Ira M. Freed, CPA - Return on Investment Analysis

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return on investment analysis

Return on Investment Analysis

INTRODUCTION

This paper presents an example of the calculation of the rate of Return on Investment (ROI). Such ROI calculations are often prepared to facilitate comparing the projected results of different investment opportunities.

The basic method of this investment analysis is to compute the cash flows at the beginning of the investment, during the period that the investment is held, and at the end of the investment (when it is disposed of). The three monetary stages of the life of the investment can be summarized as follows:

	The initial cash outflow to purchase the investment property.

	The net cash inflows or outflows each year that the investment is held.

	And the net cash inflow upon disposition of the investment property.

When these cash flows have been computed, the rate of return on the investment (all the net cash outflows) is calculated using the Internal Rate of Return (IRR) method. While the IRR calculation method has some limitations, it is useful to compare the result of the calculation to the investor's expected or acceptable rates of returns for investments of comparable risk. A high IRR indicates a favorable investment opportunity.

Usually, the rate of return calculations are made as part of projections about the future outcome of potential investments to see if they might yield desirable results. The rate of return calculation reduces to a single number all the projected cash outflows and inflows.

This method of analysis can also be applied after an investment is sold to compute the rate of return that was achieved. For example, such an analysis answers the question: did that real estate deal actually earn a good rate of return? It is not always easy to know if a good return was achieved because of the various amounts of income received and the expenses paid over a number of years. However, an investor does not have to wait until the investment property is sold to compute a tentative rate of return achieved. The calculations can also be made by estimating the current market value of the property and expenses to sell the property. Then the analysis is made as if the property were being sold.

CAUTION

The results of calculations of the sort presented here are heavily influenced by the assumptions used in the model. The key assumption in rate of return models is the annual rate of appreciation of the property. This rate is the annual percentage increase in the value of the investment necessary to raise the value of the property to what the investor thinks (or hopes) the property will be worth after a certain number of years. Except for a guaranteed investment, such as a government insured bank certificate of deposit or a government bond, the value of an investment after a number of years is a GUESS. To make an educated guess, one has to know as much as possible about the kind of investment being made. Even so, future economic events rarely turn out just as predicted.


EXAMPLE: RATE OF RETURN ON INVESTMENT CALCULATION

The investment property is rental real estate.

Terms of Investment and Assumptions
	Cost (purchase price of investment property)	$ 100,000
	Fees paid (in connection with the purchase)	$ 1,000
	Amount of purchase financed (debt assumed)	$ 60,000
	Annual operating or investment income, exclusive of depreciation and debt service	$ 5,000
	Annual debt payments	$ 6,000
	Portion of the cost of the real estate allocated to land	30%
	Combined federal and state tax bracket	33.0%
	Annual rate of appreciation of investment property (A BIG ASSUMPTION)	5.0%
	Sale at end of year	5
	Commission and selling expenses as percent of sales price	7.0%

	Assume that this investment is not a "Passive Activity" as defined by the U.S. Internal Revenue Code.
	Or, if the investment is a "Passive Activity", the deduction of the annual taxable loss, if any, is not limited by the "Passive Activity" rules.
	The annual depreciation deduction for tax purposes has been approximated, based on the statutorily allowed recovery period of 27.5 years for residential real estate.
	The allocation of the annual debt payments between principal and interest has been assumed to be the same each year. (This is usually not the case, except for an interest-only loan.)


Preliminary Computations of Amounts to be Used in Cash Flow Summary

	Initial cash outlay
		Cost (purchase price of investment property)		100,000
		Fees paid (in connection with the purchase)		1,000
		Total acquisition cost		101,000
		Less amount financed (debt)		(60,000)
		Cash spent		41,000

	Annual taxes on investment earnings
		Annual taxable income (loss)
			Operating or investment income	5,000
			Less interest portion of debt payments (assumed)	(4,000)
			Less depreciation	(2,571)
			Net taxable income (loss)	(1,571)
		Combined federal and state tax bracket		33%
		Tax on taxable income (tax benefit of taxable loss)		(518)


