# The economics of rent-to-own contracts.

The Economics of Rent-to-Own ContractsRent-to-own contracts are a common form of contractual arrangement for many types of durable goods, such as television sets, washers, dryers, pianos, and furniture. With rent-to-own contracts, the consumer is under no obligation to make payments for a given length of time (that is, the contract can be terminated at any time upon return of the product), yet if payments are made through a certain term, the consumer receives ownership of the product. While payments are made on the rent-to-own contract, the dealer usually agrees to maintain and repair the product, unlike a strict purchase arrangement. (1)

In most states, rent-to-own contracts are exempt from usury ceilings. Rent-to-own contracts have been criticized for their allegedly high interest rates implicit in the payment stream. For example, in comparing the retail price of the product offered by the dealer to the stream of payments on the rent-to-own contract, the North Carolina Attorney General's office has calculated APRs ranging from 70 percent to over 300 percent on televisions and appliances (Thornburg 1987. In a sample of rent-to-own contracts from Atlanta stores, Swagler (1986) found estimated APRs ranging from 117 percent to 168 percent.

A flaw in the previous studies of rent-to-own contracts is lack of consideration of the complexities of rent-to-own contracts; that is, the studies have not considered that the contracts are part rental contract and part purchase contract. Calculation of APRs has been done as if rent-to-own payments are pure purchase payments. The purpose of this paper is to examine the complex economics of rent-to-own contracts and to use the resulting conclusions to calculate implicit interest rates on a sample of rent-to-own contracts. An attempt is also made to explain the variation in implicit interest rates among dealers.

DERIVATION OF THE RENT-TO-OWN PAYMENT

Consider the derivation of a pure-rental payment (RENT) for a consumer durable good. For the owner-dealer of the durable good to rent the good in period i willingly, the rental payment, [RENT.sub.i], must equal or exceed four component costs (Nicholson 1983). The first cost is depreciation of the good in period i, measured by the product of the depreciation rate in i([D.sub.i]) and the cash value of the good at the beginning of the period, P. The second cost is due to maintenance and repair paid by the owner-dealer and is measured by the product of the maintenance rate in period i([m.sub.i]) and the cash value of the good. The third cost stems from the expense of servicing the contract (collecting and processing payments), which are assumed to be unrelated to the cash value of the good. Servicing costs in period i are thus represented simply by [S.sub.ri]. The last cost is the opportunity cost of having the cash value, P, committed to the good rather than in an investment earning the current interest rate. This periodic cost is [r.sub.i]P, where [r.sub.i] includes a risk componet equal to the same level of risk associated with the alternative use of $P in the form of renting the durable good. Thus the minimum required rent payment in period is

[RENT.sub.i] = [d.sub.i]P + [m.sub.i]P + [r.sub.i]P + [S.sub.ri].

For simplicity, assume tht [d.sub.i] and [m.sub.i] are constant fractions of P, that [S.sub.ri] and [r.sub.i] are constant over all periods, and assume simple interest earnings for the oppportunity cost. Then (1) becomes

[RENT.sub.i] = dP + mP + rP + Sr.

The derivation of ownership payments is more straightforward. If the owner-dealer of the durable good sells the good to the consumer and if the consumer makes periodic payments for a total of n periods, then each periodic payment, [BUY.sub.i], is

[BUY.sub.i] = PA(r) + [S.sub.o'

where A(r) is the annuity factor,

A(r) = r/1 - 1 - [(1 + r).sup.-n],

r is the interest rate including a risk compoent, in is the number of payments periods, and [s.sub.o] is the cost of servicing the purchase contract.

To formulate the minimum payment required on a rent-to-own contract, consider the cost faced by the dealer-owner. Because dealers promise to maintain and repair the good with a rent-to-own contract, dealers incur the periodic cost mP. Dealer-owners absorb depreciation costs, dP, if the customer does not complete the rent-to-own contract and returns the product. Let [p.sub.r] be the probability that the consumer returns the product taken out with the rent-to-own contract. Then the dealer faces expected depreciation costs equal to [p.sub.r]dP. assume contract servicing costs are the same whether the consumer rents or buys the product; thus [S.sub.r] = [S.sub.o] = s, so servicing costs on the rent-to-own contract are s per period. Finally, the dealer-owner faces an opportunity cost of rP per period if the consumer does not rent for the period required for ownership and returns the product, or the dealer-owner would charge PA(r) per period if the consumer completed payments and bought the product. The expected cost of this component is [p.sub.r]rP + (1 - [p.sub.r])PA(r). Total rent-to-own costs (RTO) per period are thus:

RTO = mP + [p.sub.r]dP + s + [p.sub.r]rP + (1 - [p.sub.r])PA(r).

