Lesson 19 Exercises – Valuation of Leased Personal Property (The Income Approach to Value)

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  1. A national manufacturer leases reproduction machines to various businesses within your county. The machines are leased for a one-year term. The rental income is based on the volume of copies produced. The average annual gross income of all machines on lease is reported as $2,700 per machine. The rental income includes a component for sales tax. The reported income appears to be economic in this market.

    You have determined that the machines have an average total life of seven years; however, the average remaining economic life of the machines on lease, as of the lien date, is estimated at four years. Property taxes are 1 percent of the full cash value. Yield rates derived from sales indicates a 13½ percent return. The return on the investment is based on a level terminal income stream premise.

    Other pertinent information:

    • The manufacturing cost per machine is $2,000.
    • The number of new machines held in inventory at the manufacture's warehouse, which is located in your county, is 10 machines.
    • The number of machines on lease in your county as of the lien date is 50.
    • Typical annual expenses (per machine) of machines on lease are $500 for maintenance and $200 for insurance. The expenses are borne by the manufacturer.
    • The salvage value per machine is $500.

    Estimate the taxable value of the machines owned by the manufacturer in your county.

A. Valuation of the Rental Income
Per Machine
Total Machines
Market Potential Gross Income (PGI)
$2,700
$135,000
Market Vacancy & Collection Loss (V&CL)
(0)
(0)
Market Effective Gross Income (EGI)
$2,700
$2,700
Maintenance
$200
Insurance
$500
$700
$35,000
Market Net Income Before Recapture & Taxes (NIBT)
$2,000
$100,000
$2,000 (NIBT) / [0.339693 (PR, 13½%, Ann, 4 yrs)] + [1% (ETR)]
=
$5,719
$285,965

Alternate methods:

$2,000 NIBT ÷ 0.346729 PR {14½%,Ann,4yrs} = $5,768 per machine,

$100,000 NIBT ÷ 0.346729 PR {14½%,Ann,4yrs} = $288,410 total value;

$2,000 NIBT × 2.884098 PW1/P {14½%,Ann,4yrs} = $5,768 per machine,

$100,000 NIBT × 2.884098 PW1/P {14½%,Ann,4yrs} = $288,410 total value.

B. Valuation of the Salvage Income:
Per Machine
Total Machines
Salvage Price
$500
$25,000
PW1, (13½% Yield Rate + 1% ETR), Ann, 4 yrs
0.581806
0.581806
Present Value of Salvage Income
$291
$14,545
C. Total Property Value:
Per Machine
Total Machines
Present Value of Rental Income
$5,719
$285,965
Present Value of Salvage Income
$291
$14,545
Total Value
$6,010
$300,510
  1. You are assigned the task of valuing a group of thirteen photocopiers owned by a leasing company.

    These copiers are all on lease in the same city under two-year leases of $1,375 annually per copier. In addition to this flat fee, a charge of 1¼¢ per copy is made, and each machine makes an average of 32,000 copies per month.

    The lessee pays for all delivery costs, the toner and developer fluids, and paper. The company provides all services and maintenance as part of the lease terms, and pays all property taxes. Expenses to the lessor equate to 12 percent of the gross income.

    The machines have a seven-year remaining economic life; with no salvage value at the end of the seven years.

    The appropriate discount rate is considered equivalent to the yield on AAA corporate industrial bonds, which currently is 12½ percent. The effective property tax rate is 1 percent.

    Estimate the taxable value of the photocopiers owned by this leasing company in your county.

Valuation of the Rental Income

Per
Machine
Total
Machines
Potential Gross Income [PGI]
Annual Rental
$1,375
$17,875
Income from copies:
+ $4,800
+ $62,400
Vacancy & Collection Loss [V&CL]
− $0
− $0
 
Effective Gross Income [EffGI]
$6,175
$80,275
Expenses at 12%
− $741
− $9,633
 
Net Income Before deducting for recapture & Taxes (NIBT)
$5,434
$70,642
÷ (12½% Y + 0.097603 SFF{12½%,Ann,7yrs} + 1% ETR)
÷ 0.232603
÷ 0.232603
 
Indicated Property Value
$23,362
$303,702

Alternate methods

using the Periodic Repayment factor:

$5,434 NIBT ÷ 0.229641 PR {13½%,Ann,7yrs} = $23,663 per machine,

$70,642 NIBT ÷ 0.229641 PR {13½%,Ann,7yrs} = $307,620 total value;

using the Inwood Coefficient:

$5,434 NIBT × 4.354630 PW1/P {13½%,Ann,7yrs} = $23,663 per machine,

$70,642 NIBT × 4.354630 PW1/P{13½%,Ann,7yrs} = $307,620 total value.