This article was co-authored with Prof. Janakiraman at my alma mater, IIM Lucknow, and was published as part of IIM Lucknow's working paper series in 1999. The article was based on my experience as a sales executive with Philips, where I was intrigued by the relationship between volume discounts offered to authorized dealers and the prevalence of wholesaling between authorized dealers and sub-dealers. It was great fun to create a theoretical model to estimate the "optimum" volume discounts in various scenarios, though I am pretty sure this article does not have any practical utility at all.
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A STUDY OF COSTS & PROFITABILITY
IN A DISTRIBUTION CHANNEL FOR DURABLES
Contents
INTRODUCTION
Case 1. all brands have equal margin, but no volume discounts
Case 2. brands have unequal margins, but no volume discounts
Case 3. volume discount, but no quantity slab
Case 4. volume discount with slab, but no wholesaling
Case 5. volume discount with slab and with wholesaling
Figures 1 - 25
INTRODUCTION
In managing its distribution channel, a durables brand in the Indian market has to control the key channel variables :
(a) number of dealers / wholesalers / distributor's retailers to be serviced,
(b) the margin to be given to the dealer / wholesaler / distributor's retailer,
(c) the value of the volume discount to be given to the dealer for bulk purchase,
(d) the minimum quantity to be purchased by the dealer to qualify for the volume discount
Durables brands in India usually decide on these variables on the basis of experience and judgement. There is at present no theory to explain how these channel variables impact the profitability of the brand and the dealer, and to help the brand determine the optimum margins, number of dealers to be serviced, etc. This paper attempts to build up a theory of the channel dynamics for durable goods, by analysing the channel in terms of its costs and profitability.
In doing so, our theory must take into account that distribution channels in India have several complicating factors :
(a) brands may use more than one channel structure ( direct dealers / wholesaling / distributor channels ) at the same time,
(b) dealers usually try to 'convert' customers from low-margin brands to those which give them high dealer-margins,
(c) large dealers often buy in bulk from brands offering volume discounts, and sell ( 'wholesaling' ) to smaller dealers, sharing the volume discount among them,
(d) customers check out prices across several showrooms before buying, thereby causing the dealers' selling prices to converge to a 'market-ruling price',
(e) when brands offer credit to dealers for their purchases, and when customers pay for their purchases in cash, dealers stand to make huge profits even if they give large discounts to customers to clinch the sale.
To analyse the impact of all these variables, we first consider the case of a simple dealer channel where these complications do not exist, and then factor in these complications one by one, to arrive at a more comprehensive model that captures the dynamics of our real-life markets.
The simple model we first consider, in Chapter -1, assumes that :
(a) all brands have equal dealer margins
(b) dealers do not hold excess stock
(c) dealers do not engage in wholesaling among themselves
(d) consumers' dealer-preferences are independent of their brand preferences
(e) brands do not give credit to dealers for their purchases
(f) brands do not offer volume discounts to dealers for bulk purchases
Note : All figures are shown at the end.
1. all brands have equal margin, but no volume discounts
1.1 Consider a simple dealer channel for durables in the Indian context. Assume that there are a large number of dealers in the market, and a small number of brands. Assume that all dealers sell all brands, and assume that brands sell directly ( i.e., not wholesaling or distributor channel ) to the dealer. Assuming there is no wholesaling or carrying of excess stock, the dealer buys from the brands whatever quantity is purchased by the customer. If there is no difference between the margins or other terms offered by the different brands, the dealer will have no reason to prefer one brand over another. Thus the brand-wise sales made from his shop will mirror exactly the brand-wise purchase preferences expressed by the customer. The brand-wise purchase preferences expressed by the customers will be a function of the relative perceived costs and benefits of the various brands. Assuming that whatever customer segments and brand preferences exist in one area will also exist in other areas in the given market ( city / state ), the demand for each brand can be expressed as a certain fixed fraction of the total market. For example, the cost / benefits for a brand 'A' might be so perceived by the various customer segments that 15 % of total customers in the given market ( city / state / etc. ) prefer brand 'A'. Similarly 20 % of all customers in the market might prefer brand 'B', 5 % for brand 'C', and so on. This proportion of demand is assumed to hold good for the entire market, so the demand for the product as experienced by each dealer will also be in the same proportion. If 100 customers walk into dealer 1's showroom in a month, they will buy 15 pieces of brand 'A', 20 of brand 'B', 5 of brand 'C', and so on. This assumes that customers' preference for a particular dealer will be related only to attributes like distance from place of residence, accessibility of dealer's location, decor and service, reputation, etc., and not to the brand preference. Essentially, we assume that a customer's brand-preferences are independent of his dealer-preferences. Thus the sales volumes in each dealer's showroom may vary, but the brand-wise preference proportions will remain the same.
1.2 The proportion of customers in a market who express a purchase preference for a particular brand can be termed the 'PREFERENCE SHARE' for that brand in the given market. The 'preference share' is unique for each brand, depending on its perceived costs and benefits. If the dealer does not prefer one brand to another ( which happens if brands are identical in the terms they offer to the dealer ), the brand-wise proportion of sales from his shop will be identical to the preference-shares for the different brands, which is what the customers would have demanded on their own. For the market as a whole, the market-shares of the different brands will be equal to their preference-shares.
1.3 Thus if M is the size of the given market (city or town) in sets per year, and if X'A, X'B, X'C are the preference-shares for brands A, B and C, then their sales (in sets per year) in the given market, SA, SB, SC, can be expressed by Equation - 1 :
SA = X 'A. M ..... ( Eq. 1 )
SB = X 'B. M
SC = X 'C. M, and so on.
