Fundamentals of Business

Lease and Rental charges

How much to charge? Alibaba Catering Services buys freezers for £1000 each and lease them to Kebab Shops. What quartely rental should Alibaba charge to recover the expenditure within two years and generate 15% annual return?

The problem might be rephrased as If Alibaba puts £1000 on deposit at 15% per annum compounded quartely and withdraws it over eight quarters, what is the regular withdrawal?

R = PV ÷ [{1 -(1 + r)-n} ÷ r] where r = 0.15/4 = 0.0375
Therefore R = 1000 ÷ [{1 - (1 + 0.0375)-8} ÷ 0.0375] = 147.06

£147.06 is Alibaba's desired rental charge per quarter

Deciding whether to rent or buy

Should Tariq rent the freezer at £147.06 per quarter or buy at the retail price of £1500? Tariq believes the life of the freezer is the the two year warranty, He currently has the money on deposit at 6% a year compounded quartely.

The approach is to find the stream of payments that the deposit will produce in eight quarters Therefore r = 0.06/4 = 0.015
Rental charge R = PV ÷ [{1 -(1 + r)-n ÷ r], That is, R = 1500 ÷ [{1 - (1 + 0.015)-8} ÷ 0.015]
Therefore R = £200.80
£200.80 is more than £147.06

Tariq should leave the money in the bank, draw it to cover rental charge and pocket the surplus. and vice versa if R was less than rental charge per quarter, Tariq should rather buy the freezer.

NOTE

These examples have ignored taxes, mainteanance, residual value of equipment. Allowance must be made for such factors in real life by adjusting the payments up and down. Discount for cash
Convert the discount into annual percentage and see if it is better than the interest you earn on your deposit or less than interest you pay on your loan.

Example

A supplier is proposing full payment within default period of 30 days or 0.5% discount for immediate settlement, is offering you a flat 0.5% interest payment for 30 days use of your money.

Solution

0.5% per month in one year (12 months) = 6% ( not compounded). If your cash on deposit is less than 6% a year, get the discount If you have to borrow the money from your bank, the discount is worthwhile if the loan costs less than 6% a year. In effect, you could be borrowing from your bank at say 5% and lending your supplier for 6% , thus, you would make a 1% annual return.
Note:
Do not forget to include administration costs, taxes e.t.c