Help with a CG exam question

[gville81]

The appraiser determines the highest and best use of the subject to be a five-year interim use as an office building. After five years, the building will be razed for expansion of the hospital next door. The office building currently generates $15,000 of net operating income growing 3% per year according to the terms of the lease. The yield rate is 9%. What is the current interim use value of the office building, rounded to the nearest $100?

A) $48,700
B) $250,000
C) $166,700
D) $61,600

I'm assuming you would use R=Y-CR, then just use the income and divide by the cap rate. But, the building will be razed and I wonder if you would use the discounted income back to PV? I guess it's fee simple at the end of the day on not leasehold.

 

[Functional Obs]

Wish I knew the answer... Can you ask one of your instructors? The ones I've had through the Appraisal Institute and McKissock have usually provided their email addresses.

 

[Red Flint]

What are the two answers that are the most unlikely? With the two answers remaining, what is your guess?

You are only given an I and and R (plus escalation). What can you do with those numbers?

When the building is razed, what is the value? Is it zero?

 

[JTip]

A five-year interim use implies that we need to calculate the present value of the net operating income (NOI) for five years, with a 3% annual growth rate, and then account for the fact that the building will be razed afterward (meaning no residual value from the building itself).

Here's how to calculate the current interim use value:

1. Calculate the Present Value of the Growing Annuity (NOI for five years):

We can use the formula for the present value of a growing annuity:

PV=∑t=1n(1+r)tNOI0×(1+g)t

Where:

• PV = Present Value
• NOI0 = Initial Net Operating Income ($15,000)
• g = Growth rate (3% or 0.03)
• r = Yield rate (9% or 0.09)
• t = Year (1 to 5)
• n = Number of periods (5 years)

Alternatively, we can calculate each year's present value and sum them:

• Year 1 NOI: $15,000 \times (1 + 0.03)^1 = $15,450
• Year 1 PV: $15,450 / (1 + 0.09)^1 = $14,174.31
• Year 2 NOI: $15,000 \times (1 + 0.03)^2 = $15,913.50
• Year 2 PV: $15,913.50 / (1 + 0.09)^2 = $13,391.80
• Year 3 NOI: $15,000 \times (1 + 0.03)^3 = $16,390.91
• Year 3 PV: $16,390.91 / (1 + 0.09)^3 = $12,654.40
• Year 4 NOI: $15,000 \times (1 + 0.03)^4 = $16,882.64
• Year 4 PV: $16,882.64 / (1 + 0.09)^4 = $11,960.91
• Year 5 NOI: $15,000 \times (1 + 0.03)^5 = $17,389.12
• Year 5 PV: $17,389.12 / (1 + 0.09)^5 = $11,309.28

Sum of Present Values (Interim Use Value):

$14,174.31 + 13,391.80 + 12,654.40 + 11,960.91 + 11,309.28 = $63,490.70

2. Round to the nearest $100:

$63,490.70 rounded to the nearest $100 is $63,500.

The current interim use value of the office building is $63,500.This problem requires calculating the present value of a growing annuity (the income generated by the office building) for a fixed period (five years).

Here's the formula for the present value of a growing annuity:

PV=PMT∗r−g1−(1+r1+g)n

Where:

• PV = Present Value
• PMT = First period's payment (Net Operating Income in Year 1)
• g = Growth rate of income
• r = Yield rate (discount rate)
• n = Number of periods

Given:

• PMT = $15,000
• g = 3% = 0.03
• r = 9% = 0.09
• n = 5 years

Let's plug in the values:

PV=15,000∗0.09−0.031−(1+0.091+0.03)5

PV=15,000∗0.061−(1.091.03)5

First, calculate (1.091.03)51.091.03)5≈(0.944954)5≈0.760195

Now, substitute this back into the formulaV=15,000∗0.061−0.760195

PV=15,000∗0.060.239805

PV=15,000∗3.99675

PV≈59,951.25

Rounding to the nearest $100, the current interim use value of the office building is $60,000.

The current interim use value of the office building is $60,000.

lol thanks Gemini

 

[Gobears81]

Agree that D is the answer. I wonder why Gemini is coming out to $63500 though.

The interim use value term is a little confusing.

The R = Y-G formula is not appropriate, as it is not to perpetuity.

 

[Elliott]

The simplest method is always the best.

 

[Greg Graybadger]

We are not really valuing the building, but rather the income stream over the five year interim holding period. We are in Year 1, ("...currently generates..."} so no escalation is applied to its $15,000 cash flow. Cash flows escalate by 3% each year, so they are CF1=$15,000; CF2=$15,450; CF3=$15,913.50; CF4=$16,390.91; CF5=$16,882.63. If these cash flows are produced by a 9% yield rate, the Present Value is $61,637.85. This is rounded to $61,600 which is exactly choice D. We could argue that this is not actually "the interim use value of the office building" but remember that this is just the test to start working as a Certified General Appraiser, so that terminology is probably used loosely.