1.4 A dealer's sales level can be expressed in terms of his counter-size, which gives the monthly sales ( sets per month ) of the dealer. If CS1, CS2, CS3 are the counter-sales of dealers 1, 2 and 3, then
M = CS1 + CS2 + CS3+ - - - ..... ( Eq. 2 )
What is true for the market must be true for each dealer, so we have
sA1 = X 'A . CS1 ...... ( Eq. 3 )
sB1 = X 'B . CS1
and so on, where sA1 is the sales for brand A from dealer 1, sB1 is the sales for brand B from dealer 1, etc.
Assuming all dealers stock and sell all brands, we have
CS1 = sA1 + sB1 + - - - ...... ( Eq. 4 )
CS2 = sA2 + sB2 + - - -
For brand A, its sales in the market, ( SA ) will be composed of the counter-wise sales it gets from all dealers, as shown below
SA = sA1 + sA2 + sA3 + - - - ...... ( Eq. 5 )
= X 'A . CS1 + X 'A . CS2 + X 'A . CS3 + - - -
= X 'A . ( CS1 + CS2 + CS3 + - - - )
= X 'A . M
which is the same as Eq. 1.
1.5 Counter-size varies from dealer to dealer, depending on their location, stock-carrying capacity, decor, display, demos given, advertisements, discounts given, and so on. While dealers situated in important locations and with large showrooms get a lot of customers, those in more remote locations and with smaller showrooms get fewer customers. The top few dealers often sell several times what the medium size dealers sell, and they in turn sell many times what the smaller dealers sell. If we were to rank dealers in the order of their counter-sales, and if we were to plot their counter-sales in a chart, we would get the chart shown in Figure 1 (all figures are shown at the end).
1.6 Assuming all dealers sell all brands, the counter-sales curve in Figure 1 can be broken down into a series of brand-wise dealer-wise sales curves shown in Figure 2. For a particular brand, the dealer-wise sales will be as shown in Figure 3.
1.7 The cumulative sales of a given set of dealers in a market is described by its 'market reach'. For a given set of dealers, market reach is defined as the ratio of the total sales of the set of dealers to the sales of all dealers in the market. This is shown by the 'Market Reach' curve in Figure 4. All dealers put together - i.e., 100 % of the dealers - account for 100 % of the market size, M. Just 10 % of the dealers ( in decreasing order of counter-size ) may account for as much as 50 % of the total market, 20 % of the dealers may account for 70 % of M, 30 % of the dealers may account for 80 % of M, and so on. Thus the market reach 'MR' of the top 10 % of the dealers would be 0.5, and that of the top 20 % of the dealers would be 0.7, and so on.
1.8 If the brand A sells to 100 % of the dealers in the market, it will have a sales level of SA . Consider a case where the brand sells only to a limited set of dealers - upto N dealers, say. Assuming that customers are not band-loyal enough to search for a showroom that stocks their preferred brand, its sales will be
sales = X 'A . ( CS1 + CS2 + CS3 + - - + CSN )
The market reach of this set of N dealers, MR1, is given by
MR1 = ( CS1 + CS2 + CS3 + - - + CSN ) / M .... ( Eq. 6 )
Thus brand A's sales will be
sales = X 'A . MR1 . M ...... ( Eq. 7 )
From dealers 1, 2, 3 - - - upto N, brand A will continue to get the same level of sales as before, but for dealers after N, it will get no sales at all. .
1.9 Thus if the brand sells to just 10 % of the dealers (in decreasing order), it will have a sales level of 0.5 SA, if it sells to 20 % of the dealers it will have a sales level of 0.7 SA, and so on. If a brand A sells to a limited number of dealers, such that the market reach of the given set of dealers is MR1 (say for example MR1= 0.7 corresponding to 50 % of dealers being covered), then its sales will be
sales = MR1 . ( X 'A . M )
and its market share will be
market share = MR1 . X 'A ....... ( Eq. 8 )
Unless the brand sells to all dealers in the market, its market-share will be less than its preference-share. The larger the proportion of dealers it sells to ( i.e., the higher its market reach ), the closer its market-share approaches its preference-share.
1.10 To maximise sales - upto its maximum potential level of ( X 'A . M ) - the brand should maximise its market reach. Other things being equal, a brand will try to sell to all dealers in the market, so that its market reach becomes 100%, and so that its sales reaches ( X 'A . M ). But as a firm sells to more and more dealers, other things don't remain equal. Its costs rise disproportionately with the number of dealers it has to service. By increasing the number of dealers it sells to, a brand benefits through (a) larger contribution from sales, as the fixed contribution margin is applied over a larger sales volume, and (b) the effect of economies of scale, due to which the contribution margin itself rises as the sales volume rises ( beyond a point, however, diseconomies of scale set in, and the contribution margin falls as sales volume rises ). The costs associated with increasing the number of dealers is the incremental 'transaction cost' ( both fixed and variable ) in servicing the extra dealers. When a brand has a small dealer base, its incremental market reach ( and hence incremental sales ) for every single new dealer being added is higher than it is for a brand already having a large number of dealers. As the brand adds more dealers, its incremental market reach diminishes continuously. This follows from the diminishing counter-sales curve of Figure 1 : while the new dealers added initially are big dealers, ultimately the brand will have to add smaller and smaller dealers.
