An Alternative Way to Measure Private Equity Performance

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1 An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate equty nvestments. It s wdely recognzed that there are problems wth IRR. One problem s that IRR uses a dscount factor (the IRR tself) that may have no relaton to the relatve dscounted values that ratonal nvestors would assgn to cash flows that occur at dfferent ponts n tme. When IRR s hgh the dscounted values of later cash flows can be too low, and so earler dstrbutons can be unreasonably preferred over much larger but later dstrbutons. Conversely, f IRR s low the dscounted values of later cash flows are exaggerated. Another measure of prvate equty performance s Modfed IRR (MIRR). Whle we beleve that MIRR s an mprovement over IRR n some ways, we show that t has a potentally serous problem. Another common measure of performance for prvate equty nvestments s the Investment Multple (or TVPI, for Total Value over Pad In) whch s smply the rato of total dstrbutons 1 dvded by total nvestment. The problem wth Investment Multple s that t does not consder the tmng of cash flows a payout of $10 n year or year 10 s treated the same. Here we propose two new alternatve measures of prvate equty performance: Dscounted Investment Multple (DIM) s smlar to the standard Investment Multple except that cash flows are dscounted usng approprate dscount rates. We beleve DIM can provde nvestors wth a more relable ndcator of prvate equty nvestment performance. Annualzed Equvalent Return ( ) s qute smlar to MIRR but solves a sgnfcant problem wth MIRR. The calculaton of also produces an addtonal useful statstc, Equvalent Years ( ), whch gves the average length of tme that captal was nvested. When s presented along wth nvestors can get a more complete understandng of nvestment performance. Problems wth Exstng Measures of Performance Problems wth IRR The varous problems wth IRR are well recognzed. Wkpeda gves a good descrpton of these problems. Here are some quotes from the Wkpeda artcle: 1 Any resdual value s treated lke a fnal dstrbuton. We assume ths treatment of resdual values throughout ths paper. See 1

2 As an nvestment decson tool, the calculated IRR should not be used to rate mutually exclusve projects (.e., should not used to compare nvestment alternatves). IRR overstates the annual equvalent rate of return for a project whose nterm cash flows are renvested at a rate lower than the calculated IRR. Snce IRR does not consder cost of captal, t should not be used to compare projects of dfferent duraton. Despte a strong academc preference for NPV [net present value], surveys ndcate that executves prefer IRR over NPV. Despte such advce to the contrary the wde use of IRR to compare prvate equty nvestments apparently perssts. We beleve that one reason for ths s that the common explanaton of the man problem wth IRR IRR assumes renvestment of nterm cash flows n projects wth equal rates of return may not suffcently resonate wth nvestors. An alternatve way to look at the problem s that IRR uses a dscount factor (the IRR tself) that may have no relaton to the preferences of a ratonal nvestor. Consder the followng example cash flows for two prvate equty nvestments: Example 1. Investment A Investment B Cash Flow Cash Flow Cash Flow Dscounted Cash Flow Dscounted Year by IRR by IRR Sum % 110.% The dfference n the cash flows for the two nvestments s that Investment A gets an extra dollar n year 1, whereas Investment B gets an extra twenty dollars n year 5. The IRRs are nearly dentcal. However, would actual nvestors see these two nvestments as equally desrable? Maybe wth hypernflaton! The problem s that by defnton the IRR s beng used to dscount the cash flows so that the sum of the dscounted cash flows s zero. Gven the hgh IRR, the $0 n year 5 gets a nearly neglgble present value of 9 cents. The Problem wth Modfed IRR Modfed IRR 3 (MIRR) has been suggested as an mprovement to IRR. The calculaton of Modfed IRR (MIRR) s actually very dfferent than IRR. It uses two pre-specfed dscount rates: a fnance rate (FR) 3 See

