Question

On April 1st, Bob the Builder entered into a contract of one-month duration to build a barn for Nolan. Bob is guaranteed to receive a base fee of $5,000 for his services in addition to a bonus depending on when the project is completed. Nolan created incentives for Bob to finish the barn as soon as he can without jeopardizing the structural integrity of the barn. Nolan offered to pay an additional 30% of the base fee if the project finished 2 weeks early and 10% if the project finished a week early. The probability of finishing 2 weeks early is 30% and the probability of finishing a week early is 60%. What is the expected transaction price with variable consideration estimated as the expected value?

Answer 1

Answer:

• $5,750

Explanation:

The expected transaction price with variable consideration as the expected value is the calculated as the sum of the products of each price transaction by the corresponding probability.

1. Without bonus for early finishing:

Price transaction:

• $5,000                    

Probability:

• 100% - 30% - 60% = 10% = 0.10

Product:

• $5,000 × 0.10 = $500

2. Finishing 2 weeks early:

Bonus:

• $5,000 × 30% = $1,500

Price transaction:

• $5,000 + $1,500 = $6,500

Probability:

• 30% = 0.30

Product:

• $6,500 × 0.30 = $1,950

3. Finishing a week early:

Bonus:

• $5,000 × 10% = $500

Price transaction:

• $5,000 + $500 = $5,500

Probability:

• 60% = 0.60

Product:

• $5,500 × 0.60 = $3,300

4. Expected value of the 3 scenaries:

Sum the products obtained above:

• $500 + $1,950 + $3,300 = $5,750