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6.3. Exercise 6.2: The Decision to Discount

Let us begin to apply the terms of sale mathematics and logic outlined in Exercise 1 with reference to the Slash Music Company. It is considering the launch of self-tuning guitars that cost £1,000 to manufacture at a mark-up of £150. For the first time, they intend to offer prospective wholesalers credit of (2/10:30) rather than their usual cash on delivery (C.O.D.) terms.


Use the data (supported by your reading of either core text) to evaluate whether it is rational for customers to take the discount based on the Slash Company's annual cost of trade credit defined by Equation (13).

An Indicative Outline Solution

Optimum debtor policies defined by a company's terms of sale are determined by the division between its discounting and non-discounting customers.

With the information for the Slash Company, we can calculate the cash (C.O.D.) discount and credit prices actually paid, now or in the future, based on a uniform invoice price (P= £1,150)) and uniform terms of sale (c/t: T = 2/10: 30).

Price Options

Now (C.O.D.) £1.150:

Seven Days (Discount £23) £1.127:

Thirty Days £1.150

Obviously, no rational customer would pay COD today. They would opt for the lower discount price. Less obvious, is who chooses the credit period option. And this is where modeling the terms of sale, based on the time value of money concept, comes into play.

As we revealed in Exercise 6.1, the decision to discount should be based on the relationship between a creditor firm's annual cost of offering trade credit (k = 365c /T-t) and the customer's cost of borrowing from alternative sources to finance its purchases. This is measured by the customer's annual opportunity cost of capital rate (r).

Since the annual cost of trade credit (k) represents the cost to the customer of not taking the discount, it follows that if the customer's opportunity borrowing rate:

r < k = 365c / (T-t) (they take the discount) r > k = 365c / (T-t) (they opt for the credit period) r = k = 365c / (T-t) (the discounting decision is irrelevant)

Given the Exercise data, it should therefore be obvious why no rational customer in today's economic climate would opt for the credit period. As the following table illustrates, the prospective terms of sale offered by the Slash Company produce an annual cost of trade credit that far exceeds current "real world" opportunity cost of capital rates (alternative costs of borrowing) for any client with whom it intends to trade. So, all debtors take the discount

The Annual Cost of Trade Credit

k = (365c /T-t) = 36.5% [given (c/t:T) = (2/10: 30)]

6.4. Exercise 6.3: The Effective Price Framework

The previous Exercise can also be formulated using the time value of money to validate the discounting decision for any class of customer within a framework of effective prices.


For a prospective clientele trading with the Slash Company whose annual opportunity cost of capital rate is 10 per cent, compared to a six per cent norm throughout the economy.

1. Calculate the credit price (P') and discount price (P") associated with the "effective" price reductions arising from delaying the cash payment (P) over the credit or discount period,

2. Briefly explain your results.

3. Comment on the consequences of substituting (2/10:30) credit terms for C.O.D. from the Slash Company's perspective

An Indicative Outline Solution

Given typical six per cent financing costs, companies with 10% opportunity rates would be classified as reasonably high risk, perhaps experiencing liquidity problems. You might think they should therefore forego the cash discount offered by the Slash Company over the shorter discount period, delay payment and opt for the much longer credit period. If so, you would be wrong, unless ineffectual debtor-control procedures by the manufacturer allowed the wholesaler to remit payment well beyond the legitimate terms of sale (and perhaps still take the discount).

Whilst this is a common practice when debtor companies are strapped for cash (explained in our companion texts and the following Exercise) for the moment let us simply assume that the company's clientele can borrow at 10 per cent and are also ethical and rational. Customers therefore adhere to the declared terms of sale (2/10: 30) compare the available effective prices and opt for the lowest.

1. The Effective Price Framework

Using Equation (13) from our referenced reading, the discounting decision based on a customer's annual opportunity cost of capital rate (r = 10%) relative to the creditor firm's annual cost of trade credit (k = 36.5%) reveals that:

r =10% < k =36.5% = 365c / (T-t) = 365x2 / (30-10) So, all such wholesalers trading with the Slash Company would logically take the discount.

We now need to confirm whether the decision to discount for a high risk customer with an annual 10 per cent opportunity cost of borrowing in excess of the norm, is validated by the effective discount or credit prices they must pay for the new guitars. For easy reference, the table below summarizes the effective price formulae, relative to the annual cost of trade credit decision rules presented earlier, for any COD price (P) on terms (c/t: T) and a customer opportunity rate (r)

Now, let us apply all the data from the previous Exercise to these price formulae.

2. Conclusions

Given the customers' opportunity cost of capital, the "effective" price framework confirms their discount decision, relative to the creditor firm's annual cost of trade credit dictated by its terms of trade. Even customers with a relatively high opportunity cost of 10 per cent would fund their purchases by borrowing to pay the lower discount price, rather than the higher credit price.

3. The Creditor Firm's Perspective

If a reduction in price relates to an increase in demand, the movement from cash to discount and credit sales with their associated time value of money benefits should increase turnover. But there are "hidden" costs.

The (2/10:30) credit terms offered by the Slash Company are common throughout the UK and elsewhere. So, perhaps the Slash Company has decided to adhere to their competitors' policy with its new product launch. However, no customer trading with the firm (or others) who opts for the discount need borrow at 36.5%. Within the context of the credit period, the discount policy is far too generous. Despite established convention, it is a wasteful concession to debtors leaving the company to count the cost of sub-optimal terms of sale, which reduce the effective discount price too far below its cash and effective credit prices.

o Without detailed reference to the price elasticity of demand, underpinned by customer borrowing rates (all of which may be unique to the Slash Company) future profitability could be inhibited unnecessarily.

o Before launching the new guitar, the company should reconsider the terms of sale offered to its wholesalers.

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