Valuing Options in Commercial Real Estate

INSY 6630 Real Options/Decision AnalysisSpring 2015 Class Project

Mohamed Abraar AhmedJames Greenwell

Zane TrottDonghuang Li

Instructor: Dr. Chan. S. Park

Introduction

A Kellogg School of Management Case Study: Hasperat Inc. (tenant) is leasing Kelly Building from

Koenig Capital (lender), while have option to buy this building at four specified points of time in the following 16 years.

The Problem: What is the value of the buy-option in the lease

contract?The Simple NPV Approach the analyst proposed in the case is deficient:1. It is viewed from the perspective of the lender2. Simple NPV approach without considering the value of

flexibilityOur Approach:3. View from the perspective of the tenant4. FNPV approach

The OptionPresent date: April 2012

The tenant has 4 options: Buy at the end of year 2013, thereby paying lease payments and parking

fees for year 2013, and paying management fees and capital expenditures every year from 2014 till 2028;

Buy at the end of year 2018, thereby paying lease payments and parking fees from 2013 till 2018, and paying management fees & capital expenditures after that till 2028;

Buy at the end of year 2023, thereby paying lease payments and parking fees before that, and paying management fees and capital expenditures after that till 2028;

Paying lease payments and parking fees till 2028, and deciding whether to buy or not at the end of year 2028;

Compute Cash Outflow Items

Step 1: Re-generate Cash Flow Statement Using data provided in the case and assumptions from the

analyst, we generated the CF Statement which exactly matched with case Exhibit 5, which means we followed the correct basis of calculation.

Step 2: Re-arrange the Potential Cash Flows from the tenant’s perspective The Lease & Parking Payments are Cash-Inflows for the lender

but Cash-Outflows for the tenant; Management Fee and Capital Expenditure are Cash-Outflows

for the Current Owner of the Building, no matter who the owner is;

Depending on the tenant’s decision, the tenant incurs different Cash-Outflow patterns.

Estimate Cash Inflow

For the value of the building, if bought, we decided to use Reversion Sales Price Net of Commission instead of the property value estimated by the analyst from the lender’s perspective. The implication of that is, the tenant will not have any extra income after the building has been bought, but will earn a “salvage” value at year 2028. For simplification, we assume this salvage value is the same for both companies.

Volatility Estimation was done using the historical returns for Koenig. To do this we convert the quarterly standard deviation to a yearly for use in the binomial lattice.

Risk-free Rate was chosen by looking at average return of 20 year treasury bonds during April 2013.

Cash FlowsYear

HASPERAT 2013 2014 2015 2016 2017 2018

Lease Payment $ 1,961,850.00

$ 1,987,354.05

$ 2,013,189.65

$ 2,039,361.12

$ 2,065,872.81

$ 2,092,729.16

Parking Payment $ 144,624.96

$ 146,505.08

$ 148,409.65

$ 150,338.98

$ 152,293.38

$ 154,273.20

Total Lease Cash Outflow (never buy)

$ 2,106,474.96

$ 2,133,859.13

$ 2,161,599.30

$ 2,189,700.09

$ 2,218,166.20

$ 2,247,002.36

NPV $ 18,294,919.56

Total Buy Cash Outflow (buy at 2013)

$ 26,106,474.96

$ 267,297.46

$ 272,374.55

$ 277,549.68

$ 282,824.77

$ 288,201.77

NPV Investment $ 25,961,803.74

NPV $ -18,883,606.20

Total Buy Cash Outflow (buy at 2018)

$ 2,106,474.96

$ 2,133,859.13

$ 2,161,599.30

$ 2,189,700.09

$ 2,218,166.20

$ 27,848,093.07

NPV Investment $ 25,587,038.97

NPV $ -18,508,841.43

Total Buy Cash Outflow (buy at 2023)

$ 2,106,474.96

$ 2,133,859.13

$ 2,161,599.30

$ 2,189,700.09

$ 2,218,166.20

$ 2,247,002.36

NPV Investment $ 25,313,337.78

NPV $ -18,235,140.24

Total Buy Cash Outflow (buy at 2028)

$ 2,106,474.96

$ 2,133,859.13

$ 2,161,599.30

$ 2,189,700.09

$ 2,218,166.20

$ 2,247,002.36

This is just a sample, the complete cash flow can be found in the excel file.

Building Decision Lattice Four-stage Binomial Lattice Tree from 2013 to 2028, each

stage is 5 years;

Call-Option at each tree node including the first node.

The Cash-Outflows are viewed as Investment Costs, occurring in different pattern depending on the tenant’s decision. The values are discounted back to current time, then compounded to the time when the decision is actually made as Exercise Price (K) for each stage

The NPV of Reversion Sales Price Net of Commission is viewed as the Underlying Asset Price (S).

    2013 2018 2023 2028

  $ 39,320,781.47

  $ 30,149,037.99  

  $ 23,116,643.62

$ 23,116,643.62

Underlying Asset Lattice V0 $ 17,724,585.85

$ 17,724,585.85  

  $ 13,590,249.03

$ 13,590,249.03

  $ 10,420,264.27  

  $ 7,989,692.26

     2013 2018 2023 2028Investment Cost if exerice at each year K

$ 25,961,803.74

$ 29,662,390.92

$ 34,019,009.26

$ 39,126,823.09

     2013 2018 2023 2028

  $ 193,958.37

  $ 122,717.47  

  $ 77,643.35

$ -

Buy Option Value C $ 49,124.95

$ -  

  $ -

$ -

  $ -  

          $ -

Calculation ResultsVolatility 11.88%u 1.30421347d 0.766745646R 1.161834243w 0.860707976q 0.735092556

r(Risk Free Rate) 3.0%

VT(2028) $ 27,614,327.22

V0(2013) $ 17,724,585.85

Sensitivity Analysis $ 49,124.95 -15% -10% -5% 0 5% 10% 15%

Cap Rate $

1,806,595.40 $

1,155,680.41 $ 573,282.80

$ 49,124.95

$ -

$ -

$ -

Discount Rate $

- $

- $

- $

49,124.95 $ 439,921.84

$ 808,476.90

$ 1,156,268.46

Volitility $

- $

- $

- $

49,124.95 $ 421,471.06

$ 757,419.49

$ 1,063,181.44

Risk Free Rate $

1,183,392.71 $ 840,279.09

$ 462,632.13

$ 49,124.95

$ -

$ -

$ -

Inflation $

- $

- $

352.96 $

49,124.95 $

98,504.32 $ 148,497.18

$ 199,109.66

-20% -15% -10% -5% 0% 5% 10% 15% 20% $-

$200,000.00

$400,000.00

$600,000.00

$800,000.00

$1,000,000.00

$1,200,000.00

$1,400,000.00

$1,600,000.00

$1,800,000.00

$2,000,000.00

InflationRisk Free RateVolitilityDiscount RateCap Rate

Conclusion Although the analysis was carried out from the perspective of

the tenant, we must shift to the lender’s perspective to arrive at a conclusion.

From Koenig Capital’s perspective, any amount lesser than $49,125 is an acceptable amount to purchase the buy option from Hasperat Inc.

Inflation is a factor we have very little control over. However, as the economy is currently strong, any upward movement in the inflation rate will only increase the value of the buy option.

The discount rate and volatility seem to have a drastic effect on the buy option. We believe that we have taken a fair estimation of both and recommend that Koenig Capital proceed with purchasing the buy option for the Kelley Building before December 2013 for any amount lesser than $49,125.