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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
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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. • Slide ini dapat didownload di: http://andiwijayanto.blog.undip.ac.id
