Asset Finance Quotation System

Dual Rate of Return

When measuring the rate of return on a transaction, we are trying to relate the profit made to the amount lent over time.

For transactions which are not loans, it is convenient to express the rate of return as an equivalent loan rate.

We can think of a transaction as being equivalent to a loan at a certain rate if both possible investments have the same balance of funds lent throughout the investment, and return the same total profit after tax. If we can determine the rate of interest on the loan which equates the loan investment to the transaction being analysed, then it makes sense to think of that rate as the rate of return on our transaction.

Another (related) way of looking at the problem is to ask "If I had to borrow all funds invested in the lease, at which borrowing rate would I break even?". The break-even funding rate can then be thought of as the yield on the transaction. This is the approach that we will use in the following examples, designed to explain the method of calculation used in the program.

Example:

Consider a tax system with a rate of 40% and a single tax instalment paid one year after the balance date.

The leased item costs:	$10,000.00 provided in July 2012
Residual:	$3,000.00 two years hence
Rentals:	2 × $5,000.00 annually in arrears
Depreciation:	24% prime cost
Fees:	2% of cost up front
Balance Date:	31 July

Cashflows to the lessor arising before tax are:

Lessor's Cashflows
Month	Advance	Rentals	Residual	Fees	Total
July 2012	(10,000)	–	–	(200)	(10,200)
July 2013	–	5,000	–	–	5,000
July 2014	–	5,000	3,000	–	8,000
Total	(10,000)	(10,000)	3,000	(200)	2,800

Assessable income in each year is:

Assessable Income
Year Ended	Depreciation	Rentals	Residual	Fees	Total
July 2012	–	–	–	(200)	(200)
July 2013	(2,400)	5,000	–	–	2,600
July 2014	(7,600)	5,000	3,000	–	400
Total	(10,000)	(10,000)	3,000	(200)	2,800

After-tax cashflows arising from the transaction are thus:

Cashflows
Month	Pre-tax Cashflow	Tax Cashflow	After-tax Cashflow
July 2012	(10,200)	0	(10,200)
July 2013	5,000	80	5,080
July 2014	8,000	(1,040)	6,960
July 2015	0	(160)	(160)
Total	2,800	(1,120)	1,680

Note that the total after-tax cash flow is the after-tax profit made on the transaction.

Suppose we can borrow funds at 16.236% p.a. to invest in the lease. Interest is paid annually in arrears, and is tax deductible. Let us further suppose that all cash flows and tax savings generated by the lease, and tax savings arising from the interest deductions are used to pay off the borrowed money. If there is insufficient cash in any month, more money is borrowed at the same rate. Any cash left over after the loan is paid off represents a profit above and beyond the funding cost to the lessor.

Consider the following table, which follows the lease transaction and funding arrangements over time.

Example 1
Month	After-Tax Cashflow	Tax Saved on COF	Total After-Tax Cashflow	Interest	Principal	Balance
July 2008	(10,200)	0	(10,200)	0	(10,200)	(10,200)
July 2009	5,080	0	5,080	1,656	3,424	6,776
July 2010	6,960	662	7,622	1,100	6,522	254
July 2011	(160)	440	280	41	239	15
July 2012	–	16	16	2	14	1
July 2013	–	1	1	0	1	0
July 2014	–	0	0	0	0	0
Total	1,680	1,120	2,800	2,800	0	–

In July 2008, $10,200 is borrowed and disbursed.
In July 2009, the investor receives a rental of $5,000 and a tax saving of $80.00. Interest of ($10,200 × 0.16236) = $1,656 is paid, leaving $3,424 to pay off the loan balance.
In July 2010, the investor receives $8,000 from the lessee and pays tax of $1,040. There is a $622 tax saving ($1,656 × 0.40) on the previous year's interest payment, giving a net cashflow of $7,622 before funding. Of this $1,100 = (6,776 × 0.16236) is paid in interest and $6,522 is paid off the loan.
The same process continues until July 2013, by which time there are no cashflows remaining. There is no excess cash, so the investor has exactly broken even. If the investor had borrowed at less than 16.236%, a profit would have been made. Conversely, borrowing at more than 16.236% would have resulted in a loss. The yield achieved by the lessor is therefore 16.236% pa.

Note that we did not explain how the figure of 16.236% p.a. was derived. In practice, the program guesses the yield, evaluates the profit and corrects its previous guess of the yield repeatedly until the break-even point is reached.

Usually, the actual cost of funds to the lessor is less than the break-even cost of funds, otherwise there would be no reason for the lessor to write the lease.

The difference between the yield and the actual funding rate represents a margin earned by the lessor. If we express the yield as:

yield = cost of funds + margin

then we can break the yield (or break-even cost of funds) into two parts as follows (assuming an actual COF of 15% and margin of 1.236%, for example):

Example 2
Month	Actual COF⁽¹⁾	Margin⁽²⁾	Yield^{(1) + (2)}	Tax Savings on COF⁽³⁾	Tax Savings on Margin⁽⁴⁾	Total Tax Savings^{(3) + (4)}
July 2008	0	0	0	0	0	0
July 2009	1,530	126	1,656	0	0	0
July 2010	1,016	84	1,100	612	50	662
July 2011	38	3	41	406	34	440
July 2012	2	0	2	15	1	16
July 2013	0	0	0	1	0	1

The idea of allowing a notional deduction for the lessor's margin may seem counter intuitive, but emerges as a necessary part of the break-even analysis.

There is one further complication to the dual rate method. If the cashflows are such that the investment balance changes sign, a different interest rate must be used on the negative balance.

A negative balance indicates that rather than borrowing funds, the investor temporarily has a surplus of funds which can be invested to earn interest. Since deposit rates are generally lower than borrowing rates, a conservative assumption is that the sinking fund (as the negative balance is known) earns a rate equivalent to or less than the cost of funds. The use of two interest rates, (one for borrowing and one for lending) gives this method of analysis its name.