.
It will sound a bit non-finance sense to borrow, let’s say 8% and invest the money to the project earning 12% if the shareholders could go the Expanded View, where he/she himself/herself borrow the money at 8% and use the money to fund the project and for that, the shareholders require 20%, the return that he/she could get by putting that money to the stock market (big assumption: the project and the stock market investment has equally risky profile of return and risk).
So under the Expanded view, all projects expected cash flows should be discounted at the equivalent rate of return that the shareholders could earn from alternative equally-risky investments. In this example above, 20% to use to discount the project.

In this case, we don’t even need all those WACC calculation.

In a nutshell, either the project is financed with a mix of debt and equity = since the shareholders could borrow by themselves instead of the company making the borrowing, all projects should be discounted at the rate that the shareholders could earn from other equally-risky investment.

My argument, this Expanded view is very feasible, in United States of America, we know there is pass-through company, called S Corporation. A shell company.

What do you think?

Respondent 1 to Karnen:

In short, I think I agree with everything you say; in particular, ” … all projects expected cash flows should be discounted at the equivalent rate of return that the shareholders could earn from alternative equally-risky investments. In this example above, 15% to use to discount the project.  In this case, we don’t even need all those WACC calculation.”  There is excellent theory (originally developed by Modigliani and Miller) to support this view too and it basically says that except when there is either (1) significant transaction cost differences between enterprise / business sale transactions and debt / equity investment transactions, or (2) information asymmetries between enterprise management and debt / equity investors, the project discount rate (on the assets) would be exactly the same as WACC (see Section 5.3. in the attached).  My personal opinion is that, in most cases, it’s very difficult to determine whether (1) or (2) exists; so I tend to assume the asset project rate = WACC and then just avoid estimating WACC on that basis.

And, yes, I agree with your argument and estimation methods that you suggest as well.

Karnen to Respondent 1:

Could you kindly elaborate further when you said:

so I tend to assume the asset project rate = WACC and then just avoid estimating WACC on that basis. 

Will that mean you don’t use WACC? 

May I know what you are doing when you come to estimate the discount rate?

Seems to me this discount rate is a kind of elusive concept. Different people could have a different way to come up with the discount rate. So meaning there is no single rate or even one range of rates that even two people could agree upon.

I guess the issue is (i) we need to infer Ku (unlevered risk) from Ke or even Kd (and this will lead to a long debatable topic), and second, we don’t have at the moment, the theory to calculate directly the project unlevered risk.

Though there are many books out there showing us to unlever and relever Ke, but all of this will really depend :

whether we assume using fixed book-value leverage ratio

whether we assume using fixed market-value leverage ratio

whether we assume using preset debt

whether we assume periodically adjusted debt

what discount rate assumption we use for TS

etc.

If we read MM 1958 paper, the authors themselves, never figured out how to calculate the cost of capital and they put there that  question must be deferred to a subsequent paper. Though MM gave us a definition of the company’s cost of capital was the opportunity cost of not putting money into the shares of a different firm in the equivalent return class, however, again, they never really defined what that was supposed to mean.

It is interesting to note that you bring up the Certainty Equivalent Method and risk-neutral pricing. However, I am not too often in practice, to see analysts using this kind of method to do their pricing, and this method seems to me has not gone to the mainstream in valuation.

If you could share the way you calculate your discount rate, that will be great.

Respondent 1 to Karnen:

I’ll try to answer in sequence:

(1) “so I tend to assume the asset project rate = WACC and then just avoid estimating WACC on that basis.  Will that mean you don’t use WACC?”

That’s correct: If I can support the assumptions that (i) there are no substantial information asymmetries between an enterprise’s management and the acquirer (e.g., if the acquirer has done adequate due diligence and the target’s management has incentives to properly disclose all significant matters), and (ii) there are likely no substantial differences in transaction costs between an “all equity deal” and a “leveraged deal,” then it follows that Ra = Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) = WACC. So, I just use Ra; the estimated risk-adjusted rate of return on the assets / project. 

And, I agree, MM (1958) just introduced the concepts / ideas without really working out all the theory.  I worked out the modern theory in my book based on the fundamental economic identity for resources and claims against resources (ASSETS := LIABILITIES + EQUITY), and an application of information asymmetry and transaction cost theory under the no-arbitrage principle (following Ross (2004), etc.).

