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CALCULATING Compound Interest, IRR AND NPV 1 Calculating Compound Interest, IRR and NPV This tutorial presents the steps for calculating Internal Rate of Return (IRR), Net Present Value (NPV), simple interest, and compound interest. About this Guide The content, format, and problems in this guide derive from coursework designed by Professor Robert J. Nahigian for REALTOR® University’s Master of Real Estate CRIA course series. For more information, inquiries may be directed to the REALTOR® University Library. The figures in this guide are calculated using Microsoft Excel. Many commercial real estate practitioners use the HP-12C or HP-2B calculator when calculating these formulas. Financial calculators sometimes round numbers in a different manner than Excel, so it is always good to compare numbers in Excel to those calculated using a financial calculator as a means of double checking work. If you do not have either calculator on-hand, check out your smartphone or tablet’s app store, as some app stores offer HP-12C or HP-2B apps. Disclaimer The information contained in this guide is intended for informational and educational purposes only, and does not constitute legal, tax, investment or other professional advice. Those using this guide should independently verify all information provided to ensure its accuracy and compliance with applicable law. Definitions: Internal Rate of Return (IRR) → The IRR is a way for the real estate investor to create a single figure that represents the four economic advantages of real estate, which include: (1) Property appreciation; (2) Cash flow; (3) Tax shelter; (4) Equity build-up). Then this single figure can be used to compare to other real estate investment opportunities (Cassidy, 1986, p. 30). Simple Interest → “interest computed on the original principal alone” (Celec, 1981, p. 128) Compound Interest → “Interest computed on the original principal together with its accrued interest” (Celec, 1981, p. 128). The simple definition is “interest earned on interest.” For an illustrative example, see the Khan Academy’s video Introduction to Compound Interest Net Present Value (NPV) → “NPV is the sum of the present values of an investment’s positive cash flows and the present values of its negative cash flows. CALCULATING Compound Interest, IRR AND NPV 2 This calculation results in a single sum that can be positive or negative” (Valachi, 2000). Question 1: What is your lease rate in Year 5 for the scenario below? Details: Current rental rate: Compound interest rate: $22.51 psf (annual) 3% (annual) Process: 1. This is a compound interest problem, meaning that each year interest is earned upon interest. 2. We will calculate this scenario by hand, so you can learn how compound interest works. 3. Create three columns in an Excel spreadsheet: a. Title the first column “N” b. Title the second column “Amount” c. Title the third column “Notes” 4. In the first column, title the rows 0 through 4 (0 is the current year; 4 is the fifth year of the lease) 5. In the Amount column for year 0 (B2), enter $22.51 6. In the Amount column for year 1, enter =(B2*.03)+B2 7. In the Amount column for year 2, enter =(B3*.03)+B3 8. In the Amount column for year 3, enter =(B4*.03)+B4 9. In the Amount column for year 4, enter =(B4*.03)+B4 10. In the Notes column enter “Y1” in cell C2, “Y2” in C3, and so on. Tip: If calculating compound interest over the course of many years, a shortcut to entering formulas by hand is to enter the first formula in cell B2, then when clicked into cell B2, mouse over the bottom right corner until you get a “+” Click on the + symbol and drag your mouse down for the number of years you wish to calculate compounder interest. The formula should carry over while filling the series of cells with incremental increases (e.g. B3, B4, B5, B6, et seq.). CALCULATING Compound Interest, IRR AND NPV Answer 1: The lease rate in Year 5 is $25.34 psf. 3 CALCULATING Compound Interest, IRR AND NPV Question 2: What is the Internal Rate of Return for the scenario below? Details: Purchase price: Annual NOI: Period: Sale: $1,500,000 $10,500 in Y 1, 2 & 3; $15,300 in Y 4 & 5 5 years Sell property and end of year 5 for $1,935,000 Process: 1. Create three columns in an Excel spreadsheet: a. Title the first column “N” b. Title the second column “Amount” c. Title the third column “Notes” 2. In the first