1.11 To service each set of new dealers, the brand will have to appoint new salesmen, and bear the costs of salary, order-booking, transportation, accounting and so on. For the most part, these costs are directly proportional to the number of dealers added by the brand, and the incremental cost ( say Rs. 50,000 per annum per new dealer added ) is fairly constant over a large range. The incremental contribution from adding new dealers, we have seen, falls steeply as the number of dealers increases. To decide the appropriate number of dealers it must service, the brand has to compare the incremental contribution gain from adding new dealers to the incremental transaction cost involved. The net incremental profit in adding new dealers ( i.e., the difference of the incremental contribution over the incremental transaction cost ) normally falls as the firm adds more and more new dealers, owing to the behaviour of the two costs over different sales levels. There could be rare instances where this net incremental profit is always positive for the brand, for any number of new dealers it adds ( i.e., the brand must ideally sell to all dealers in the market ). There could also be rare instances where this net incremental profit is always negative for the brand, for any number of new dealers it adds ( i.e., it must not add any new dealers, and it must ideally reduce the number of dealers it has ). But in most cases, we would expect that the net incremental profit ( which is continuously diminishing at every stage ) is positive upto a point, and then turns negative as more new dealers are added. This point, where the net incremental profit turns negative, represents the optimum number of dealers for the brand.
1.12 The incremental contribution and the incremental transaction cost for a brand can be studied in terms of two variables, 'effective Contribution Margin' and 'Transaction Cost per set'. The 'effective Contribution Margin' is the contribution margin per set retained by the brand after the fixed selling expenses have been taken care of. For example, if the transfer price from the factory to the selling division is 70 %, the contribution margin is 30 %, or Rs. 3000 per set if the selling price is Rs. 10,000 per set. If the fixed selling expenses ( the per annum cost of office space, furniture, computers, support staff, etc. ) is Rs. 50 lacs per year, then the 'per set fixed expenses' come to Rs. 1,000 per set for a sales volume of 5,000 sets per year. The difference between the two, i.e., Rs. 2,000 per set, is the 'effective Contribution Margin' ( or 'effective CM' ) faced by the selling division, at a volume of 5,000 sets per year. The 'effective CM' can be viewed as a kind of transfer price facing the selling division, after the production costs and the fixed selling costs are met. The 'fixed cost per set' varies with the sales volume ( and hence with the number of dealers), and so does the 'effective CM'. So long as the transaction costs for new dealers is less than this 'effective contribution margin', the brand will appoint new dealers. In Figure 5, the 'effective contribution margin' curve is shown as the difference between the 'contribution margin' curve and the 'fixed cost per set' curve, for different sales volumes.
1.13 The 'Transaction Cost per set' ( or 'TC per set' ) for a brand is the variable cost incurred by it in selling one additional set - it includes the salary and travel costs of the salesman, transportation cost, etc. The 'TC per set' can be obtained from dividing the 'Transaction Cost per dealer' by the 'sales per dealer'. The cost of servicing a dealer varies according to the size of a dealer. Larger dealers need to be visited more often, need more frequent deliveries, and need more management time than small dealers, hence the transaction cost per dealer is greater for larger dealers than for smaller dealers. Firms usually classify dealers into A - B - C categories depending on their sales potential ( which, we assume, is directly related to their counter-sales volume ), and stipulate different dealer-contact norms for various categories. Thus for an "average" dealer if the 'TC per dealer' is Rs. 50,000 per annum, and if all dealers have equal dealer contact norms, the 'transaction cost per dealer' would be Rs. 50,000 per dealer for all dealers. Since dealer contact norms are unequal, a large dealer might have a 'TC per dealer' of Rs. 200,000 per annum, a medium dealer might have a 'TC per dealer' of Rs. 50,000 per annum, and a small dealer might have a 'TC per dealer' of Rs. 25,000 per annum, for instance. The 'TC per dealer' curve is thus a steadily falling curve, as shown in Figure 6. The 'sales per dealer' curve, as shown in Figure 1, is also a steadily falling curve, but falls more steeply ( for reasons we needn't go into here ) than the 'TC per dealer' curve. As seen from Figure 7, 'TC per dealer' divided by 'sales per dealer' is smaller for small dealer-strengths than it is for higher dealer-strengths, since the 'sales per dealer' curve falls more steeply than the 'TC per dealer' curve. Since 'TC per set' is simply 'TC per dealer' divided by 'sales per dealer', we conclude that 'TC per set' is a steadily rising curve, as shown in Figure 8.
1.14 The net incremental profit for the brand is calculated as the difference between 'CM effective' and 'TC per set', for various levels of dealer-strength. This is graphically shown in Figure 9. The 'TC per set' curve cuts the 'CM effective' curve at two levels of dealer strength, indicated by D1 and D2. For dealer strengths less than D1 and for dealer strengths greater than D2, the net incremental profit margin is negative. Below D1, the fixed selling-cost component is so high that the net incremental profit is negative. Above D2, the TC / set becomes so high that it exceeds the CM effective. Thus the feasible dealer strength for a brand lies in the range D1 to D2.
2. brands have unequal margins, but no volume discounts
2.1 When brands have unequal margins, dealers have an incentive to sell more of the high-margin brands and less of the low-margin brands. If customers do not have sufficient information to make their brand choice, or if their brand-preferences can be over-ridden by the dealer's recommendation, the dealer will be able to 'convert' customers from the low-margin brand to the high-margin brand. If the customers' brand-preferences are very fixed and they cannot be 'converted', the dealer will be forced to sell brands in the same proportion as is demanded by the customer by their natural preferences. The dealer incurs a 'conversion cost' in pushing his favourite brand - this includes the extra time spent by the sales staff in giving demonstrations to the customer, making a sales pitch, countering the customer's objections, offering discounts to close the sale, cost of keeping larger stock and better display, and so on. While some customers can be converted easily, others can be converted only with great difficulty, and other customers fall somewhere in the middle of this continuum. Thus the conversion cost faced by the dealer varies from customer to customer. For a given margin differential between brands, the dealer will find it worthwhile to convert customers only upto a point. Beyond this the dealer will have to convert increasingly 'tougher' customers, and his conversion cost could exceed the margin differential. Thus the degree of brand conversion done by the dealer is directly proportional to the magnitude of the margin differential. If dealer margins are unequal, the dealer will try to convert customers from other brands to the one offering the highest margins, but it can rarely happen that the conversion cost for the dealer for all his customers ( even the most loyal customers of other brands ) is more than the fixed margin differential he gets. Due to diminishing returns, the brand will not find it economically viable to offer the huge margin differentials required to help the dealer get 100 % conversions. Moreover, the brand which focuses on the 'dealer push' strategy will have much less customer pull than another which focuses on the 'customer pull' strategy, hence the dealer will find it more difficult to convert. This is why, even with the wide margin differentials prevalent in the market, rarely do we find dealers focusing exclusively on one brand.
