# Problem Statement by ewghwehws

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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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