Computations Upon Disposition of Investment Property to Arrive at the Net Proceeds from Sale, Net of Taxes
	Amount realized upon sale of investment property
		Annual growth rate				5.0%
		Years property held				5
		Appreciation % (change in value, based on annual growth rate and number of years property held)
						27.628%
		Initial value				100,000
		Sales value after 5 years				127,628
		Commission and selling expense @			7.0%	(8,934)
		Amount realized				118,694

	Mortgage balance at time of sale
		Amount borrowed				60,000
		Less principal payments made (assumed)	5 years	@	2,000	(10,000)
		Remaining balance to payoff upon sale				50,000

	Income taxes on sale of investment property
		Amount realized				118,694
		Less cost				(101,000)
		Profit on sale				17,694
		Add back depreciation allowed				12,855
		Gain on sale				30,549

		Recapture tax on portion of gain attributable to depreciation @			25%	3,214
		Capital gains tax on profit @			20%	3,539
		Total federal tax				6,752
		State tax on gain @			6%	1,833
		Combined federal and state taxes on sale				8,585

	Net proceeds from sale, net of taxes
		Amount realized upon sale of investment property				118,694
		Less payoff of debt				(50,000)
		Net proceeds from sale				68,694
		Less taxes paid on sale of investment property				(8,585)
		Net proceeds from sale, net of taxes				60,109


Cash Flow Summary and Rate of Return on Investment Calculation

					Net
		Annual		Annual	Proceeds
		Operating	Annual	(Taxes)	from Sale,	Net
		or Investment	Debt	or Tax	Net of	Cash
	Investments	Income	Payments	Benefit	Taxes	Flows
Year
0	(41,000)					(41,000)
1		5,000	(6,000)	518		(482)
2		5,000	(6,000)	518		(482)
3		5,000	(6,000)	518		(482)
4		5,000	(6,000)	518		(482)
5		5,000	(6,000)	518	60,109	59,627

	(41,000)	25,000	(30,000)	2,590	60,109	16,699


	Achieved Rate of Return on Investment ------------>					6.94%
		This figure was calculated by applying the IRR method to the Net Cash Flows


Proof of Rate of Return Computation
		Increase
	Investments	in Value @	Investments
	(Cash	6.94%	+	Investment
	Outflows)	per year	Increase	Balance
Year
0	41,000		41,000	41,000
1	482	2,845	3,327	44,327
2	482	3,076	3,558	47,885
3	482	3,323	3,805	51,689
4	482	3,587	4,069	55,758
5		3,869	3,869	59,627

	42,928	16,699	59,627

This schedule computes the annual increases in the value of the investment (i.e., the annual earnings) for the initial and subsequent amounts invested. The annual earnings are computed by applying the IRR, computed in the previous table, to the value of the investment at the end of the prior year. This schedule is a mathematical "proof" that the computed IRR is correct. In reality, most investments, except for bank deposits and certain kinds of bonds, do not increase in value by the same percentage each year. The IRR computation computes the annual increase in value that was achieved by the investment AFTER it has been disposed of, according to the hypothetical terms of the model.

SENSITIVITY
As stated above, a key assumption in this rate of return model is the annual appreciation rate - the percentage increase in the value of the property each year it is held. The rate of return is "sensitive" to this variable. It is logical to ask WHAT IF the assumed rate of appreciation is more or less than the amount assumed in the above calculations. To answer this question, the "sensitivity analysis" below computes the IRR for each specified annual rate of appreciation in column B. The values in column C are the annual rates of return (or earnings) on the amounts of cash invested.

Since many people think of an investment growing from the time of purchase to the time of sale, column A below calculates the increase in value of the investment over the period it is held for each of the tested annual rates of appreciation in column B.


SENSITIVITY ANALYSIS
A	B	C
Increase in Value of Investment (Col. B compounded over 5 years)	Equivalent Annual Rates of Appreciation	Resulting Internal Rates of Return

15.93%	3%	3.82%
27.63%	5%	6.94%
40.26%	7%	9.94%
53.86%	9%	12.85%
68.51%	11%	15.68%
84.24%	13%	18.45%
101.14%	15%	21.16%
119.24%	17%	23.81%

Computations Upon Disposition of Investment Property to Arrive at the Net Proceeds from Sale, Net of Taxes

SENSITIVITY ANALYSIS

Computations Upon Disposition of Investment Property to Arrive at the
Net Proceeds from Sale, Net of Taxes