2.2 Consider brand A whose margin mA is higher than the margin m'A given by the all other brands, such that
mA = m'A + ( d m'A )
where ( d m'A ) is the margin differential offered by brand A
Since the dealer will now try to convert customers of other brands to brand A, the proportion of brand A in his showroom sales will go up from the previous X 'A. Let the new proportion be X A = X 'A + ( d X 'A ). Thus brand A's new sales in the market will be
SA = X A . CS1 + X A . CS2 + X A . CS3 + - - -
= X A . M
The old and new dealer-wise sales curve for brand A is shown in Figure 10.
2.3 While the margin differential will cause the brand-wise sales proportions from the dealers to change, we assume that it will not cause any changes in the counter-sales of the dealers. For the brand that has hiked its margins, its 'sales per dealer' will go up, but its 'TC per dealer' will not change. Its 'CM effective' will go down, as the extra margin reduces the selling price, as shown in Figure 11. As 'sales per dealer' goes up, and 'TC per dealer' remains the same, the 'TC per set' also comes down, as shown in Figure 12. The drop in 'TC per set' is substantial initially, but diminishes as we go towards the smaller dealers.
2.4 As both the 'CM effective' and the 'TC per set' decrease, the net incremental profit also changes. The change in the net incremental profit depends on whether the increased sales due to the extra margin is sufficient to decrease the 'TC per set' more than the reduction in 'CM effective'. This is shown in Figure 13.
2.5 Before the hike in the margin from ( m'A ) to ( m'A + d m'A ), the sales of the brand A in the market was
SA = X 'A . M
assuming all dealers sell all brands. With the hike in the margin, the new sales level for the brand is
SA = ( X 'A + d X 'A ) . M
The incremental sales for the brand, in sets per annum, is
( d SA ) = M. ( d X 'A )
The incremental contribution generated by the hike in the margin is
= M. ( d X 'A ) . P. c ..... ( Eq. 9 )
where P is the selling price of the set in Rupees, and c ' is the contribution margin for the brand.
The incremental cost incurred by the brand in getting this extra volume of sales is
= ( d m'A ) . ( X 'A + d X 'A ) . M ...... ( Eq. 10 )
For the brand to break-even in giving this extra margin, this extra cost ( Eq. 10 ) must be matched by the extra contribution ( Eq. 9 ). Thus at break-even, we have
M. ( d X 'A ) . P. c = ( d m'A ) . ( X 'A + d X 'A ) . M
Thus
( d X 'A ) / [ ( X 'A + d X 'A ) ] = ( d m'A ) / [ P. c ]
Since ( d X 'A ) is far less than ( X 'A ), we have
( d X 'A ) / ( X 'A ) = ( d m'A ) / ( P. c ) .... ( Eq. 11 )
2.6 Given P, c and ( X 'A ) for a brand, ( Eq. 11 ) gives the minimum degree of conversion ( d X 'A ) required for a dealer margin hike ( d m'A ) to be feasible. If the brand is not able to get this minimum degree of conversion, the hike in the margin will not make sense.
3. volume discount, but no quantity slab
3.1 Here we consider the case of a brand which offers a volume discount, but does not keep a minimum offtake restriction. All dealers, irrespective of their offtake, can avail of this volume discount. Thus a volume discount without a minimum slab has the same effect as an increase in the normal dealer margin. The impact of such a volume discount on the brand's net incremental profit is exactly the same as in the previous case of the increase in the dealer margin.
3.2 Due to the volume discount, the 'sales per dealer' goes up for the brand, while the 'TC per dealer' remains the same. Hence the brand's 'TC per set' goes down. The 'CM effective' for the brand comes down, since effectively the selling price has been reduced. From the 'TC per set' and the 'CM effective' curves, we can arrive at the 'net incremental profit' curve, as in the previous case ( shown in Figure 13 ).
3.3 If ( d yA ) is the amount per set being offered by brand A as the volume discount, then the extra sales generated by the volume discount is, as before,
d SA = M. ( d X 'A )
The incremental contribution obtained by the brand is M. ( d X 'A ) . P. c.
The incremental cost borne by the brand in getting this extra sales is
= ( d yA ) . ( X 'A + d X 'A ) . M
For break-even, we have
M. ( d X 'A ) . P. c = ( d yA ) . ( X 'A + d X 'A ) . M
Thus
( d X 'A ) / [ ( X 'A + d X 'A ) ] = ( d yA ) / [ P. c ]
As before, for ( X 'A ) > > ( d X 'A ), we have
( d X 'A ) / ( X 'A ) = ( d yA ) / [ P. c ] ...... ( Eq. 12 )
3.4 If the brand cannot get its dealers to generate at least this minimum level of conversion ( i.e., d X 'A ), it is not viable for the brand to launch this volume discount. Given P, c and ( X 'A ) , our ( Eq. 12 ) gives the minimum levels of conversion ( d X 'A ) required for break-even, for various levels of volume discount ( d yA ) that the brand can offer. From experience or from limited-scale experimentation, a brand can estimate the different levels of conversion it can expect for different levels of volume discount that it might offer. For any level of volume discount, if the level of conversion is less than the break-even required, the volume discount is not feasible for the brand.
