Question

For the past several years, you’ve been purchasing a product from a supplier at a high-volume cost and reselling the product at a lower price than your customers could buy it. However, you’d like to improve the product but the manufacturer isn’t interested in doing this. You are trying to determine if it would make sense to buy the equipment and make it yourself with better quality.

Construct two decision trees (one for each scenario), including expected money value, for the following scenario information.

Scenario A:

• Equipment = $500,000 + 100,000 for training
• Chances of a good market next year are 60%
• A good market will yield $1,000,000 in gross revenue, a poor market will yield $200,000 in gross revenue
• If you continue selling the product as you currently do, a good market will generate $300,000 in gross revenue and a poor market $50,000 in gross revenue
• Estimated costs for working with you supplier are $30,000/yr

Scenario B:

• How would this change if the probability for good market increases to 80% and the probability of a good/poor market for purchasing remain the same?

Answer 1

Scenario A:

You have 2 options

1. Make the product after buying the equipment for $500,000 + 100,000
   1. If a good market year with a probability of 0.60, payoff is $1,000,000 - ($500,000 + 100,000)=$400,000
   2. If a poor market year with a probability of 0.40, payoff is $200,000 - ($500,000 + 100,000)=-$400,000
2. Purchase the product as you currently do at a cost of $30,000/yr
   1. If a good market year with a probability of 0.60, payoff is $300,000 -$30,000 =$270,000
   2. If a poor market year with a probability of 0.40, payoff is $50,000 - $30,000=$20,000

The following is the decision tree

Moving from the right to left

chance node 2: Make the product

The expected value is

chance node 3: Purchase the product

The expected value is

Decision node 1

You have 2 options, each with the following expected values

1. Make the product at an expected money value of $80,000
2. Purchase the product as you currently do at an expected money value of $170,000

ans: Since the EV if  purchase the product is higher than if make, you should continue purchasing the product from your current supplier

Scenario B

if the probability for good market increases to 80% and the probability of a good/poor market for purchasing remain the same

You have 2 options

1. Make the product after buying the equipment for $500,000 + 100,000
   1. If a good market year with a probability of 0.80, payoff is $1,000,000 - ($500,000 + 100,000)=$400,000
   2. If a poor market year with a probability of 0.20, payoff is $200,000 - ($500,000 + 100,000)=-$400,000
2. Purchase the product as you currently do at a cost of $30,000/yr
   1. If a good market year with a probability of 0.60, payoff is $300,000 -$30,000 =$270,000
   2. If a poor market year with a probability of 0.40, payoff is $50,000 - $30,000=$20,000

The following is the decision tree

Moving from the right to left

chance node 2: Make the product

The expected value is

chance node 3: Purchase the product

The expected value is

Decision node 1

You have 2 options, each with the following expected values

1. Make the product at an expected money value of $240,000
2. Purchase the product as you currently do at an expected money value of $170,000

ans: Since the EV when make the product is higher than when purchase, you should buy the equipment and start making the product.