Given values for RTO, m, p, [p.sub.r], d, s, and n, an iterative procedure can be used to find the implicit interest rate, r, which satisfies equation (4). (2)

COMPARISON OF IMPLICIT INTEREST RATES

An important questio is whether the implicit interest rate, r, in equation (4) is smaller or larger than the implicit interest rate calculated by other researchers of RTO contracts (e.g. Swagler). Other researchers have simply used an equality between RTO and PA(r) to calculate, r, that is:

RTO = PA(r').

Call r' the implicit interest rate calculated from (5).

If the RTO contract is a pure purchase contract, as assumed by other researchers, then, [p.sub.r] is 0 and (4) reduces to:

RTO = mP + s + PA(r")

or

RTO - mP - s = PA(r").

Call r" the implicit interest rate calculated from (6). Because the RTO payment in (6) is reduced by maintenance and repair costs (mP) and service costs (s) before the implicit interest rate (r") is calculated, r" is less than r'.

Chances are that [p.sub.r] is between 0 and 1. To see what happens in this case, rewrite (4) as:

RTO - mP - s - [p.sub.r]rP = (1 - [p.sub.r])PA(r).

The implicit interest rate calculated from (7) is simply r. The RTO payment has now been further reduced by expected depreciation costs ([p.sub.r]dP) and by expected opportunity, or rental, costs ([p.sub.r]). The right-hand side of (7) is now also smaller than the right-hand side of (5), because (1 - [p.sub.r]) is less than 1. The left-hand side of (7) is the "net purchase payment," because the expted costs of the dealer, including the expected rental payment, are subtracted from RTO payment. The right-hand side of (7) is the product of the "net purchase amount" [(~ - [p.sub.r])] and the annuity factor. The point is that the net purchase payment in (7) is less than the purchase payment in (5) (RTO), but the net purchase amount in (7) is also less than the purchase amount (P) in (5).

Can one say whether r is smaller or larger than r'? Consider equation (7) again and assume that r has been calculated. The left-hand side of (7) is less than the left-hand side of (5) by the quantity [ - (mP + s + [p.sub.r]dP + [p.sub.r]rP)], and the right-hand side of (7) is less than the right-hand side of (5) by the quantity [ - [p.sub.r]PA(r)]. If [mP + s + [p.sub.r.dP] + [p.sub.r.rp]] [is greater than] [[p.sub.r.PA(r)]], then r [is less than] r' because the purchase payment is reduced by more (5) to (7) than the purchase amount is reduced. If [mP + s + [p.sub.r.rP]] [is less than] [[p.sub.r.PA(r)]], then r [is greater than] r' because the purchase amount is reduced by more from (5) to (7) than the purchase payment is reduced. Divide both sides by P. The comparison is then between:

[m + s/P + [p.sub.r]d + [p.sub.r]r] and [[p.sub.r]A(r)], or

[m + s/P + [p.sub.r]d + [p.sub.r]r] - [[p.sub.r]A(r)] = C.

If C [is greater than] 0 then r [is less than] r', and if C [is less than] 0 then r [is greater than] r'.

If m, s, [p.sub.r], and d are fixed, then the critical relationship is between r and A(r). For short loan terms common to rent-to-own contracts (18 months or less), A(r) will be greater than r. The more A(r) exceeds r, the smaller will be C and the more likely that r will exceed r'. Conversely, as A(r) exceeds but approaches r, the larger will be C and the more likely that r' exceeds r.

Table 1 shows values 3f A(r) - r for alternative combinations of r and n. The largest values for A(r) - r are italicized. A(r) - r is highest for low values of r and/or low values of n. Therefore, (r - r') should be larger for RTO contracts with low r and/or low n values, and (r - r') should be smaller for RTO contracts with high r and high n values.

