Name – Onoriode Ovuorie
Matric number – 179029144
Course – EMB 824 – Data Analytics for Business Decision
DECISION TREE ANALYSIS FOR MR. JOHNSON’S CONSTRUCTION DECISION
Problem Statement:
To assist Mr. Johnson in deciding whether to start construction now or keep the land vacant for one year,
we will create and analyse a decision tree. This decision tree will incorporate the different scenarios and
calculate the expected values for each decision.
Step 1: Plot the Decision Tree
Let's first visualize the decision tree for clarity. We will have two main decisions:
1. Start construction now.
2. Keep the land vacant for one year and then decide based on market conditions.
Assumptions:
1. The construction time remain unchanged.
2. Equal probability of the market being either buoyant or sluggish
3. Yearly rental per apartment unit is $0.7m
4. There is a risk-free interest rate of 10% per annum.
Decision Tree Outline:
We need to consider the two potential outcomes for keeping the land vacant: a buoyant market and a sluggish
market, both with equal probability.
Decisions and Outcomes
1. To start construction now.
2. To keep the land vacant for one year
Building 10 Apartments:
Construction cost = $60M
Immediate sale @$8M/unit: $8M x 10 units = $80M
Profit: $80M - $60M = $20M
Building 15 Apartments:
Construction cost = $102.5M
Immediate sale @$8M/unit: $8M x 15 units = $120M
Profit: $120M - $102.5M = $17.5M
Keep Land Vacant for One Year:
Market turns buoyant: each apartment is sold at $9.1M
Market turns sluggish: each apartment is sold at $7.5M
Profit: $80M - $60M = $20M
Step 2: Calculate Expected Values for Each Scenario
Before we calculate, we will need to consider two possible scenarios under the “Keep Land Vacant for One
Year”.
Option A: Start Construction Now (Earn Rental, Sell in One Year)
Building 10 Apartments:
Rental Income: 10 apartments x $0.7M = $7M rental income after one year
If the market becomes buoyant in a year, each apartment sells for $9.1M
If the market becomes sluggish in a year, each apartment sells for $7.5M
Revenue (Buoyant) = $9.1M * 10 units = $91M
Revenue (Sluggish) = $7.5M * 10 units = $75M
Expected Revenue = (0.5 * $91M) + (0.5 * $75M) = $45.5M + $37.5M = $83M
Total Expected Cash Flow (including rental) = $83M + $7M = $90M
Present Value of Total Expected Cash Flow = $90M x 0.909 = $81.81M
Profit = $81.81M - $60$ (Construction Cost) = $21.81M
Building 15 Apartments:
Rental Income: 15 apartments * $0.7m = $10.5M rental income after one year.
Revenue (Buoyant) = $9.1M x 15 units = $136.5M
Revenue (Sluggish) = $7.5M x 15 units = $112.5M
Expected Revenue = (0.5 x $136.5M) + (0.5 x $112.5M) = $68.25M + $56.25M = $124.5M
Total Expected Cash Flow (including rental) = $124.5M + $10.5M = $135M
Present Value of Total Expected Cash Flow = $135 x $0.909 = $122.72M
Profit = $122.72M - $102.5M (Construction Cost) = $20.22M
Option B: Wait One Year
10 Apartments (No Rental Income):
Using calculations from before:
Expected Revenue = ($83M)
Present Value of Expected Revenue = $83M x 0.909 = $75.447M
Profit = $75.447M - $60M (Construction Cost) = $15.447M
15 Apartments (No Rental Income):
Expected Revenue = ($124.5M)
Present Value of Expected Revenue = $124.5 x 0.909 = $113.1805M
Profit = $113.1805M - $102.5M (Construction Cost) = $10.6805M
Step 3: Compare Expected Profits
Start Construction Now:
10 apartments: Profit = $21.81M
15 apartments: Profit = $20.22M
Keep Land Vacant for One Year:
10 apartments: Profit = $15.447M
15 apartments: Profit = $10.6805M
Step 4: Decision Analysis
If Mr. Johnson constructs now: Constructing 10 apartments yields the highest profit of $21.81m,
due to rental income and expectation of market prices.
If Mr. Johnson waits: Expected profit values are lower due to the lack of rental income and
discounting.
Conclusion
Based on the expected profit calculations:
Mr. Johnson should start construction now and construct 10 apartments because it maximizes
profit with an expected profit of $21.81m.
0
