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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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