Real estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions

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1 Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 3-1 a) Future Value = $12,000 (FVIF, 9%, 7 years) = $12,000 ( ) = $21,936 (annual compounding) b) Future Value = $12,000 (QFVIF, 9%, 7 years) = $12,000 ( ) = $22,375 (quarterly compounding) c) Equivalent annual yield: (consider one year only) Future Value of (a) = $12,000 (FVIF, 9%, 1 year) = $12,000 (1.09) = $13,080 ($13,080 - $12,000) / $12,000 = 9.00% effective annual yield Future Value of (b) = $12,000 (QFVIF, 9%, 1 year) = $12,000 ( ) = $13,117 ($13,117 - $12,000) / $12,000 = 9.31% effective annual yield Alternative (b) is better because of its higher effective annual yield. Problem 3-3 Find the present value of $15,000 discounted at an annual rate of 10% for 10 years. Present Value = $15,000 (PVIF, 10%, 10 years) = $15,000 (.38554) = $5,783 (annual compounding) The investor should not purchase the lot because the present value of the lot (discounted at the appropriate interest rate) is less than the current asking price of $7,000. If the investor purchases the lot, the effective yield on the investment will be: Effective Yield = (15,000/7,000) ^.1-1 = ( ) ^.1-1 = 7.9% (rounded) Problem 3-4

2 Find the present value of $45,000 discounted at an 18% annual rate compounded quarterly for a six year period. Present Value = $45,000 (QPVIF, 18%, 6 years) = $45,000 (.34770) = $15,647 should be paid today Note that a quarterly interest factor is used in this problem because the investor indicates that an annual rate of 18% is desired. Problem 3-7 Year Amount Deposited FVIF Future Value 1 $2,500 x (FVIF, 9%, 4 yrs.) or $3,529 2 $0 x (FVIF, 9%, 3 yrs.) or $0 3 $750 x (FVIF, 9%, 2 yrs.) or $891 4 $1,300 x (FVIF, 9%, 1 yr.) or $1,417 5 $0 $0 Total Future Value = $5,837 The investor will have $5,837 on deposit at the end of the 5th year. *Each deposit is made at the end of the year Problem 3-9 a) Find the present value of 8 years of monthly payments, or 96 payments, of $750 (end-of-month) discounted at an interest rate of 17 percent compounded monthly. Present Value = $750 (MPVIFA, 17%, 8 years) - ordinary annuity = $750 ( ) = $39,223 should be paid today b) The total sum of cash received over the next 8 years will be: 8 years x 12 payments per year x $750 per month = $72,000 c) Total cash received by the investor $72,000 Initial price paid by the investor $39,223 Difference: Interest Earned $32,777 The difference represents the total interest earned by the investor on the initial investment of $39,223 if each $750 payment received earns 17 percent compounded monthly Problem 3-11 Annual sinking fund payments required to accumulate $50,000 after ten years Future Value = Payment x (FVIFA, 10%, 10 years) Payment = Future Value / (FVIFA, 10%, 10 years)

3 = $50,000 / ( ) = $3,137 per year Note to Instructor: In problem 3-11(b), the text requests that annual payments be calculated, that is, 12 x monthly payments.

4 Monthly sinking fund payments required to accumulate $50,000 after ten years. Future Value = Payment x (FVIFA, 10%, 10 years) Payment = Future Value / FVIFA, 10%, 10 years) = $50,000 / ( ) = $ per month Note: Some text use a sinking fund factor (SFF) that can be multiplied by the desired ending amount in order to find the payment. As an example, $50,000 x (SFF, 10%, 10 years) would give the $3,137 annual payment. The SFF is nothing more than 1/ (FVIFA, 10%, 10 years) or the reciprocal of the appropriate future value of an annuity interest factor. Problem 3-12 What will be the rate of return (yield) on a project that initially costs $100,000 and is expected to pay out $15,000 per year for the next ten years? The solution must be interpolated: Present Value = Payment x (PVIFA,?%, 10 years) $100,000 = $15,000 (PVIFA,?%, 10 years) = (PVIFA,?%, 10 years) Looking to the annual tables, we are seeking a value of in the column for a 7 year period. This value falls between 7% and 10%. Interpolation yields the following estimate: 7% = % = % = Desired PVIFA = / x (10.0% - 7.0%) = 1.22% 7.0% % = 8.22% An exact calculator solution is: 8.14% This is a poor investment for Buildsmart because the IRR of 8.14% does not exceed Buildsmart s desired return of 9%. Problem 3-13 What will be the rate of return (yield) on a project that initially costs $75,000 and is expected to pay out $1,020 per month for the next 25 years? The solution must be interpolated: Present Value = Payment x (MPVIFA,?%, 300 months) $75,000 = $1,020 (MPVIFA,?%, 300 months)

