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 $5,400 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 20% of the base fee if the project finished 2 weeks early and 15% if the project finished a week early. The probability of finishing 2 weeks early is 20% and the probability of finishing a week early is 65%. What is the expected transaction price with variable consideration estimated as the most likely amount

Answer 1

The expected transaction price with variable consideration, estimated as the most likely amount for Bob the Builder, is $5,926.50.

Step-by-step explanation:

The student is asking for the expected transaction price with variable consideration estimated as the most likely amount in a contract situation.

Firstly, we calculate the additional bonus amounts:

20% of $5,400 for finishing 2 weeks early = $1,080.

15% of $5,400 for finishing 1 week early = $810.

Given the probabilities, we multiply the bonus by their respective probabilities to find the expected values:

Expected value for 2 weeks early: 0.20 x $1,080 = $216.

Expected value for 1 week early: 0.65 x $810 = $526.50.

Since we are looking for the most likely amount, we add the base fee and the higher expected value (from finishing 1 week early, as it has the higher probability):

Expected transaction price = Base fee + Expected value for 1 week early
= $5,400 + $526.50
= $5,926.50

Answer 2

$6,210

Step-by-step explanation:

The expected transaction price with variable consideration estimated as the expected value:

• original cost $5,400 if job is finished in one month (15% probability)
• bonus price for finishing 2 weeks earlier $5,400 x 1.2 = $6,480 (20% probability)
• bonus price for finishing 1 week earlier $5,400 x 1.15 = $6,210 (65% probability)

expected transaction price = ($5,400 x 15%) + ($6,480 x 20%) + ($6,210 x 65%) = $6,142.50

The expected transaction price with variable consideration as the most likely amount?

$6,210, since it has a 65% probability