(2) “May I know what you are doing when you come to estimate the discount rate? Seems to me this discount rate is a kind of elusive concept. Different people could have a different way to come up with the discount rate. So meaning there is no single rate or even one range of rates that even two people could agree upon.”

I agree about the wide variation in practice on estimating discount rates, and I think this has mainly to do with the fact that arbitrage pricing theory (APT, Ross 1976) is still rarely taught in university; mainly because people (even professors) think APT is just the same as CAPM but with additional risk factors.  But APT and CAPM are quite different theories: CAPM is based on a priori assumptions like (i) there is such a thing as an observable risk-free asset and rate, and (2) the capital markets are in equilibrium.  If these assumptions don’t hold, then CAPM’s theoretical predictions would not be valid.  In contrast, APT needs neither of these assumptions.

So, I use either an APT-based estimate of risk-adjusted expected rate of return, or I discount estimated certainty-equivalent cash flows using observable risk-free asset yields. 

(3) Regarding levered and unlevered “beta”

If one actually believes CAPM is valid, then using the Hamada equation to work out the relationship between levered and unlevered beta–and, so, estimated discount rates–makes sense.  But I’ve actually tested CAPM many times on equities that *should basically meet the CAPM assumptions* (e.g., Boeing) and the real world data is almost always inconsistent with CAPM theory.  So, I never have used the Hamada equation for anything; basically because it’s based on CAPM being true. 

And, yes, I agree … some of the many assumptions that need to be made along with CAPM and the Hamada equation seem (to me) to be beyond rational belief.

My valuation friends always say to me “But you have to use CAPM because it’s the only accepted theory there is!”  But the actual history is that APT and certainty-equivalent pricing (“risk-neutral pricing”) were developed in the mid- to late-1970s to solve the problems with CAPM.  So, we do have other accepted theories and methods … and the methods are much simpler as well.  It’s just that university professors like to teach CAPM, and hate to teach APT as it was intended.

I’ve attached an redacted example (from an actual, recent valuation report) of using APT to estimate the risk-adjusted discount rate.  I certainly don’t think any theory or estimation method is perfect, but I do think the APT method is more theoretically valid, simpler, and does not require inappropriate assumptions.

Karnen to Respondent 1:

Can you clarify further, how to operationalize this equation? the formula seems to me is not new, this is exactly WACC formula.

Ra = Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) = WACC  

Second, you draw my attention to APT. Yes, APT is a sort of mystery to me even up to now. The corporate finance textbooks give just a glimpse of the APT and its implementation. I believe most of the finance professors just stop after they finished up explaining the CAPM, and shy away from elaborating more on APT. To be honest, I can’t find one good book on putting APT on par with CAPM, meaning the book gives the same proportion as that CAPM. As far as I remember only Financial Theory and Corporate Policy (by Copeland, Weston and Shastri) textbook that is able to explain that to me. Stephen Ross wrote one book : Neoclassical Finance, but it is too technical, I guess, we need one book that could bring this APT concept to more a operational level for valuation analyst to fall in love in using them.

Respondent 1 to Karnen:

On the equation …

Ra = Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) = WACC 

… I was trying to show the following, but wasn’t very clear:

(1)  Ra = is the estimated expected risk-adjusted rate of return on the *assets* (“the project”) … maybe estimated using APT.
(2)  WACC := Rl*FV(LIAB) / FV(ASSETS) + Re*FV(EQUITY) / FV(ASSETS) is the definition of WACC; with each component Rl, Re, FV(L), FV(E), FV(A) being an estimate.
(3)  If there is no significant information asymmetry or transaction cost differential, then Ra = WACC, in which case we only need the estimate of Ra (exactly as you said).