3 that s appled to nvestments (negatve cash flows) and a renvestment rate (RR) that s appled to dstrbutons. All nvestments are dscounted back to the tme of the ntal cash flow to obtan a present value (PV). All dstrbutons are dscounted forward to the endng tme to obtan a future value (FV). The MIRR s then calculated from the formula (1) where s the number of years. Ths seems lke a sensble way to calculate return, so what s the problem? Example llustrates that MIRR can be overly senstve to small changes n cash flows. Example. Cash Flows Year Investment A Investment B Sum * 3.5% 100.0% *FR=10%, RR=10% Here nvestments A and B are actually very smlar. However, the small changes n cash flows result n a bg change n MIRR because for nvestment A the number of years ( ) s 5, whereas for nvestment B t s 1. Probably t s not possble to develop a sngle annualzed return number that can relably dstngush preferable nvestments when those nvestments can be over very dfferent tme perods. For example, 50% sounds better than 35%, but s t better to get 50% for 1 year or 35% for 3 years? Problems wth the Investment Multple (TVPI) Investment Multple (or TVPI, for Total Value over Pad In) s smply the rato of the total value of dstrbutons dvded by the total nvestment. For example, f $100 s pad n, and $175 s eventually pad out, then TVPI s The problem wth TVPI s that t does not consder the tmng of cash flows a payout of $10 n year or year 10 s treated the same. Snce cash flows from prvate equty nvestments can occur over many years t s smply not reasonable to gnore the tmng of such flows when consderng nvestment performance. 3

4 Proposed Alternatve Measures of Performance Dscounted Investment Multple (DIM) Net Present Value (NPV) s a wdely accepted method to evaluate the value of nvestments based on assocated cash flows. Wth NPV all cash flows are dscounted to the present (the begnnng of the nvestment) and summed. Dfferent rates mght be used to dscount nvestments and dstrbutons. The result s the gan or loss of value (n dollars) assocated wth the nvestment. Whle fundamentally sound, NPV n dollars s probably not the most convenent statstc for evaluatng nvestment performance. Fortunately t s easy to convert ths to a rato smlar to the Investment Multple. We just need to separate the postve and negatve cash flows and dscount both to the begnnng of the nvestment to obtan the Present Value of Investments (PVI) and Present Value of Dstrbutons (PVD). NPV s the sum of PVI (whch s negatve) and PVD. Dscounted Investment Multple (DIM) s defned as Ths rato s conceptually smlar to Investment Multple but a much better ndcator of nvestment performance snce t consders the tmng of cash flows. If t s desred to have just one number to compare the desrablty of prvate equty nvestments, then we would suggest that DIM s superor to ether IRR or MIRR. Annualzed Equvalent Return (AER) We can convert DIM to the form of a return by smply subtractng one, whch yelds the percentage ncrease n present value resultng from the nvestment. However, ths s not an annualzed (or maybe monthly) return lke IRR or MIRR. Snce nvestors are accustomed to per-perod (typcally annualzed) returns we have also developed an annualzed return statstc called Annualzed Equvalent Return (AER), whch we beleve has advantages over IRR and MIRR. MIRR dscounts all nvestments to the tme of the frst nvestment, and dscounts all dstrbutons to the tme of the last dstrbuton. MIRR s then calculated as f a sngle nvestment had been made at the very begnnng, and a sngle dstrbuton receved at the very end. Ths defnton of the number of years ( n equaton 1) s what causes the over-senstvty to small changes n cash flows llustrated n example. Instead we propose to calculate the Average Tme of Investments (ATI) as the (weghted) average tme of dscounted nvestments, and the Average Tme of Dstrbutons (ATD) as the average tme of dscounted dstrbutons 5. We then use ATI and ATD as the equvalent begnnng and endng dates of the nvestment. For example A ths results n an ATI of years, and an ATD of years. We then proceed smlarly to MIRR as follows: Dscount nvestments to ATI (1.886 years) at fnance rate (10%), to obtan. () See 5 For the purpose of calculatng the weght-average tme of nvestments and dstrbutons t does not matter what tme the nvestments and dstrbutons are dscounted to, snce t does not affect ther relatve weghtng. Therefore, for smplcty we dscount to tme zero.