4. volume discount with slab, but no wholesaling
4.1 We now consider a channel where a brand offers a volume discount with a minimum slab ( we still assume there is no wholesaling in the market ). Figure 14 shows the dealer-wise sales for brand A in relation to its minimum offtake slab, ( SS ). We examine in detail the case of four types of dealers - shown in the Figure 14 as G, K, M and N.
Let ( d yA ) be the amount per set being offered by brand A as the volume discount, and ( SS ) be the minimum offtake slab required for the dealer to qualify for the volume discount. Large dealers like G, whose normal offtake for brand A is more than ( SS ), will easily qualify for the volume discount. For these large dealers, brand A has effectively increased its dealer margin by ( d yA ). Brand A's sales from these showrooms will rise marginally due to the conversion effect, since the dealer's preference for brand A will increase. For these large dealers, the normal offtake without a volume discount is
X 'A . CS G > ( SS )
Due to the volume discount-induced conversion, we have
( X 'A + d X 'A ) . CS G > > ( SS )
For very small dealers ( like dealer N in Figure 14 ), their counter-size is itself smaller than the minimum slab, i.e.,
CS N < ( SS )
Assuming these dealers will not hold excess stock and will not engage in wholesaling, they will clearly not be able to qualify for the volume discount.
4.2 Dealers like ( K ) whose normal offtake from brand A is marginally less than ( SS ) will be able to avail of the volume discount if through the conversion effect they can sell more, i.e., if
( X 'A + d X 'A ) . CS K = ( SS )
If this dealer does not take the volume discount offered by brand A, his sales would be
( X 'A ) . CS K , and his margin would be mA .
If he does take the volume discount, his effective margin would be ( mA + d yA ) due to the volume discount, and his sales would be ( X 'A + d X 'A ) . CS K .
The incremental profit he gets due to the scheme is
= ( SS ) . ( d yA ) ....... ( Eq. 13 )
and the incremental sales he gets is
= ( d X 'A ) . CS M ....... ( Eq. 14 )
The incremental benefit the dealer gets by availing of the volume discount, or his 'marginal volume discount' ( MVD ), is given by
MVD = ( incremental profit ) / ( incremental sales )
From ( Eq. 13 ) and ( Eq. 14 ), we have
MVD = [ ( SS ) . ( d yA ) ] / [ ( d X 'A ) . CS M ]
= [ ( CS M ). ( X 'A + d X 'A ) . ( d yA ) ] / [ ( d X 'A ) . CS M ]
= ( d yA ) . [ ( X 'A + d X 'A ) / ( d X 'A ) ]
For ( X 'A ) > > ( d X 'A ) , we have
MVD = ( d yA ) . ( X 'A ) / ( d X 'A ) ...... ( Eq. 15 )
Consider a case where a dealer ( M ) has ( CS M ) = 200, and brand A has a normal preference share of 20 %. Thus the dealer normally sells 40 sets of brand A every month. Let the volume discount be for a minimum slab of 50 sets. The dealer will not normally be able to avail of the volume discount, since he has a shortfall of 10 sets. If the volume discount helps the dealer get an additional 5 % conversion for brand A ( i.e., 10 extra sets ), he would be able to qualify for the volume discount. Thus we have
MVD = ( d yA ) . ( 20 ) / ( 5 )
= 4 . ( d yA )
While previously the dealer would have got only his normal dealer margin for his 40 sets, he now gets his normal dealer margin and the volume discount for all the 50 sets. However, for each of the 10 extra sets he buys, he gets the normal dealer margin and 4 times the volume discount. The reason the MVD is so high is that the dealer not only gets the volume discount on the extra 10 sets, he also gets it for all the 40 sets he would have anyway bought from A even without the volume discount. For these 40 sets, he would have made a 'normal profit' with his normal margin itself, hence the volume discount for these 40 sets constitutes his 'abnormal profit'. The above example shows how profitable it is for the dealer to avail of a volume discount, even if it means 'stretching' his sales through conversion from other brands. The dealer can obtain a part of his conversion from other brands by offering the customer an additional discount for purchasing brand A's sets. In the above example, for the 10 extra sets which the dealer has to buy from brand A, he can even offer his customers a discount upto 4 times his volume discount. However, this is true only for those dealers who (a) would not have qualified for the scheme without this conversion, and (b) with the conversion, can reach the minimum offtake slab. For dealers like G who would have qualified for the minimum slab anyway, the MVD is ( d yA ) - he only gets his normal dealer margin and the volume discount. For dealers like N, there is no MVD.
4.3 Now let us consider those dealers like ( M ) whose counter-sales is such that even with the conversion effect, their monthly sales will not equal the minimum monthly offtake slab. For these dealers,
( X 'A + d X 'A ) . CS M < ( SS )
These dealers can still avail of the volume discount if they are prepared to carry over the excess stock to the subsequent month(s). Thus if the relation between their expected monthly sales and the minimum slab is such that
( X 'A + d X 'A ) . CS M . n = ( SS ) ...... ( Eq. 16 )
they should be prepared to hold stock for ( n ) months.
Assuming brands do not give dealers any credit for their purchases, if ( P ) is the price at which the dealer buys the set from brand A, if ( i ) is the monthly rate for the dealer's cost of capital, and if the dealer needs ( n ) months to completely clear out the stock ( SS ) he had taken from brand A to qualify for the volume discount ( d yA ), his incremental stock-holding cost is
= ( P / 2 ) . ( i ) . ( n ) ........... ( Eq. 17 )
since the average value of the stock held by the dealer, as it diminishes from ( P ) to zero, is ( P / 2 ).