And I agree the difference between APT and CAPM is actually very subtle; I think because if there is, in fact, only one risk factor then CAPM and APT result in the same expected rate of return.  Because of this, most professors I know just say something like “APT is just CAPM with more risk factors” … but then they don’t show that there is a difference between a *risk price* and a *risk factor* (I discuss this problem in Section 2.10 of my book).  The difference between risk price and risk factor can by thinking about the following for asset i:

APT:       Ri = Rf + B1i*RISK PRICE1 + B2i*RISK PRICE2 + B3i*RISK PRICE3 + … 

CAPM:   Ri = Rf + B1i*RISK PRICE1 = Rf + Bi*(ERm – Rf)  where (ERm – Rf) is the “capital market portfolio risk premium”

Because CAPM just assumes there is an equilibrium, (ERm – Rf) is the *risk price* for single aggregated *risk factor*.  But CAPM does not tell us how to find / estimate other risk prices, because in the CAPM equilibrium there is only the one risk price, which equals (ERm – Rf).  In contrast, APT shows how to extract risk prices from market data for any risk based on asset return sensitivities to risk factors.

I also agree with you completely with you on “all asset pricing models are about expectation- ex-ante and not ex-post, and the whole matter then revolves around the future.”  My two favorite financial economists are Fischer Black and Stephen Ross, and in my view Black was essentially a theorist and Ross an empiricist … which I think explains the difference between CAPM (Black) and APT (Ross):  In CAPM, there are unobservable / untestable assumptions; in APT there’s basically just one observable / testable assumption.

In my recent blog article, I show an example in Sections 4 and 5 of CE method valuation, and I also show in Section 5 what is most critical in asset pricing: estimating return sensitivity to risk factors.  If there is a *statistically stable* sensitivity of market returns to a risk factor, then we can reasonably make the argument that ex post risk prices can be used to estimate ex ante expected returns … or at least that’s how I think of it.

Respondent 2 to Karnen:

For myself, I guess, all asset pricing models are about expectation- ex-ante and not ex-post, and the whole matter then revolves around the future. Can use historical data to draw a conclusion or even use it to test the future? I gather, all we need is just to rely on a sense of the prob of the future events. Fisher Black once said that we should put our trust only in logic and theory and forget about statistical empirical results. (quoted from Capital Ideas Evolving by Peter L. Berstein. John Wiley & Sons, Inc.. 2007. Page 94.)

My first understanding and reaction is that if the equity holders do what you say and invest in the firm/project, clearly the wacc reduces to Ke.

Karnen to Respondent 2:

Yes. However, my point, since the shareholder could borrow by him/herself to finance the project (in reality, I have seen this before, where the equity fund is indeed coming from bank loan), then computing WACC for the project is not necessary. All project cash flows could hypothetically be discounted at Ke, even for the case, where the company borrows the money directly from the bank.

Respondent 2 to Karnen:

I don’t see clearly why if the financing with debt is done by the firm, you still say that any project could be discounted with Ke. Explain, please…

Karnen to Respondent 2:

What I would like to say is that:

The forecast cash flows of a project should not be discounted at wacc (debt and equity), but by Ke (cost of equity), the required return that the shareholder could earn from other alternative equally risky investment (in this case, I use return from stock market).

WACC becomes irrelevant since the shareholder could borrow by himself to finance the project and flow the bank loan proceeds in the form of equity.

So whether the company or the shareholders the entity that have the borrowings, it is not relevant, and thus the way discount rate is calculated from WACC.

The value of the company that itself obtains the loan (A) and the value of the company that through its shareholder obtains the bank loan proceeds (in form of equity) B)= both companies A and B should have the same value. In other words, Ke is the appropriate discount rate for both Company A and B. Otherwise Arbitrage will creep into.

Respondent 2 to Karnen:

Not sure.

Just a naive question: how would the firm know if shareholders have financed the investment in the firm?

The firm will not know. The firm will “see” that the project/firm will be financed by equityholders only  if they ask the firm pay all debt, and ok, the firm will know that the firm will be 100% by equity.

If the firm keeps debt it will have to pay interest on debt. And it will earn TS. If this is the situation, it is not clear to me why the firm should discount its projects/investments CFs at Ke and not at WACC or even at Ku in case the firm perceives that equityholders has 100% of capital. In the best case of your proposal, it would be a 100% equity funded firm and in that case the DR would be Ku and not Ke. 

In short, if the firm perceives that it is financed X% by debt and (1-X%) by equity, it might discount any project with WACC etc. If there is no debt, the project/firm CFs should be discounted at Ku.

Karnen to Respondent 2:

Let’s give you one example:

Company A: have 50%:50% mix of debt + equity

Company B: 100% equity but behind that equity, the shareholders have a mix of 50%:50% debt and equity

Do you think the value of Company A the same or not with Company B?