5 = (MPVIFA,?%, 300 months) In the annuity tables, we are seeking a value of in the MPVIFA column for a 25 year period. This value falls between 15% and 20%. Interpolation yields the following estimate: 15% = % = % = Desired PVIFA = / x (20.0% %) = 1.23% 15.0% % = 16.23% An exact calculator solution is : 16.01% The total cash received will be: $1,020 x 25 years x 12 months = $306,000 How much is profit and how much is return on capital? Total Amount Received $306,000 Total Capital Invested (returned) $75,000 Total Profit (interest earned) $231,000 The total cost of the investment, $75,000, is capital recovery. The difference between the total amount received and the capital recovery is total profit earned. Problem 3-16 a) Find the ENAR for 10% EAY - Monthly Compounding. ENAR = [( 1 + EAY) ^ (1/m) - 1] x m = [( ) ^ (1/12) -1] x 12 = [ ] x 12 = [ ] x 12 = or 9.57% b) Find the ENAR for 10% EAY - Quarterly Compounding ENAR = [( 1 + EAY) ^ (1/m) x m = [( ) ^ (1/4) -1] x 4 = [ ] x 4 = [ ] x 4 = or 9.56% Problem 3-17 Part 1, calculate annual returns compounded annually: (Note: calculator should be set for one payment per period) The Annual Rate compounded Monthly: Solution: N = 28 PMT = 1,000 PV = -24,000 FV = 0 Solve for the yield:

6 I = The monthly rate can now be used to calculate the equivalent annual rate. The Annual Rate compounded Annually = Solution: PV = -1 I = PMT = 0 N = 12 Solve for the future value: FV = The annual rate of interest (compounded annually) needed to provide a return equivalent to that of an annual rate compounded monthly is: FV - PV = = % This return is far greater than the annual rate compounded monthly Mo.yld x no. mos.=1.0957x12 = % This tells us that an investor would have to find an investment yielding % if compounding occurred on an annual basis (once per year) in order for it to be equivalent to an investment that provides an annual rate of % compounded monthly. Chapter 3: The Interest Factor in Financing Sample Exam Questions MC 3-1 The future value of a single deposit of $1,000 will be greater when this amount is compounded: A. annually B. semi-annually C. quarterly D. monthly MC 3-3 If you saw a table containing the following factors, what kind of interest factor would you be looking at? A. Present value of a single amount B. Future value of a single amount C. Present value of an annuity D. Future value of an annuity MC 3-7 If an investment earns 12% annually, End of Year 6%

7 A. an equivalent monthly investment would have to earn a higher equivalent nominal rate to yield the same return. B. an equivalent monthly investment would have to earn a lower equivalent nominal rate to yield the same return. C. an equivalent monthly investment would have to earn the same equivalent nominal rate to yield the same return. D. a relation cannot be determined between a monthly and annual investment. MC 3-8 The internal rate of return: A. is also known as the investment of investor s yield. B. represents a return on investment expressed as a compound rate of interest. C. is calculated by setting the price of an investment equal to the stream of cash flows it generates and solve for the interest rate. D. can be defined by all of the above. The following questions are true-false. TF 3-11 In order to solve a compounding problem, you must know all four of its basic parts. TF 3-12 One way to calculate the present value of a single payment is with the following formula: PV = FV * (1+i) n. TF 3-13 At 6%, the present value of a $1 payment in 12 months is At 7%, the present value of a $1 payment in 12 months is TF 3-14 The future value of $800 deposited today would be greater if that deposit earned 8% rather than 7.75%. TF 3-15 You are able to calculate the present value of an annuity by understanding the following relationship: FV = PV (1+I) TF 3-16 You usually see an ordinary annuity used in business and rarely see an annuity due used in business. TF 3-17 The internal rate of return is the good feeling you get inside when you earn a return on your investment. TF 3-18 An investment may have more than one internal rate of return. TF 3-19 Assume that an investment, with an single initial cost of $1,000 and a yield of $50 monthly for 10 years, had a 7% IRR in the 60th month and a 7.2% IRR five months later. The IRR can be 6.8% in the 62nd month. TF 3-20 The future value of a $1 annuity compounded at 5% annually is greater than the future value of a $1 annuity compounded at 5% semi-annually.

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