# Comments on "risk and reasonableness for nonmarket occupancy".

In their April 2003 Appraisal Journal article, Richard L. Parli, MAI, and Jeffrey D. Fisher, PhD, present a technique for valuing a leased fee interest that adjusts the fee simple estate for income detriment or benefit associated with below-market rent, below-market occupancy and above-market rent. While all the conclusions of impact to fee simple value generally appear sound, the supporting rationale for Case II-Below-Market Occupancy strikes me as not only confusing, but also suspect.In this case study an example is given of a property suffering above-market vacancy Although the presumption is for eventual market occupancy, the income forecast is considered less certain, and, therefore, riskier than that of a stabilized asset. Added exposure associated with the absorption has upward influence on a yield rate appropriate for projected income.

Various tools are available to address this problem. The overall anticipated income stream could be discounted with a blended rate recognizing component risk accruing to contract and speculative revenue. Alternately, risk-appropriate discount rates could be applied separately to these two components. A third option selected by the authors measures the impact that market income shortfalls have on the fee simple estate.

The reader is led along a circuitous path in the effort to support a premise that rent shortfalls must be discounted at a lower than fee simple rate. The conclusion for relativity of rates is sound, but the reasoning falls short.

The position is taken in the third full paragraph, page 140 that "... the leased fee income from existing leases and lease renewals in this case is more risky and must be discounted at a higher rate (with a lower rate applied to the rent loss)." This statement is backed up with footnote 5 "... income from projected leasing of occupied space is what makes this more risky than in the case of the below-market lease."

I am at a loss to understand the logic. Why is projected lease renewal in this example viewed as more risky than when under-market rents were formerly present? Of course, tenant-favorable rent carries less risk for collection, but how does this bear on market-executed renewals? All other things equal, attainable rent is no less certain on the re-lease of space formerly under-performing than for space previously rented at market. In fact, the argument could be made, with some merit, that increasing below-market rent is a riskier effort due to possible "sticker shock" reactions from existing tenants.

Another attempt is made to justify the discount rate conclusions in the first full paragraph of column two, page 140, with the assertion "... the income based on projected income from occupancy due to existing leases and (emphasis added) projected rent-up of space would have to be discounted at a higher rate." No argument is made with this statement when it stands alone. However, it does not work when combined with the first part of the same sentence "... rent loss is discounted at a lower rate."

What it becomes is a three-part solution to a two-part issue. If a risk-adjusted yield rate is applied to income from both existing leases and projected rent-up, the problem is solved. There remains no room in this leased fee equation to include an offset for income lost through vacancy.

The authors' approach becomes clear when rent shortfalls are addressed for what they are: negative cash flow to the fee simple estate. With negative cash flows, lower yield rates convey greater risk, as they distance the loss further from zero. When this is understood, the temptation disappears to find additional support rationalizing a reduced rate.

This article conveys the proper result of adjusting fee simple value for rent loss accruing during the lease-up phase. However, it misfires on the mechanics.

Dan P. Mueller, MAI

St. Paul, Minnesota

Response--Comments on "Risk and Reasonableness for Nonmarket Occupancy"

We appreciate Mr. Mueller's interest in our article and taking the time to comment on our discussion of the discount rate for the rent to below-market occupancy. We believe that what appears to be a difference in opinion regarding the theory or logic that we used in this case is really a misunderstanding by Mr. Mueller as to how we defined rent loss and other income streams discussed in the article. In fact, as we will point out, once you get past the semantics, you find that we are all in agreement regarding the use of a lower discount rate. Mr. Mueller states "the conclusion for relativity of rates is sound;" he just doesn't follow our reasoning. We hope to clarify that below.

Mr. Mueller asks, "Why is projected lease renewal in this example viewed as more risky than when under-market rents were formerly present?" We never made this claim. In Exhibit I we show projected income from lease rollovers and indicate it is higher risk (than income from existing leases), which would imply using a higher discount rate. Similarly in Exhibit II we state that projected income from leasing of vacant space would be the greatest risk (relative to the other income streams in that exhibit) and indicate that it would have a higher discount rate. The risk for these two income streams could be exactly the same in both cases (both exhibits). There was never any direct comparison of the two.