If the same, why, and if not why?

That’s my very basic question about this.

Respondent 3 to Karnen:

Clearly, the value of Company A is not the same as that of Company B (assuming their expected FCFs are identical, EBIT>int, no financial distress costs). 

Va=Vu+VTS > Vb=Vu

If we go to compare the wealth of shareholder in A (Wa) and the wealth of a levered shareholder in B (Wb), then with a simple algebra one can see that the conclusion depends on the income tax rates. If the tax rate for the shareholder in B equals the corporate tax rate, then Wa=Wb, otherwise Wa and Wb will differ with the sign depending on which tax rate is higher.

To avoid confusion, one should not mix the value of a project (firm) and the overall wealth position of an investor in the project (firm).

My humble beliefs

A project’s generic risk is the risk of its FCF with the associated required return Ku equivalent to the expected rate of return from an alternative equally-risky investment. 

Rates to discount the project’s cash flows will depend on a composition of claims on project’s assets (i.e. distribution of the project’s cash flow and risk) 

For all equity capital structure (only equity claim exists) the discount rate for the FCF is Ku, and for a mix of debt and equity it is WACC.

One may prefer to value an equity claim on the project directly, and in this case CFE should be discounted at Ke (with a premium to Ku for the risk of having to serve the debtholder claims on the project’s FCF first). 

Where the shareholder obtained funds to invest in the project is irrelevant, a determinant of the discount rate is the risk of the cash flow being discounted.  

Discounting FCF and Ke is visibly inconsistent and produces senseless result

Judgement by comparing the projects return with the borrowing rate makes no sense.

Karnen to Respondent 3:

Thanks for your generous comments.

You said: Clearly, the value of Company A is not the same as that of Company B (assuming their expected FCFs are identical, EBIT>int, no financial distress costs).

How come the value of Company A is not the same with that of Company B as both they are exactly the same company and produce the same forecasted cash flows)?

Pls remove first all discussions on tax, assuming we are living in a perfect MM world.

I put all these hypothetical example (all else remains the same, only the financial structure is different)

Company A: have 50%:50% mix of debt + equity

Company B: 100% equity but behind that equity, the shareholders have a mix of 50%:50% debt and equity

Other information:

  • Alternative equally risky investment return for that project = 15% (I took from stock market if the shareholder put his/her money in the stock market)
  • Borrowing rate (either going to company A or going to shareholder) = 5%

My questions:

For Company A : how much discount rate will you put there?

For Company B : how much disocunt rate will you put there?

Respondent 3 to Karnen:

Sure, sure… if we alter assumptions to a perfect MM world, then Va=Vb and tax considerations are irrelevant. However, other statements remain valid, just WACC reduces to Ku.

Let’s see how it goes in the hypothetical example suggested

An implicit assumption is “project  firm”. If not, discount rates for the firm and project would differ

It’s not clear what 15% return from an alternative equally risky investment is. Since it is said to be a return a shareholder obtains from the stock market, 15% could be Ke, if return comes from investing in a share of a levered firm, or 15% could be Ku, if the firm is unlevered. 

Let’s assume 15%=Ku (either observed directly or obtained by unlevering Ke)

Since we are in a perfect world, cost of debt capital = borrowing rate

Discount rates are as follows:    

Va = Value(Company A) = PV[ FCF at WACC ] = PV[ FCF at Ku ] = PV[ FCF at 15% ] 

Ea (or Ve(A) depending on a choice for notation) = Value(Equity claim in the Company A) = PV[ CFE at Ke ] = PV[ CFE at 15%+(0.5/0.50)(15%-5%) ] = PV[ CFE at 25% ] = 0,5Va

Vb = Value(Company B) = PV[ FCF at Ku ] = PV[ FCF at 15% ] = Value(Equity claim in the Company B) = Eb 

Obviously, Ea=0,5Eb. However, if we look at a shareholder wealth position, then in full compliance with MM  0,5Va =Ea = Wa = Wb = 0.5Eb = 0.5Vb

Indifference of a shareholder wealth position doesn’t imply that ALL cash flows could be discounted at one and the same rate.

Things become a bit more complicated if we introduce taxes

I suppose comments from Respondent 2 above have an underlying idea similar to comments above.