column, title the rows 0 through 5 3. In cell B2 enter -$1,500,000 4. In cells B3 through B5 enter $10,500 5. In cell B6 enter $15,300 6. In cell B7 enter =$1,935,000+15,300 7. In cell C3 enter Y1 and fill series in this column to Y5 8. In cell A8 enter IRR 9. In cell B8 enter =IRR(B2:B7) a. Right click B8 and select “Format Cells” b. Click on the “Number” tab c. Click on “Percentage” for the Category d. Under “Decimal Place” type “2” e. Click “OK” Answer 2: The Internal Rate of Return (IRR) is 5.97% 4 CALCULATING Compound Interest, IRR AND NPV Question 3: What is the Internal Rate of Return for the scenario below? Details: Initial Investment: Income: Period: Sale price in year 10: $115,000 none 8 years $152,300 Process: 1. Create three columns in an Excel spreadsheet: a. Title the first column “N” b. Title the second column “Amount” c. Title the third column “Notes” 2. In the first column, title the rows 0 through 10 3. In cell B2 enter -$115,000 4. In cells B3 through B9 enter $0 5. In cell B10 enter =$152,300 6. In cell C3 enter Y1 and fill series in this column to Y8 7. In cell A11 enter IRR 8. In cell B11 enter =IRR(B2:B10) a. Right click B11 and select “Format Cells” b. Click on the “Number” tab c. Click on “Percentage” for the Category d. Under “Decimal Place” type “2” e. Click “OK” Answer 3: The Internal Rate of Return (IRR) is 3.57% 5 CALCULATING Compound Interest, IRR AND NPV Question 4: What can the tenant below pay today to get out of her lease? Details: You: Terms of lease: Monthly payments: Goal: Discount rate: Tenant 1 year left $9,825 Buy out of lease 9.25% Process: 1. Set up a table in Excel with three columns: type, amount, notes 2. Since we are calculating a year’s worth of rent, we need to find the total rent for one year; in cell B2 type =9825*12 3. In row 3 enter the monthly payment amount ($9,825) 4. In row 4 enter the discount rate (9.25%) 5. In row 5 enter the period of the lease (1 year) 6. In row 6 enter the number of payments (12) 7. Next we need to calculate the simple interest a. The formula for simple interest is Interest = Principal x Rate x Time b. Title row 7 “Interest” c. In cell B7 we will use Excel’s IPMT formula and enter =IMPT(B3,B4,12,B2,1) d. Or alternately, in cell B7 you can enter =B2*B4*B5 8. Now we need to subtract the Principal from the Interest to find what the tenant pays today a. Title row 8 “Tenant Pays Today” b. In cell B8 enter =B2+B7 c. If calculating using simple interest formula, type =B2-B7 6 CALCULATING Compound Interest, IRR AND NPV Answer 4: The tenant can pay $106,994 today to get out of the lease. Question 5: What is the Net Present Value (NPV) for the scenario below? Details: Annual Payment: Period: Discount Rate: $275,000 5 years 3.5% Process: 1. Create three columns in an Excel spreadsheet: a. Title the first column “N” b. Title the second column “Amount” c. Title the third column “Notes” 2. In the first column, title the rows 1 through 5 3. In cell B2 through B6 enter $150,000 4. In cell B7 enter Discount 5. In cell C7 enter 7.5 a. Right click C7 and select “Format Cells” b. Click on the “Number” tab c. Click on “Percentage” for the Category d. Under “Decimal Place” type “2” e. Click “OK” 6. In cell A8 enter NPV 7. In cell B8 enter =NPV(B7,B2:B6) 7 CALCULATING Compound Interest, IRR AND NPV Answer 5: The Net Present Value (NPV) for this scenario is $1,241,639 References Cassidy, T. C. (1986). Breaking down the IRR. Commercial Investment Real Estate Journal, 5(2), 26-30. Celec, S. E. (1981). Is the truth in lending being told with the annual percentage rate as the measure of the cost of credit? The Journal of Consumer Affairs (Pre-1986), 15(1), 128. Retrieved from http://search.proquest.com/docview/222249935?accountid=41020 Nahigian, R. (2013). Commercial real estate investment an analysis (CRIA) 540: Advanced analytics for real estate investments. Chicago, IL: REALTOR® University. Valachi, D. J. (2000). Excel at financial analysis calculations. Commercial Investment Real Estate. Retrieved from http://www.ccim.com/cire-magazine/articles/excelfinancial-analysis-calculations © 2014 REALTOR® University. All rights reserved. These documents are intended for the sole use of REALTOR® University faculty and students. No part of these materials may be reproduced, in any form or by any means, without the permission in writing by REALTOR® University. Contact the REALTOR® University Library to request permission. 8