The dealer's MVD is now
MVD = [ ( SS ) . ( d yA ) ] / [ ( SS ) - CS M . ( X 'A ) ]
= [( X'A + d X'A ) . CSM . n] . ( d yA ) / [( X'A + d X'A ) . CSM . n] - [CSM . ( X'A )]
= ( d yA ) . [ n. ( X 'A + d X 'A ) ] / [ n. ( X 'A + d X 'A ) - ( X 'A ) ]
= ( d yA ) . [ ( X 'A + d X 'A ) ] / [ d X 'A + ( X 'A ) . ( n - 1 ) / n ]
For ( d X 'A ) < < ( X 'A ), we have
MVD = ( d yA ) . ( X 'A ) / [ d X 'A + ( X 'A ) . ( n - 1 ) / n ] ...... ( Eq. 18 )
For ( n ) = 1, we have
MVD = ( d yA ) . ( X 'A ) / ( d X 'A ) ....... ( Eq. 19 )
which is same as ( Eq . 15 ).
For ( n ) > > 1, and for ( d X 'A ) < < ( X 'A ), we have
MVD = ( d yA ) . ( X 'A ) / [ ( d X 'A ) + ( X 'A ) ]
= ( d yA ) ..... ( Eq. 20 )
4.4 If the dealer M has to hold stock only for a short duration ( i.e., small values of (n) ), his MVD is enormous ( as given by ( Eq. 19 ) ), and his stock holding cost is low. But if he has to hold stock for a long duration ( i.e., large values of (n) ), his MVD is very small ( as given by ( Eq. 20 ) ) and his large interest cost will exceed the MVD. The maximum duration of time ( nmax ) for which the dealer can hold excess stock without losing out on holding cost is at that point when his holding costs just equal his MVD. Thus from ( Eq. 17 ) and ( Eq. 18 ) we have :
( d yA ) . ( X 'A ) / [ d X 'A + ( X 'A ) . ( nmax- 1 ) / nmax ] =
( P / 2 ) . ( i ) . ( nmax )
( P / 2 ) . ( i ) = ( d yA ) . ( X 'A ) / [ ( d X 'A + X 'A ) . ( nmax) - ( X 'A) ]
For ( d X 'A ) < < ( X 'A ), we have
( X 'A ) . ( nmax) - ( X 'A) = ( d yA ) . ( X 'A ) . 2 / ( P . i )
( nmax - 1 ) = 2 . ( d yA ) / [ ( P ) . ( i ) ]
( nmax ) = 1 + 2 . ( d yA ) / [ ( P ) . ( i ) ] ....... ( Eq. 21 )
Given ( d yA ), ( P ) and ( i ), the above equation gives ( nmax ), the maximum duration for which it is worthwhile for the dealer to hold stock while accepting the volume discount. If he has to hold stock for more than this duration, his MVD will be wiped out by the holding cost.
4.5 The above value of ( nmax ) also places a limit on the quantity offtake that the dealer M can take for accepting the volume discount. We have, from ( Eq. 16 ),
( X 'A + d X 'A ) . CS M . n = ( SS )
The maximum feasible value of ( n ) as obtained from (Eq. 21) when substituted in (Eq. 16) gives us the maximum value of the volume discount, (SS), that the dealer can achieve, given his counter-size (CSM) and brand A's new preference-share, (X 'A + d X 'A). Thus the maximum value of the volume discount, (SSmax), that the dealer can achieve is given by (Eq. 21) and (Eq. 16) as :
( SS max ) = ( X 'A + d X 'A ) . CS M . [ 1 + 2 . ( d yA ) / ( P ) . ( i ) ]
For ( d X 'A ) < < ( X 'A ), we have
( SS max ) / CS M = ( X 'A ) . [ 1 + 2 . ( d yA ) / ( P ) . ( i ) ] ..... ( Eq. 22 )
4.6 Given (d yA), (P), (X 'A) and (i), (Eq. 22) gives a maximum value of the volume discount, ( SS max ), that the dealer with a counter-size ( CS M ) can achieve. Beyond this value, his MVD will be wiped out by his holding cost. Alternatively, ( Eq. 22 ) gives the minimum counter-size ( CS M min ) that the dealer must have in order to be able to qualify for a given offtake slab ( SS ). Dealers whose counter-size is below this will not be able to qualify for the volume discount.
As seen from Figure 15, the volume discount with a minimum slab has two main effects :
(a) for all dealers to the left of D1', the sales per dealer increases due to the conversion effect, [ ( X 'A + d X 'A ) . CS ]
(b) for dealers in the range D1' to D2', whose counter-size is greater than ( CS M min ), the sales per dealer increases to ( SS ).
For dealers beyond D2', the sales per dealer remains unchanged.
4.7 By offering the volume discount, the brand's 'TC per dealer' does not change, only its 'sales per dealer' and 'CM effective' change. From the 'TC per dealer' curve ( unchanged, as in Figure 6 ) and the new 'sales per dealer' curve in Figure 15, we arrive at the new 'TC per set' curve in Figure 16. For dealers to the left of D1', the TC per set is reduced since the sales per dealer has gone up and the TC per dealer has not changed. For dealers to the right of D2', the TC per set is unchanged, since the sales per dealer is also unchanged. For dealers in the range D1' to D2', the TC per set curve goes down, following the 'TC per dealer' curve ( since 'TC/set' is 'TC/dealer' / 'sales/dealer', and the 'sales/dealer' curve remains flat ). Thus the real impact of the volume discount is that dealers in the range D1' to D2' have a much lower TC per set than they had before the volume discount, while it is only marginally lower for dealers before D1'. The reduction in TC per set at D2' due to the volume discount, compared to its previous value without the volume discount, is shown as ( d TC ).