The difference between Exhibit I and Exhibit II is in the interpretation of income from leases currently in place, which is the bottom curve in both exhibits. In the case of below-market leases, the rent is below market. Cleary there is less risk the more that existing leases are below current market rents. The risk is that market rents fall below the rent level from existing leases, wiping out the leasehold value. The lower the contract rent, the less risk that this will happen. But in the case of below-market occupancy, we are NOT saying that rents are below market. We are trying to isolate below-market rent (Case I) from below-market occupancy (Case II). So in the case of below-market occupancy, existing leases are at market rents, which is why it states in the exhibit that it would have "roughly the same risk and discount rate as income as if at market occupancy."

So if we focus on Exhibit II, as stated above, income based on leases currently in place at market rent (bottom curve) is about the same risk as income as if stabilized at market occupancy (top curve). And we already established (and Mr. Mueller agrees) that projected income from leasing vacant space is riskier. Therefore, the sum of the income based on leases currently in place plus the projected income from leasing vacant space (which is the total leased-fee income) has to be greatest risk. (The second quote Mr. Mueller uses from our article used the word "and" which he put in bold in his letter. Perhaps this word should have been "plus" because we are referring to the addition of these two income streams to get the leased-fee income.)

From the above discussion it should be clear that the leased-fee income (when there is below-market occupancy) is riskier than income as if stabilized at market occupancy and, therefore, has a higher discount rate than would be applied to the income as if stabilized at market occupancy. Therefore, the "income loss" (which is the shaded area in Exhibit II) MUST have a lower discount rate because the leased fee income plus the income loss (income from lease-up of the occupied space) is equal to the income as if stabilized at market occupancy.

It is interesting that at the end of Mr. Mueller's comments he seems to be agreeing with us when he states "The authors' approach becomes clear when rent shortfalls are addressed for what they are: negative cash flow to the fee simple estate. With negative cash flows, lower yield rates convey greater risk, as they distance the loss further from zero. When this is understood, the temptation disappears to find additional support rationalizing a reduced rate." So he is agreeing that there should be a lower rate to the rent loss. If he wants to think of it as "negative cash flow to the fee simple" that is fine with us. The point of our article was simply to point out that everything that appraisers might consider deductions from fee simple to arrive at a leased-fee value should not be discounted at the same rate and in some cases the rate would be lower than the fee simple rate and in some cases the rate would be higher than the fee simple rate.

We also agree with Mr. Mueller that applying a risk-adjusted discount rate to the income from existing leases and projected rent-up is appropriate IF you can come up with the correct discount rate. That is also one of the main points of our article--how do you test for the reasonableness of the discount rate? One way is to be sure the rate is consistent with the implied rate for the fee simple estate and the rent loss.

Jeffrey D. Fisher, PhD, CRE

Bloomington, IN

Richard L. Parli, MAI

Fairfax, VA

Questions on "Risk and Reasonableness for Nonmarket Occupancy"

I enjoyed "Risk and Reasonableness for Nonmarket Occupancy" by Richard L. Parli, MAI, and Jeffrey D. Fisher, PhD (April 2003). I understand the point of the article to be that appraisers need to analyze the cause for nonmarket occupancy in order to develop a reasonable opinion about whether the discount rate should be greater than or less than the discount rate for the valuation of the fee simple interests. I use this methodology in my practice.

The article shows the impact on value for various assumptions for the discount rate on the differential rent. However, I would like to have seen the authors address an important potential error in selecting the discount rate for the rent differential.

I refer readers to page 139 of the article to view Table 3--Rent Differential Valuation--Below-Market Rent, in which the rent differential is calculated with an 18% discount rate. I have added below Table 3A with a discount rate of 25% and Table 3B with a discount rate of 15%.

