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Discounting Problems
Andi Wijayanto, S.Sos, M.Si

Simple Discounting Problems
Example 1
 What is the present value of the right to receive
$25,000 in five years, discounting at 6.5% per
annum?
 Function required:
=PV(rate, nper, pmt, fv, type)
=PV(6.5%,5,0,25000,0)
= –$18,247.02
 The following cross-check formula does indeed return
$25,000
=FV(6.5%,5,0,-18247.02,0)

Simple Discounting Problems
EXAMPLE 2
 A property yields a rental of $25,000 for the next 25
years. If I discount at 8%, how much should I pay?
Assume a zero value after 25 years and that rent is

paid annually in arrears.
 Function required: PV(rate, nper, pmt, fv, type)
 The following formula returns –$266,869.40:
=PV(8%,25,25000,0,0)
 This result can be checked using the RATE function.
This formula returns 8.00%:
=RATE(25,25000,-266869.40,0,0)

Simple Discounting Problems
EXAMPLE 3
 A property currently worth $2,000,000 is subject to a lease
at a peppercorn rent for five years. A purchaser has paid
$1,750,000 for it. Assuming no future growth in value,
what was the discount rate?
 Function required: RATE(nper, pmt, pv, fv, type, guess)

=RATE(5,0,-1750000,2000000,0)
= 2.706609%
 To check the answer, use this formula :

=FV(2.706609%,5,-1750000,0)

Simple Discounting Problems
EXAMPLE 4
 A leasehold interest in a property was recently sold
for $230,000. The lease had four years to run, and
rent was payable at $6,000 per month in advance
without rent review or escalation. If we accept a yield
of 0.75%, what profit rent is shown by the
transaction? Profit rent is the rental value minus the
rent paid.
 Function required: PMT(rate, nper, pv, fv, type)
 The following formula returns $5,680.95:
=PMT(0.75%,48,-230000,0,1)

Complex Discounting Problems
EXAMPLE 5
 If I discount at 0.75% per month, how much should I pay
for a property yielding $25,000 per month in advance
(which I estimate will be worth $5,000,000 in five years)?

 Function required: PV(rate, nper, pmt, fv, type)
 The following formula returns –$4,406,865.34:
=PV(0.75%,60,25000,5000000,1)
 This example uses a rate per month, and payments are
monthly. Therefore, the nper argument has been converted
to months.
 We can check this calculation by using the RATE function.
The following formula returns 0.75%:
=RATE(60,25000,-4406865.34,5000000,1)

Complex Discounting Problems
EXAMPLE 6
 I paid $1,200,000 for a property that yields a rent of
$12,000 per month in advance. If I sell it in five years for
$1,500,000, what yield will I receive?
 Function required: RATE(nper, pmt, pv, fv, type, guess)
 The following formula returns 1.29136%:
=RATE(60,12000,-1200000,1500000,1)
 This result can be verified by using the PV function. The
following formula returns –$1,200,000.00:

=PV(1.29136%,60,12000,1500000,1)

Complex Discounting Problems
EXAMPLE 7
 A property has been purchased for $1,600,000. It yields a
rent of $10,000 per month in advance. If I am to secure a
yield of 1% per month, what must the property be worth in
five years when I plan to sell it?
 Function required: FV(rate, nper, pmt, pv, type)
 This formula returns $2,081,851.05:
=FV(1%,60,10000,-1600000,1)
 This result can be verified using the following formula
(which returns –$1,600,000):
 =PV(1%,60,10000,2081851.05,1)

Referensi
 Walkenbach, John. 2001. Excel 2002

Formulas. New York: M&T BooksAn imprint
of Hungry Minds, Inc.

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