Karnen to Respondent 3:

Yes, under MM super perfect world, WACC = Ku, this will lead to the same valuation of Company A and Company B.

Stock market return, that I put there, that is not specific industry, we could use a portfolio of shares, since I guess, nowadays, nobody only puts his/her eggs in one company’s shares. I heard many times in the discussion with the investors, they just said that they earned such return rate from putting their money in the stock markets, and use that as the benchmark.

In practice, again, I did remember from my very early email exchanges with Ignacio, bringing Ku to the table of discussion, this is hard, since Ku is not observable. And one question to Ignacio, hopefully he still remembered that, is most of the time, (i) we need to infer Ku from Ke or even Kd (and this will lead to a long debatable topic), and (i) we don’t have at the moment, the theory to calculate directly the Ku.

Though there are many books out there showing us to unlever and relever Ke, but all of this will really depend :

whether we assume using fixed book-value leverage ratio

whether we assume using fixed market-value leverage ratio

whether we assume using preset debt

whether we assume periodically adjusted debt

and Ignacio’s favourite topic, what discount rate assumption we use for TS

etc.

I just sent you a couple of days before, one paper by Clifford S. Ang, CFA and Andrew Lin, CFA, CAIA : The Valuation Impact of Using the Wrong Leverage Ratio to Unlever Betas (http://quickreadbuzz.com/2020/04/29/business-valuation-ang-lin-the-valuation-impact-of-using-the-wrong-leverage-ratio-to-unlever-betas/, accessed on 3 June 2020)  which gives us conclusion that:

The above analysis shows that using the improper leverage ratio to unlever betas can lead to substantial valuation differentials. In a significant percentage of cases, the valuation differentials can exceed 10%. In some cases, the valuation differentials can exceed 50%. The size of the error rate is likely concerning to most valuation analysts.

Nonetheless, the point that you bring something to me is you are talking about the view from total shareholders’ wealth, which sounds interesting to me.

Respondent 3 to Karnen:


I would admit that the extensive argument you provide didn’t persuade me to give up my view: whatever the pass one takes to settle a hurdle rate for an investment decision, it doesn’t make much sense to discount all cash flows of a project (not to say all projects) at this one rate. I see you smoothly move away from your initial question to a related, but different topic, and this is another story.

Karnen to Respondent 3:

However, I came up with this question when in practice, I see even two analysts valuing the same project (part of a company) could come up with two different single rate or two different ranges of rates. When they structure the financing either the loan going direct to the company or thru the shareholders, this has brought up a different way to come up with discount rate. Again, unlever and re-lever is a painful process to explain away, which one to use and again that another debatable topic.

Again, as I put in early email to this discussion, even if we could get 5% loan, but invest in a project returning 12% while the shareholders could earn 15% from the stock market, then that project still is not feasible to go. Put something to discount rate (either WACC, whatever) for the project’s cash flows, in my practice, brings too much complication to the table.

My proposition, if the shareholder “could” borrow the loan to finance the project and flow it to the project, then he/she could increase their expected return (even higher than 15%) and then use that a benchmark to compare against the IRR of the project’s cash flows. This brings discussions becoming lighter to talk and get across. I am trying to avoid as much as possible, about Ku, re-lever & relever beta (or Ke), target leverage ratio, etc.

Respondent 3 to Karnen:

Ok, let me try to explain the point another way. I don’t see much problem, if any, with discounting at Ke (or whatsoever one may call it) regardless of who is levered, a shareholder or a firm. However, If the shareholder takes a levered position (borrows herself and pours money into the project as equity), then it would be inconsistent (in fact, a common mistake) to discount the project’s cash flow (FCF in this case) at that Ke, or compare the project’s IRR to it.

Karnen to Respondent 3:

Under Company B, all FCFs of the projects flow to shareholders, so that FCF Project = FCF Equity = CFE, and we could compare that to Ke. What is the issue with that?

Something that I need to clear off with you, again back to the stock market return. Hypothetically the money from loan creditor and shareholders, could be invested by the company as well into the stock market return, and let’s say it earns the same rate of 15%. Meaning that this investment in the stock market could be made by the shareholders themselves and by the company itself. Leaving with the option for the company, to put the money into the project (IRR 12%) and put the money into the stock market (15%), then it takes no brainer that the company should not take up that project. If you accept with the above notion, then the company doesn’t need WACC or whatever discount rate for the project. All we need to make assessment is only the IRR of the project, and the benchmark other alternative investment (in stock market or other market).