The indicated values and overall discount rates for the leased fee interests at these discount rates on the differential rents are shown below:

Discount Rate for Value of Leased Overall Differential Rents Fee Interests Discount Rate 15% $938,909 11.90% 18% $942,160 11.81% 25% $948,656 11.63%

Increasing the discount rate on the differential rent increases the value of the leased fee interests and decreases the overall discount rate. Both changes are counterintuitive. An analysis of the below-market occupancy from Table 4 (on page 139) indicates the same problem. The indicated values and overall discount rates for the leased fee interests at discount rates of 4%, 6%, and 9% on the differential are as follows:

Discount Rate for Value ot Leased Overall Differential Rents Fee Interests Discount Rate 4% $923,682 12.33% 6% $926,916 12.23% 9% $931,342 12.11%

An analysis of the above-market rent from Table 7 (on page 143) does not indicate the same problem. The indicated values and overall discount rates for the leased fee interests at discount rates of 15%, 18%, and 25% on the differential rents are as follows:

Discount Rate for Value of Leased Overall Differential Rents Fee Interests Discount Rate 15% $1,065,927 12.13% 18% $1,061,441 12.25% 25% $1,052,722 12.47%

Increasing the discount rate on the differential rents decreases the value of the leased fee interests and increases the overall discount rate. Both changes make sense, so the expected relationships among the discount rate on the differential rents, the overall discount rate, and the value of the leased fee interests hold true for positive rent differentials but not negative ones. Can you explain this?

James A. Fourness, MAI

Appleton, WI

Response--Questions on "Risk and Reasonableness for Nonmarket Occupancy"

Thank you for your insightful comments. Our article was not intended to be a comprehensive treatise on nonmarket occupancy and you point out an area we neglected. The choice of the discount rate to apply to the differences should be a function of the timing, market conditions (in the case of below-market occupancy), and tenant quality (in below/above market rent). We addressed the former lightly in explaining the logic of using a "safe" rate. Reconciling a proper rate given a specific property and market is only possible with good market analysis. However, knowing the impact (and sensitivity) of the choice is certainly an advantage.

It is interesting that in both the below-market occupancy and below-market rent cases, increasing the discount rate of the income loss decreases its impact and thus increases property value (which results in a lower property discount rate)--the inverse is true for above-market rent (increasing the discount rate on the differences results in a relatively lower property value which results in a higher property discount rate). The reason to do with how the quotient is applied--in the latter it is added so there is a direct relationship; in the former it is subtracted so there is an inverse relationship. What we find most interesting is that in the former cases, as the discount rate in each instance approaches the fee simple rate (in this case 12%), the value approaches the value indicated if the cash flows were not segregated but all discounted at the fee simple rate. So what is being accomplished by segmenting the cash flow is a divergence from the value indicated by the fee simple rate--property value is relatively higher in the below-market rent case because the rate is increased; below-market occupancy diminishes the relative value because the rate is decreased.

We hope this is helpful.

Richard L. Parli, MAI

Fairfax, Virginia

Jeffrey D. Fisher, PhD, CRE

Bloomington, IN

Table 3A Rent Differential Valuation--25% Discount Rate for Below-Market Rent Year 1 2 3 Market Income $100,000 $102,000 $104,040 Realized Income ($72,500) ($79,785) ($87,216) Difference $27,500 22,215 $16,824 PV Factor @ 25% 0.80000 0.64000 0.51200 PV of Cash Flow $22,000 14,218 $8,614 Total Present Value $51,344 Year 4 5 6 Market Income $106,121 $108,243 $110,408 Realized Income ($94,795) ($102,526) Difference $11,326 $5,717 PV Factor @ 25% 0.40960 0.32768 PV of Cash Flow $4,639 $1,873 Total Present Value Table 3B Rent Differential Valuation--15% Discount Rate for Below-Market Rent Year 1 2 3 Market Income $100,000 $102,000 $104,040 Realized Income ($72,500) ($79,785) ($87,216) Difference $27,500 $22,215 $16,824 PV Factor @ 15% 0.86957 0.75614 0.65752 PV of Cash Flow $23,913 $16,798 $11,062 Total Present Value $61,091 Year 4 5 6 Market Income $106,121 $108,243 $110,408 Realized Income ($94,795) ($102,526) Difference $11,326 $5,717 PV Factor @ 15% 0.57175 0.49718 PV of Cash Flow $6,476 $2,842 Total Present Value

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Title Annotation: | letters to the editor |
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Publication: | Appraisal Journal |

Date: | Jul 1, 2003 |

Words: | 2507 |

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