5 Dscount dstrbutons to ATD (3.079 years) at renvestment rate (10%) to obtan. Calculate the Equvalent Years (EY) as We beleve that EY can be a useful number to help evaluate a prvate equty nvestment, along wth AER. Calculate AER from equaton 3, whch s nearly dentcal to equaton 1. (3) Ths ndcates that example A s smlar to a sngle nvestment for 1.19 years and returnng 78.8% annually. Rather than call ths new calculaton somethng lke mproved modfed IRR we propose to call t Annualzed Equvalent Return because as defned t results n an annualzed number, and because t s calculated as the return of an equvalent nvestment wth a sngle cash flow n and out. We propose that EY should be presented along wth AER to gve nvestors a better understandng of prvate equty nvestments. Annualzed Equvalent Return Example Calculaton Snce ths procedure for calculatng AER may seem a lttle complex let s work through an example n more detal: Example 3. Year Cash Flow Dscounted to year Agan we are usng a dscount rate of 10% for both fnance and renvestment. Though not needed for the calculaton of AER, we can calculate DIM from these dscounted cash flows usng equaton as 5

6 The average tme of nvestments s ATI P 0 P DCF P 0 DCF 0 ( 100) 1 ( 5.5) ( 100) ( 5.5) The average tme of dstrbutons s ATD P 0 P DCF P 0 DCF Thus on average nvestments were made at tme years, and dstrbutons were receved at tme years. On average, captal was nvested for = 3.58 years (ths s EY). Now we dscount the cash flows to tmes ATI or ATD, as shown n the followng table: Fnally, we calculate AER from Year Cash Flow Dscounted Dscounted to ATI to ATD Total Whle ths s by no means a trval calculaton, t s actually much smpler than IRR. We can supply an Excel functon to calculate ths to anyone who s nterested. Dscusson of Dscount Rates MIRR, DIM, and AER all allow for nvestments and dstrbutons to be dscounted at dfferent rates. Investments should certanly be dscounted at a rate that reflects the cost of fnancng. It may make sense to dscount dstrbutons at a hgher rate. In the case of MIRR ths was defned as the renvestment rate, mplyng the rate avalable for renvestment of dstrbutons. Ths could also be vewed as a Requred Rate of Return that n addton to fnance cost ncludes a component to account for the extra return (rsk premum) requred by an nvestor to compensate for uncertanty and llqudty. However, ths approach has been crtczed by some because the compoundng of the rsk premum over years may exaggerate the relatve rsk assocated wth later cash flows. In general ths s a complex topc whch we won t at- 6

7 tempt to resolve here. We note that n the case of DIM, f a rsk premum s ncluded n the rate used to dscount dstrbutons then any multple above 1.0 should be vewed as attractve. If no rsk premum s ncluded then a hgher threshold of attractveness would be warranted. In the case of AER we beleve that t s better not to nclude any rsk premum when dscountng dstrbutons. The resultng return then has no rsk adjustment and s thus more convenently comparable to other returns that typcally are not rsk adjusted. It can be compared to the return the nvestor expects to acheve wth smlarly rsky nvestments. Summary of Examples The followng table restates the results of examples 1- ncludng all statstcs we have dscussed. Cash Flows for Examples Year 1A 1B A B IRR 110.0%A 110.% 76.0% 100.0% 50.0% TVPI MIRR 110.0% 37.6% 3.5% 100.0% 36.5% DIM AER 110.0% 68.5% 78.8% 100.0% 7.7% EY Note that AER by tself does not pck example 1B as a preferable nvestment to 1A. However, wth the addtonal nformaton provded by EY (equvalent years) the nvestor can get a better pcture and see that 1B s lkely preferable. Concluson We suggest that Dscounted Investment Multple (DIM) provdes a better overall ndcator of prvate equty performance than IRR or MIRR. It s closely based on the theoretcally well-establshed Net Present Value, but rearranged n the form of a rato that s more convenent for comparng nvestments. We also suggest that Annualzed Equvalent Return (AER) provdes a useful ndcator n annualzed return form that should always be preferable to the smlar MIRR, and also has some advantages over IRR. When AER s presented together wth the related Equvalent Years (EY) t should convey a better understandng of an nvestment than IRR or MIRR alone. 7

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