Next discussion will see what is inside the interest, since interest rates are a key factor being included in determining the cost of capital and it provides benchmarks against which to make financial and investment decisions.

Just pick up the interest rate from the market (Note: since it is relatively easier, since the rate is OBSERVABLE and updated INSTANTLY) without really understand what factors are driving the interest rate (or the yields required to induce investments of various types), it might be like a boy with a hammer, which to him, everything looks like a nail.

Question to Respondent 4:

A project will be funded by debt and equity. If the equity holder obtains his/her fund from the bank (somehow bank wants to finance this long-term equity investment in one project, through the shareholder, instead of directly funding the project. The reason might be that the loan thru the shareholder is guaranteed by other shareholder’s assets) with effective annual rate, let’s say 10%. The equity holder have two options hypothetically, invest the proceeds from the bank loan into the project, or put that into the equally risky stock investment in the capital market, yielding expected return of 15%.

My question, for the expected cost of equity for that project (which fund is obtained from loan), do we use 10% or 15%?

Respondent 4 to Karnen:

Hello Sukarnen,

This is a big issue in project finance.  In particular there is something called an Equity Bridge Loan where equity holders borrow their investment and pay it back later.  My opinion about all of the divisions in equity is that first, the overall equity IRR should be evaluated.  In addition you can compute the distribution of equity and investors that have put less risk in the development should accept a lower IRR.


Unlike corporate finance, you can find real data on the cost of capital from transactions where projects are bought and sold and there is a good estimate of the returns investors are willing to accept.



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Effective Annual Interest Rate in Topping Up Your eMoney or eWallet

Readers,

I am a bit intrigued to think about the top up fee that we need to pay to replenish our eMoney or eWallet, for example, I found the example, where we need to pay Rp 1,000 for each top up transaction. Since this world is driven by interest, which is the mother of economy, then I guess, somehow I should relate this top up fee to interest that I have to pay implicitly.

How to do this?

Let’s say, the case is:

  • we want to top up Rp 300,000 with a top up fee Rp 1,000.
  • we replenish this top up every two weeks, meaning that Rp 300,000 will be used up to buy food, transportation, etc.

So how much is the implicit effective annual interest rate that we need to pay:

The analysis is shown below.

The implicit effective annual interest rate is 8.43%. This seems to me quite high since this is not too far from working capital borrowing interest rate, though we don’t borrow anything from anybody, as that’s pretty much our own money.

I will go further by having sensitivity analysis with one-factor change, that is the replenished amount, and keep the remaining assumption constant.

Sensitivity (1) One Factor : The Replenished Amount (IDR)

The chart below demonstrated that the effective annual interest rate will fly from 62% for replenished amount of Rp 50,000 declining to near to 5% for the replenished amount of Rp 500,000. This will mean that the higher amount that we replenished, then the lower effective annual interest rate that we need to pay for this top up transaction.

How about if we keep all assumptions constant, but the frequency of the top up?

Sensitivity (2) One Factor : The Frequency of the Top Up (in Days)

From the above chart, we could see that the longer days that we do this top up transaction, then the interest will decline from near 30% (if we fill up the top up every 5 days) to near 2% (for every 60 days) with the amount of Rp 300,000 every time we top up the emoney or ewallet.

How about if we make the amount of the replenishment and the frequency of the top up becoming variable?

Sensitivity (3) Two Factors : The Replenished Amount (IDR) and the Frequency of the Top Up (Days)

The above table gave us that the effective annual interest rate is quite far by wide margin. If we top up Rp 50,000 every 5 days, then the interest rate will be 324%…wow is this really what we paid?

If we top up Rp 500,000 every 2 months (+/- 60 days), then the interest is around 1,18%, this sounds very low.

So what we could get something out of this analysis:

  1. All fees that we pay, there is implicit effective annual interest rate that we need to pay to the service provider.
  2. The top up fee of Rp1,000 may sound small money, but when we link that fee to the frequency of the top up transactions and the amount being replenished, that small amount might give us interest rate that shoots through the roof.
  3. The old adage will ring again, watch your spending habits. My two-cents suggestion: drive your car till it drops!