# calculating Internal Rate of Return (IRR), Net Present Value (NPV)

```CALCULATING Compound Interest, IRR AND NPV
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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.
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:
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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
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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.
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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%
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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%
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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
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
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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)
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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),
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