EMPIRICAL RESULTS

Information on 12 rent-to-own contracts, seven for televisions and five for washers, are used in the analysis. The contract data are given in Table 2. The data were collected from rent-to-own dealers in Raleigh, North Carolina, during the summer of 1987. Values are given for P, RTO, and n. The stated purchase price, P, is the cost to the consumer of purchasing the product outright from the dealer. (3)

To calculate the implicit interest rate, r, values must be assumed for the parameters m, [p.sub.r], d, and s. Estimates for the parameters are taken directly fromthe rent-to-own industry. If this presents a bias, it should be toward overestimating industry expenses and underestimating implicit interest rates. In other words, in estimating the implicit rates, the benefit of the doubt is given to the rent-to-own industry. The industry estimates for the parameters are: maintenance repair costs (m) equal to 10 percent of revenues; depreciation rate (d) of 2.75 percent per month (implying a life expectancy of only 3 years); servicing costs (s) of 4 percent of revenues; and a probability of renting and returning the product ([p.sub.r]) equal to .80 (Winn 1983). The probability rate of .80 is also estimated by the National Social Science and Law Center (1987).

There are two ways to use estimates of m and s to calculate monthly maintenance and repair costs and service costs. The first is to multiply m and s by the monthly rent-to-own payment. The second way is to multiply m and s by the price of outright purchase (P), with the result equalling yearly maintenance/repair and service costs. The first method was used in the analysis presented here. The second method gave very similar results.

Table 3 compares the calculated implicit monthly interest rates for r', r", and r, and also compares r to r'. (4) As expected, r" is less than r. Of the 12 contracts, r is less than r' in eight contracts. Of the four cases in which r is greater than r', in two instances r is low (cases 5 and 6) and in two n is low (cases 1 and 11). This conforms to expectations.

Table 4 presents the same informationas Table 3 but in the form of an APR. The APR can be calculated as (monthly rate)12 or [(1 + monthly rate) (12) - 1]. For comparison with other studies, the first method is used, although the latter method is more correct from the standpoint of economic thoery.

Another question is how large the sum of maintenance, repair, expected depreciation, and service costs would have to be for the implicit interest rate to be comparable to APRs of, say 18 ot 24 percent. This can be derived from equation (7) by setting r equal to 18 or 24 percent (monthly rates of 1.5 or 2 percent) and solving for the sum of maintenance, repair, expected depreciation, and service costs. The results are in Table 5. The sum of maintenance, repair, expected depreciation, and service costs would have to be between 60 and 82 percent of RTO payments for the APR to be 18 percent and between 55 to 79 percent of RTO payments for the APR to be 24 percent.

EXPLAINING THE VARIATION IN IMPLICIT INTEREST RATES

The implicit interest rates reported in Tables 3 and 4 display noticeable variation, expecially for televisions. Can any insight be provided in addressing the reason or reasons for this variation?

One hypothesis is that the implicit interest rate varies inversely with the median income of the dealer's customers. Dealers consider low income customers to pose greater risks of default and, therefore, charge such customers higher implicit interest rates.

To test this hypothesis, the APR values presented in Table 4 are regressed on the median income of the tract in which the dealer of the product was located. Tract median income for 1987 was taken from National Planning Data Corporation. Tract median income is a proxy for customer income because there is no assurance that the tract area is the same as the dealer's market area. The regression analysis is done only for televisions because all but one of the washer rent-to-own dealers were located in the same tract.

The regression results are shown in Table 6. The implicit interest rate for televisions is inversely and significantly related to tract median income. The parameter estimates indicate that every $1,000 increase in tract median income is associated with a 1.1 percentage point reduction in the implicit interest rate.

IMPLICATIONS AND CONCLUSIONS

An economic model was used to derive the rent-to-own payment required by a owner-dealer and the required implicit interest rate. The model explicitly accounted for maintenance and repair costs borne by the owner-dealer, expected depreciation costs, service costs, expected interest earnings opportunity costs, and expected required annuity payments. These costs have been omitted in previous studies of rent-to-own contracts, which may cause previous estimates of interest rates implicitly charged on rent-to-own contracts to be too high. The model revealed that, even after considering the complexity of rent-to-own contracts and the costs paid by the owner-dealer, implicit interest rates can actually be higher than those estimated with the methodology used by previous researchers, who considered all of rent-to-own payments to be purchase payments. Parameters estimates for the owner-dealer costs were taken from the rent-to-own industry. Such estimates likely biased estimates of the implicit interest rate downward.

