Discounting Problems
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
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%:
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 :
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:
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%:
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
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):