4.8 The 'CM effective' curve is lowered due to the additional discount pay-outs, as it was in Figure 11. Combining the TC per set curve in Figure 16 and the CM effective curve in Figure 11, we get the new net incremental profit curve of Figure 17. In the region D1' to D2', the net incremental profit shoots up, since in this range the CM effective keeps rising and the TC per set actually keeps falling. Compared to the values before the volume discount, the net incremental profit at D2' has risen by an amount ( d NIP ). Until D1', the net incremental profit changes only marginally, depending on which falls more - CM effective or the TC per set. Beyond D2', the net incremental profit remains unchanged. The extra NIP gained by the brand at D2', i.e., ( 'd NIP' in Figure 17 ), is equal to the reduction in the transaction cost per set ( d TC ) shown in Figure 16. Essentially the brand's NIP increases because many dealers whose normal offtake is less than the slab will stretch themselves and buy more sets to qualify for the volume discount, at no additional transaction cost to the brand. Since the sales per dealer increases ( by d S ) without any increase in the TC per dealer, the brand's TC per set will decrease, and its NIP will increase.
4.9 For dealers to the left of D1', the MVD is only ( d yA ). Dealers beyond D2' do not qualify for the volume discount, and hence have no MVD. The MVD that dealers in the range D1' to D2' get is given by ( Eq. 18 ) as
MVD = ( d yA ) . ( X 'A ) / [ d X 'A + ( X 'A ) . ( n - 1 ) / n ]
Thus we have
MVD / ( d yA ) = ( X 'A ) / [ d X 'A + ( X 'A ) . ( n - 1 ) / n ] ..... ( Eq. 23 )
Depending upon duration ( n ) for which they hold the stock, the MVD / ( d yA ) varies as follows :
for n = 1, MVD / ( d yA ) = ( X 'A ) / ( d X 'A )
assuming ( d X 'A ) < < ( X 'A ), we have
MVD / ( d yA ) = ( X 'A ) / [ ( X 'A ) . ( n - 1 ) / n ] ........ ( Eq. 24 )
Thus we have
for n = 2, MVD / ( d yA ) = 2
for n = 3, MVD / ( d yA ) = 1.5
for n = 4, MVD / ( d yA ) = 1.33
for n = 10, MVD / ( d yA ) = 1.11
and so on, till for
( n ) > > 1, MVD / ( d yA ) = 1
This is shown in the dealers' MVD curve in Figure 18.
4.10 The extra sales generated by the brand as a result of the volume discount can be calculated from Figure 19. As seen from the figure, the brand gets a sales of ( SS ) from all dealers between D1' and D2', which is more than what it would have got without the volume discount. The extra sales at D2' is given by ( dS ), while the extra sales at D1' is equal to the conversion difference, i.e., [ ( d X 'A ) . CS ]. In the range D1' to D2', the total extra sales got by the brand is the area above the old sales curve in the figure. This area is approximately equal to the area of the triangle formed by the points Q, R and S in Figure 19. The area of such a triangle, and hence the extra sales, is given by the equation
extra sales = ( 1 / 2 ) . ( d S ) . ( D2' - D1' )
Here ( d S ) = ( SS ) - ( S2 )
We have ( S1 ) = ( CS D1' ) . ( X 'A )
and . ( SS ) = ( CS D1' ) . ( X 'A + d X 'A )
hence ( S1 ) = ( SS ) . [ ( X 'A ) / ( X 'A + d X 'A ) ]
The sales curve can be approximated by the equation
S = k / D
where ( k ) is a constant and D is the dealer strength. For the old sales per dealer curve, the sales per dealer value at D1' is
( S1 ) = k / D1'
Thus k = ( S1 ) . D1'
and at D2', we have
( S2 ) = k / D2'
Substituting the value of ( k ) from above, we have
( S2 ) = ( S1 ) . D1' / D2'
Substituting here the value of ( S1 ), we have
( S2 ) = ( D1' / D2' ) . ( SS ) . [ ( X 'A ) / ( X 'A + d X 'A ) ]
Thus ( dS ) = ( SS ) - ( S2 )
= ( SS ) - ( D1' / D2' ) . ( SS ) . [ ( X 'A ) / ( X 'A + d X 'A ) ]
= ( SS ) . [ 1 - ( D1' / D2' ) . ( X 'A ) / ( X 'A + d X 'A ) ]
For ( d X 'A ) < < ( X 'A ), we have
( dS ) = ( SS ) . [ 1 - ( D1' / D2' ) ]
= ( SS ) . [ ( D2' - D1' ) / ( D2' ) ]
Thus
extra sales = ( 1 / 2 ) . ( D2' - D1' ) . ( SS ) . [ ( D2' - D1' ) / ( D2' ) ]
= ( SS / 2 ) . [ ( D2' - D1' )2 / ( D2' ) ] ...... ( Eq. 25 )
4.11 If the brand has a volume discount with two slabs, the sales, transaction cost and NIP are as shown in Figures 20, 21, 22. As seen, the brand can increase its sales and the NIP by having a large number of slabs for the volume discount. The larger the number of slabs, the more the brand's sales and NIP increases.
5. volume discount with slab and with wholesaling
5.1 When wholesaling happens, large dealers sell part of their offtake to small dealers who cannot qualify for the slab, and share the volume discount among themselves. We assume that the small dealers' sourcing decision ( buying from the brand directly vs. from a big dealer ) depends solely on the margin he gets. Then small dealers who cannot qualify for the brand's slab will prefer to buy from a bigger dealer ( and get part of the slab ) than to buy from the brand ( and get no slab at all ). This is shown in Figure 23, where we have considered a single-slab case :
- small dealers to the right of D2' stop buying from the brand and instead buy from bigger dealers to the left of D2'.
- for dealers to the left of D1' whose normal offtake from brand A is greater than the minimum slab, the MVD is only ( d yA ), and wholesaling is not abnormally profitable.
