Figure shows a decision tree with cash flows and probabilities fully specified.
ID: 2812848 • Letter: F
Question
Figure shows a decision tree with cash flows and probabilities fully specified. This is a research-and-development decision. The decision maker is a company that must decide whether to spend $2 million to continue with a particular research project. The success of the project (as measured by obtain- ing a patent) is not assured, and at this point the decision maker judges only a 70% chance of getting the patent. If the patent is awarded, the company can either license the patent for an estimated $25 million or invest an addi- tional $10 million to create a production and marketing system to sell the product directly. If the company chooses the latter, it faces uncertainty of demand and associated profit from sales.
Reconsider the research-and-development decision in Figure. If you decide to continue the project, you will have to come up with the $2 million this year (Year 1). Then there will be a year of waiting (Year 2) before you know if the patent is granted. If you decide to license the technology, you would receive the $25 million distributed as $5 million per year beginning in Year 3. On the other hand, if you decide to sell the product directly, you will have to invest $5 million in each of Years 3 and 4 (to make up the total investment of $10 million). Your net proceeds from selling the product, then, would be evenly distributed over Years 5 through 9.
Assuming an interest rate of 15%, calculate the NPV at the end of each branch of the decision tree.
Explanation / Answer
Path
Stop Development
Start Development
Patent Awarded
No Patent
License Technology
Develop Production and Marketing to sell
High Demand
Medium Demand
Low Demand
Cash Outflow year 1
0
2M
2M
2M
2M
2M
Cash inflow year 2
0
0
0
0
0
0
Cash outflow year 3x Discount factor
(5M x 0.6575)= 3.2875M
(5M x 0.6575)= 3.2875M
(5M x 0.6575)= 3.2875M
Cash inflow year 3x Discount factor
0
(5M x 0.6575)= 3.2875M
0
Cash outflow year 4x Discount factor
(5M x 0.5718)=2.85M
(5M x 0.5718)=2.85M
(5M x 0.5718)=2.85M
Cash inflow year 4 x Discount factor
0
(5M x 0.5718)=2.85M
0
Cash inflow years 5 x Discount Factor
0
(5M x 0.4972)=2.486 M
(11M x0.4972)=5.4692 M
(6.6 M x0.4972)=3.2815M
(3 M x0.4972)=1.4916M
0
Cash inflow years 6 x Discount Factor
(5M x 0.4323)=2.1615 M
(11 M x 0.4323)=4.7553M
(6.6 M x 0.4323)=2.8531M
(3 M x 0.4323)=1.2969 M
Cash inflow years 7 x Discount Factor
(5M x 0.3759)=1.875 M
11 M x 0.3759)=4.1349M
6.6 M x 0.3759)=2.4809M
3 M x 0.3759)=1.1277 M
Cash inflow years 8 x Discount Factor
11M x0.3269)=3.5959M
6.6 M x0.3269)=2.1575M
3 M x0.3269)=0.9807 M
Cash inflow years 9 x Discount Factor
11M x0.2843)=3.127M
6.6 M x0.2843)=1.8763M
3 M x0.2843)=0.8529M
Total Cash Out Flow
0
2M
8.1375M
8.1375M
8.1375M
2M
Total Cash inflow
0
12.66M
21.0823M
12.6493M
5.7498M
0
Net Present value
0
10.66M
12.9448M
4.5118M
(2.3877M)
(2M)
Path
Stop Development
Start Development
Patent Awarded
No Patent
License Technology
Develop Production and Marketing to sell
High Demand
Medium Demand
Low Demand
Cash Outflow year 1
0
2M
2M
2M
2M
2M
Cash inflow year 2
0
0
0
0
0
0
Cash outflow year 3x Discount factor
(5M x 0.6575)= 3.2875M
(5M x 0.6575)= 3.2875M
(5M x 0.6575)= 3.2875M
Cash inflow year 3x Discount factor
0
(5M x 0.6575)= 3.2875M
0
Cash outflow year 4x Discount factor
(5M x 0.5718)=2.85M
(5M x 0.5718)=2.85M
(5M x 0.5718)=2.85M
Cash inflow year 4 x Discount factor
0
(5M x 0.5718)=2.85M
0
Cash inflow years 5 x Discount Factor
0
(5M x 0.4972)=2.486 M
(11M x0.4972)=5.4692 M
(6.6 M x0.4972)=3.2815M
(3 M x0.4972)=1.4916M
0
Cash inflow years 6 x Discount Factor
(5M x 0.4323)=2.1615 M
(11 M x 0.4323)=4.7553M
(6.6 M x 0.4323)=2.8531M
(3 M x 0.4323)=1.2969 M
Cash inflow years 7 x Discount Factor
(5M x 0.3759)=1.875 M
11 M x 0.3759)=4.1349M
6.6 M x 0.3759)=2.4809M
3 M x 0.3759)=1.1277 M
Cash inflow years 8 x Discount Factor
11M x0.3269)=3.5959M
6.6 M x0.3269)=2.1575M
3 M x0.3269)=0.9807 M
Cash inflow years 9 x Discount Factor
11M x0.2843)=3.127M
6.6 M x0.2843)=1.8763M
3 M x0.2843)=0.8529M
Total Cash Out Flow
0
2M
8.1375M
8.1375M
8.1375M
2M
Total Cash inflow
0
12.66M
21.0823M
12.6493M
5.7498M
0
Net Present value
0
10.66M
12.9448M
4.5118M
(2.3877M)
(2M)
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