While reading a recent issue of Health & Fitness, a trade journal, Brandon Wilde noticed an ad for equipment he had been seeking for use in his business. The ad offered oxygen therapy equipment under the following terms:
Model BL 44582
$204,000 zero interest loan
Quarterly payments of $17,000 for only 3 years
The ad captured Wilde's attention, in part because he recently had been concerned that the interest charges incurred by his business were getting out of line. The price, though, was somewhat higher than prices for this model he had seen elsewhere.
Required:
Advise Mr. Wilde on the purchase he is considering.
SOLUTION
Obviously, no rational lender will lend money without interest. The zero interest loan described actually does implicitly bear interest. The amount and rate of interest can be inferred from either the market rate of interest at the time for this type of transaction or from the fair value of the asset being sold. The case information provides no information about either, other than that the stated price of the asset is higher than prices for this model Mr. Wilde had seen elsewhere.
If we knew, for instance, that the market rate of interest at the time for this type of transaction is 8%, we would assume that’s the effective interest rate and could calculate the price of the equipment as follows:
$17,000 x 10.57534 = $179,781
installment (from Table 4) actual
payment n=12, i=2.0% price
Both the asset acquired and the liability used to purchase it should be recorded at the real cost, $179,781. Similarly, if we knew the cash price of the equipment is $185,430, then we could calculate the effective rate of interest as follows:
The discount rate that “equates” the present value of the debt ($185,430) and the installment payments ($17,000) is the effective rate of interest:
$185,430 ÷ $17,000 = 10.9076: the Table 4 value for n = 12, i = ?
In row 12 of Table 4, the value 10.90751 is in the 1.5% column. Since payments are quarterly, this equates to a 1.5 x 4 = 6% annual rate. So, 6% is the effective interest rate. A financial calculator will produce the same rate.
In any case, Mr. Wilde will not avoid interest charges with this offer. Interest expense must be recorded at the effective rate, 8% in our first scenario, and 6% in the second.