- for dealers in the range D1' to D2', wholesaling represents an 'abnormal profit'. These dealers would normally have to hold excess stock for a finite duration, incurring certain holding costs. For these dealers the normal offtake from brand A is less than ( SS ), i.e.,
( SS ) < ( CS D2 ' ) . ( X 'A + d X 'A )
They will prefer to sell the excess offtake to smaller dealers beyond D2', so that they will not have to incur the holding cost. Thus for these dealers in the range D1' to D2', we have
( SS ) = ( CS D2 ' ) . ( X 'A + d X 'A + wA ) ....... ( Eq. 26 )
where ( wA ) is the 'wholesaling share', or the fraction of the counter-sales that the dealer buys from brand A to sell to smaller dealers. Since the brand will normally try to keep the slab ( SS ) as high as possible, ( d X 'A + wA ) must be very high, and ( wA ) must be much higher than ( d X 'A ). Thus we can modify ( Eq. 26 ) to get
( SS ) = ( CS D2 ' ) . ( X 'A + wA ) ....... ( Eq. 27 )
5.2 For the brand, the incremental sales due to the volume discount is ( CS D2 ' ).( wA ), and the incremental contribution is ( CS D2 ' ) . ( wA ) . ( P. c ).
The incremental cost borne by the brand in getting this level of sales is given by
( SS ) . ( d yA ) = ( CS D2 ' ) . ( X 'A + wA ) . ( d yA )
For break-even for the brand, we have
( CS D2 ' ) . ( wA ) . ( P. c ) = ( CS D2 ' ) . ( X 'A + wA ) . ( d yA )
Thus ( d yA ) / ( P. c ) = ( wA ) / ( X 'A + wA ) ...... ( Eq. 28 )
Given ( P ), ( c ) and ( X 'A ), the above equation gives the maximum volume discount that the brand can offer for an expected level of wholesaling. From experience or from limited experimentation, the brand can estimate the level of wholesaling for different levels of volume discount, and decide whether the wholesaling will be economically worthwhile.
5.3 For the dealer, the MVD is the ratio of the extra cash he gets, to the extra sets he has bought from brand A. This is given by
MVD = ( SS ) . ( d yA ) / [ ( CS D2 ' ) . ( wA ) ]
= ( CS D2 ' ) . ( X 'A + wA ) . ( d yA ) / [ ( CS D2 ' ) . ( wA ) ]
Thus MVD = ( d yA ) . [ ( X 'A + wA ) / ( wA ) ] ..... ( Eq. 29 )
If we were to denote [ ( X 'A + wA ) / ( wA ) ] by the term 'wholesaling fraction' for brand A, ( WFA ), we have
MVD = ( d yA ) . ( WFA )
The MVD value for different levels of the 'wholesaling fraction' is shown in Figure 24.
Similarly, the maximum volume discount the brand can offer ( from Eq. 28 ) is
( d yA ) = ( WFA ) . ( P. c )
5.4 When the big dealer in the range D1' to D2' sells his excess stock to smaller dealers beyond D2', he must share part of the volume discount with the smaller dealer. Let (d yW) be the part of the volume discount that the big dealer gives the smaller dealer. For the quantity he sells to the small dealer, the big dealer retains an amount equal to his MVD minus the shared volume discount ( d yW ). Thus his retention is
= MVD - ( d yW )
= [ ( d yA ) . ( X 'A + wA ) / ( wA ) ] - ( d yW ) ...... ( Eq. 30 )
As the big dealer tries to sell his excess stock to the smaller dealer, he needs to give a larger and larger chunk of the volume discount to the smaller dealer. The shared portion of the volume discount can be approximated by a straight line rising from zero at D1'. The maximum discount that the dealer can part with is his MVD. Thus the dealer will continue to engage in wholesaling until a maximum value of wholesaling share, ( w A max ) where the maximum discount shared with the smaller dealer is
( d yW max ) = ( d yA ) . [ ( X 'A + w A max ) / ( w A max ) ] .... ( Eq. 31 )
For large levels of wholesaling, we have ( X 'A ) < < ( w A max ), hence
( d yW A max ) = ( d yA ) = MVD
5.5 As seen from Figure 23, dealers beyond D2' do not buy anything from the brand, preferring instead to buy from the bigger dealers. For dealers to the left of D1', the brand gets increased sales, but the brand loses all the sales it previously got from dealers beyond D2' ( upto D2, which was the maximum dealer strength of brand A before wholesaling, as seen from Figure 9 ). The difference between the two will determine whether the brand makes a net gain or loss in sales. This net sales gain for the brand due to wholesaling can be found from Figure 25, which also plots the market reach for the brand at various levels of dealer strength. To simplify the analysis, we have assumed that with wholesaling, the sales for the brand in the range D1' to D2' is not ( SS ) but simply ( CS D2 ' ) . ( X 'A + wA ) , where ( wA ) is the wholesaling share for all dealers to the left of D2'.
Thus before wholesaling, the sales for brand A would have been given by
SA = X 'A . MR1 . M
and after wholesaling, the brand's sales is given by
SA = ( X 'A + wA ) . MR2 . M
The extra sales for the brand to the left of D2' is given by [ MR2 . ( wA ) ].
The sales lost in the range D2' to D2 is given by [ ( MR1 - MR2 ) . ( X 'A ) ]
The brand's net gain in sales is given by
d S = [ MR2 . ( wA ) ] - [ ( MR1 - MR2 ) . ( X 'A ) ]
= [ MR2 . ( wA ) + X 'A ) ] - [ ( MR1 ) . ( X 'A ) ]
The brand has a net gain in sales when
[ MR2 . ( wA ) + X 'A ) ] > [ ( MR1 ) . ( X 'A ) ]
or when
[ MR2 / MR1 ] > [ X 'A / ( wA ) + X 'A ) ] ..... ( Eq. 32 )
Figures 1 - 25 :
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