Transcript
NARRATOR:
Let's look at a more complicated example. A company is considering launching a new product. It can either launch immediately or in 1 year's time. If it launches immediately, there's a 0.75 chance of the launch being successful. If it's unsuccessful, then the launch will be halted at a cost of 1 million pounds and re-launch in a year's time.
If the company launches immediately, it may also opt to have a promotion. If the promotion is successful, the financial benefit is 10 million pounds. If not, it's 2 million pounds. If the company doesn't do the promotion, the benefit is 5 million pounds. If the company launches in a year's time, the benefit is 6 million pounds.
So we're considering launching a product. It can launch immediately or in one year's time. We put our two branches down. At the end, we'll go with the one with the highest expected value. If the product launches immediately, there's a 0.75 chance of the launch being successful.
This is something outside our control, so we write successful with a question mark. Yes, it will be successful, is a 0.75 chance, and therefore, no, it won't be successful, has a 0.25 chance. If it's unsuccessful, the launch will be halted at a cost of 1 million pounds. So let's write that here. -1 million pounds and re-launched in a year's time. So it'll come down here to 1 year, and we'll join those lined up in a minute.
If the company launches immediately, it may also opt to have a promotion. Well, we'll only do the promotion if it's successful. So we had another choice. Do we launch a promo? Yes or no? If we do a promotion, will it be successful? Yes or no?
The promotion has a 0.6 probability of being successful and, therefore, 0.4 probability of not being successful. If the promotion is successful, the benefit is 10 million pounds after all costs. And if it's not successful, it's 2 million after all costs.
If the company doesn't do the promotion, the benefit is 5 million pounds. Here's this line. And if the company launches in a year's time, the benefit is 6 million pounds, so these two lines join up. So we now work from right to left. We'll label this node number 1.
The expected value here is 0.6 times 10 plus 0.4 times 2, which is 6.8 million pounds. We'll write that on node 1. On node 2, where we have a choice, 'Yes' is worth 6.8 in expected value terms, whereas 'No' is worth 5. So we'd pick 'Yes' and with an expected value of 6.8.
Coming now to node 3, the expected value at this point is 0.75 times 6.8 because that's the expected value at node 2 plus 0.25. Now will launch in a year's time, but now the expected value of coming down this route is -1 plus 6, which is 5. Node 3 is therefore worth 6.35 million pounds.
The value of this route is simply 6. Nothing else happened in between. So what we can conclude, based on our diagram, is that launching a new product now has an expected value of 6.35 million pounds, whereas launching a new product in a year's time has an expected value of 6. Therefore, on this basis, we would go with the 6.35 million pounds, so we would launch now.
If we were to launch now and it was successful, we then have another choice to make at node 2. And here, we would choose 'Yes', we would promote. So our strategy is the launch now, and then, if it's successful, to launch a promotion.
Just to recap. Decision nodes are shown as squares. Chance nodes are shown as circles. Terminal nodes are the ones where their values go right at the end, and we show them as rectangles. Probabilities coming out of a chance node must total 1 because they must cover every single eventuality.
We calculated expected values moving from right to left and then carried back the expected values which formed later decisions. We saw this in the example question, do we promote? The expected value of promoting was higher than not promoting, so that node no longer becomes a decision node because we made the decision now. And then, coming right back to the beginning, you can see which initial branch gives you the highest expected value.