Discounting Problems

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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

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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%:

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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 :}

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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:}

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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%:

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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}

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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):

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Discounting Problems - Diponegoro University | Institutional Repository (UNDIP-IR)