Using a sample of rent-to-own contract data from dealers in Raleigh, North Carolina, implicit interest rates were estimated in the range of 33 percent to 125 percent annually (APRs), with most estimates above 60 percent. Most of the estimates were lower than implied interest rates estimated assuming the entire RTO payment is a purchase payment. For implicit interest rates to be 18 or 24 percent (APR), it was estimated that owner-dealer costs as a percent of rent-to-own payments would have to be in the range of 55 to 82 percent. This range is far above industry estimates.

Consumer groups in many states are concerned about the allegedly high implicit interest rates charged on rent-to-own contracts. However, these charges are open to criticism because the method used to calculate the implicit interest rate does not account for the complexity of the rent-to-own contract and dealer costs. The procedure outlined in this paper explicitly addresses this criticism; therefore, the implicit interest rates resulting from the procedure are much more defensible from criticism by the rent-to-own industry.

Still open is the question of why implicit interest rates on rent-to-own contracts, even after accounting for contract complexity and dealer costs, are still higher than typical usury ceilings. One reason may be that the industry perceives rent-to-own customers as high risk consumers. The rent-to-own industry serves low income consumers who have been denied credit and who value the ready availability of credit at rent-to-own dealers (Swagler and Wheeler 1989). Some support for this hypothesis was found in the negative relationship between dealer census tract income interest rates charged by the dealer found for televisions in the sample.

Another reason for the high implicit interest rates may be related to the option imbedded in the rent-to-own contract. Users of rent-to-own contracts may perceive a benefit in deciding at a later date, after experience with the product has been gained, whether to continue renting or whether to purchase the product. Modeling this benefity and accounting for it in the implicit interest rate is a challenge for future research.

(1) However, warranties can provide the same service for purchase arrangements.

(2) The procedure first calculates NETRTO as NETRTO = RTO -mP - [p.sub.r]dP - s and then rearranges equation (4) to be: NETRTO = [p.sub.r]rP + (1 - [p.sub.r])PA (r). The procedure selects an initial value of r and then alters r until the equality is satisfied. The procedure is available from the author upon request.

(3) If the dealer prices for outright are higher than at other retailers, then all implicit interest rates will be underestimateD.

(4) All implicit interest rates are calculated assuming payments are made at the end of the month (e.g., the first payment is made at the end of the first month). If payments are made at the beginning of the month (meaning the first payment is made when the contract is signed), then all implicit interest rates will be higher, but comparison of r, r', and r" will not be affected.

REFERENCES

National Planning data Corporation (1987), Household Income Distribution, Wake County, NC.

National social Science and Law Center (1987), "A Study of Appliance Rental Practices: Appliance Rentals and Purchases by Low-Income Consumers," Clearinghouse Review (April): 1515-1522.

Nicholson, walter (1983), Intermediate Microeconomics and Its Application, 3rd edition, Chicago, IL: The Dryden Press: 513-514.

Thornburg, Lacy H., Attorney General, State of North Carolina (1987), "Statement on H 1108--Representative Hackney's Rent-to-Own Bill," July 9.

Swagler, Roger M. (1986), "Rent-to-Own Programs: Is Consumer Protection Adequate?" Proceedings of 32nd Annual Conference of ACCI, St. Louis, MO, April 9-12.

Swagler, Roger M. and Paula Wheeler (1989), "Rental-Purchase Agreements: A Preliminary Investigation of Consumer Attitudes and Behaviors," Journal of Consumer Affairs, 23(1) (Summer): 145-160.

Winn, Ed (1983), Testimony before the Committee on Banking, U.S. Senate, regarding Bill S11-52, July 18.

Michael L. Walden in a Professor in the Department of Economics and Business, North, Carolina State University, Raleigh, NC.

Comment of John Burton, Raymond Forgue, Craig Newmark, and two reviewers are greatly appreciated. An earlier version of this paper was presented at the 35th Annual Conference of the American Council on Consumer Interests in Baltimore, MD.

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Author: | Walden, Michael L. |
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Publication: | Journal of Consumer Affairs |

Date: | Dec 22, 1990 |

Words: | 3218 |

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