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					                    Problem Statement


Suppose you purchase a parcel of land today
  for $25,000.00 (PV) and you expect it to
  appreciate in value at a rate of 10% (I) per
  year. Calculate how much your land will be
  worth 10 years (N) from now.
                Problem Identification

• Can you tell that this calculation is asking
  you to derive the future value of a LUMP
  SUM?
  – No payment stream is described in the problem
    statement.
  – No costs, income or improvements to the land
    are mentioned in the problem statement.
                                 Problem Solution

   terms       given/?             formula           solution
N (periods)       10
I (%)           10%
PV ($)      $ (25,000.00)
PMT ($)            0
FV ($)             ?      =FV("I","N","PMT","PV")   $64,843.56
     Try This One on Your Own …

You purchase a piece of real estate today for
 $15,000.00 and expect to hold the property
 for 7 years. You currently expect that the
 rate of property appreciation is 15% per
 year for this property. What is your
 expected valuation of this property in 7
 years time?
                  Problem Statement

Assume that you deposit $50.00 (PMT) per
 month in a guaranteed account offering a
 fixed return of 10% per year (I). How much
 will you have accumulated over a 12 year
 period in this account?
                Problem Identification

• Can you tell that this calculation is asking
  you to derive the future value of an
  ANNUITY?
  – No PRESENT VALUE is given in the problem
    statement (PV = $0.00).
  – Payments are accumulating at a monthly rate;
    Some care will need to be taken to properly
    perform this calculation.
                                Problem Solution

   terms      given/?           formula           solution
N (periods)     144              N *12
I (%)         0.833%             I / 12
PV ($)      $        -
PMT ($) $ (50.00)
FVa ($)          ?     =FV("I","N","PMT","PV")   $13,821.89
     Try This One on Your Own …

You purchase a parcel of land today for
 $50,000. How much will you expect to sell
 this property for in 15 years to earn both
 your $50,000 outlay and expect annual
 payments of $1,000 for taxes and insurance.
 Assume that these funds could be invested
 at comparable risk to earn a 10% per year
 return.
                    Problem Statement

If you wish to accumulate $10,000 in a bank
   account in 8 years at a 15% annual interest
   rate which compounds monthly, how much
   should you deposit in order to meet your
   cumulative goal?
                  Problem Identification

• Can you tell that this calculation is asking
  you to derive a SINKING FUND
  PAYMENT?
  – The given factors include the future value ($10,000)
  – The present value is not stated (implying PV = $0)
  – The period and compounding structure of the
    investment is given (N = 8*12)
  – And the interest factor is also given (I = 15% / 12)
                                  Problem Solution
   terms       given/?            formula           solution
N (periods)       96               N *12
I (%)         1.250%               I / 12
PV ($)      $         -
PMT ($)            ?      =PMT("I","N","PV","FV")         ($54.45)
FVa ($)       $10,000
     Try This One on Your Own …

You purchase a building (exclusive of land)
 for $50,000. The building is expected to
 depreciate to $0 over the next 50 years. If
 amounts to cover each year’s depreciation
 are taken from the building’s income and
 invested at 10% per year, how much must
 the annuities allocated for depreciation
 amount to ?
                    Problem Statement

If someone owes you $1,000 due in five years,
   that can be discounted at a 10% annual rate,
   what sum of money TODAY would clear
   such a debt?
                  Problem Identification

• Can you tell that this calculation is asking
  you to derive a PRESENT VALUE OF A
  LUMP SUM?
  – The given factors include the future value ($1,000)
  – The period and compounding structure of the
    investment is given (N = 5)
  – And the interest factor is also given ( I = 10% )
                                 Problem Solution

   terms       given/?             formula          solution
N (periods)       5                   N
I (%)         10.000%                 I
PV ($)            ?       =PV("I","N","PMT","FV")   ($620.92)
PMT ($)     $         -
FVa ($)        $1,000
       Try This One on Your Own …
You wish to purchase a property today for which the owner is
  asking $62,500. However, the property is leased to a third
  party for the next 5 years. You believe the property is still
  a good investment and decide to structure the deal so that
  you get the property ‘s title and possession at the end of the
  lease term, and where the rental income goes to the current
  owner. You concede that the property will be worth the
  same nominal amount five years from now, and insist that
  this future value be discounted at 10% per year. How
  much are you willing to pay today for the property rights
  described herein?
                     Problem Statement

If you are retiring and one of your benefit
   options is to accept annuity payments of
   $75,000 per year for 15 years, calculate the
   equivalent full distribution TODAY that
   would provide you with the same income
   using a 10% annual discount rate.
                  Problem Identification

• Can you tell that this calculation is asking
  you to derive a PRESENT VALUE OF AN
  ANNUITY?
  – The given factors include the annuity payments of
    $75,000.
  – The period and compounding structure of the
    investment is given (N = 15).
  – The interest factor is also given ( I = 10% ).
  – And the implied future value is $0.
                                Problem Solution

   terms      given/?            formula          solution
N (periods)      15                 N
I (%)        10.000%                I
PV ($)            ?     =PV("I","N","PMT","FV")    ($570,455.96)
PMT ($)     $ 75,000.00
FVa ($)         $0
     Try This One on Your Own …

Contemplate the acquisition of a property that
 will be worth $50,000 at the end of a 20
 year period, from which you expect to
 receive fixed annual payments of $10,000,
 discounted at a 10% annual rate for present
 value.
How much should you offer to pay for such
 property?
                     Problem Statement

• You want to purchase a house priced
  $80,000. You qualify for an 80% monthly
  payment loan for 29 years at an annual
  interest rate of 15%. Calculate the fixed
  monthly payment amount, and the
  percentage of the original loan amount
  covered by your monthly loan payment.
               Problem Identification

• Can you tell the purpose of this problem is
  use the mortgage constant, Rm, to calculate
  the fixed monthly payment?
  –…
                                 Problem Solution

   terms       given/?            formula           solution
N (periods)      348                N*12
I (%)            1%                 I/12
PV ($)      $ (80,000.00)
PMT ($)           ?       PMT("I","N","PV","FV")   $1,013.44
FV ($)      $         -

 Rm = PMT/PV
    = $1,013.44 / $80,000.00 = 1.267%
     Try This One on Your Own …

What percentage of the original loan amount
 is the annual total amount of your monthly
 payments (cap rate)?

				
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