91Ó°ÊÓ

(Determine Transaction Price) Jeff Heun, president of Concrete Always, agrees to construct a concrete cart path at Dakota Golf Club. Concrete Always enters into a contract with Dakota to construct the path for \(200,000. In addition, as part of the contract, a performance bonus of \)40,000 will be paid based on the timing of completion. The performance bonus will be paid fully if completed by the agreed-upon date. The performance bonus decreases by $10,000 per week for every week beyond the agreed-upon completion date. Jeff has been involved in a number of contracts that had performance bonuses as part of the agreement in the past. As a result, he is fairly confident that he will receive a good portion of the performance bonus. Jeff estimates, given the constraints of his schedule related to other jobs , that there is 55% probability that he will complete the project on time, a 30% probability that he will be 1 week late, and a 15% probability that he will be 2 weeks late.

Instructions

(a) Determine the transaction price that Concrete Always should compute for this agreement.

(b) Assume that Jeff Heun has reviewed his work schedule and decided that it makes sense to complete this project on time. Assuming that he now believes that the probability for completing the project on time is 90% and otherwise it will be finished 1 week late, determine the transaction price.

Step by step solution

01

Meaning of Transaction Price

The amount of compensation expectedin exchange for the exchange of products or serviceswith a client is referred to as transaction pricing. The price of a transaction may be constant or variable based on the time or performance of the transaction.

02

Calculate transaction price

a. Transaction Price

Expected values of the bonus:

$$\begin{gathered} \mathrm{Expected}\mathrm{value}\mathrm{of}\mathrm{the}{\mathrm{bonus}}_1=\mathrm{Performance}\mathrm{bonus}×\mathrm{Probability}\mathrm{for}\mathrm{completing}\mathrm{the}\mathrm{project}\mathrm{on}\mathrm{time} \\ =\$40,000×55\% \\ =\$40,000×\frac{55}{100} \\ =\$22,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Expected}\mathrm{value}\mathrm{of}{\mathrm{bonus}}_2=\left(\mathrm{Performance}\mathrm{bonus}-\mathrm{Amount}\mathrm{deduction}\mathrm{due}\mathrm{to}\mathrm{late}\mathrm{completion}\right)×\mathrm{Probability}\mathrm{for}\mathrm{completing}\mathrm{the}\mathrm{project}1\mathrm{week}\mathrm{late} \\ =\left(\$40,000-\$10,000\right)×30\% \\ =\$30,000×\frac{30}{100} \\ =\$9,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Expected}\mathrm{value}\mathrm{of}{\mathrm{bonus}}_3=\left(\mathrm{Performance}\mathrm{bonus}-\mathrm{Amount}\mathrm{deduction}\mathrm{due}\mathrm{to}\mathrm{late}\mathrm{completion}\right)×\mathrm{Probability}\mathrm{for}\mathrm{completing}\mathrm{the}\mathrm{project}2\mathrm{week}\mathrm{late} \\ =\left(\$30,000-\$10,000\right)×15\% \\ =\$20,000×\frac{15}{100} \\ =\$3,000 \end{gathered}$$

localid="1648541255528" $$\begin{gathered} \mathrm{Total}\mathrm{expected}\mathrm{value}=\mathrm{Expected}{\mathrm{value}}_1+\mathrm{Expected}{\mathrm{value}}_2+\mathrm{Expected}{\mathrm{value}}_3 \\ =\$22,000+\$9,000+\$3,000 \\ =\$34,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Total}\mathrm{transaction}\mathrm{price}=\mathrm{Contract}\mathrm{price}+\mathrm{Total}\mathrm{expected}\mathrm{value}\mathrm{of}\mathrm{bonus} \\ =\$200,000+\$34,000 \\ =\$234,000 \end{gathered}$$

b. Transaction Price

Expected values of the bonus:

localid="1648541273513" $$\begin{gathered} \mathrm{Expected}\mathrm{value}\mathrm{of}{\mathrm{bonus}}_1=\mathrm{Performance}\mathrm{bonus}×\mathrm{Probability}\mathrm{for}\mathrm{completing}\mathrm{the}\mathrm{project}\mathrm{on}\mathrm{time} \\ =\$40,000×90\% \\ =\$40,000×\frac{90}{100} \\ =\$36,000 \end{gathered}$$

$$\begin{gathered} \mathrm{Expected}\mathrm{value}\mathrm{of}\mathrm{the}{\mathrm{bonus}}_2=\left(\mathrm{Performance}\mathrm{bonus}-\mathrm{Amount}\mathrm{deduction}\mathrm{due}\mathrm{to}\mathrm{late}\mathrm{completion}\right)×\mathrm{Probability}\mathrm{for}\mathrm{completing}\mathrm{the}\mathrm{project}1\mathrm{week}\mathrm{late} \\ =\left(\$40,000-\$10,000\right)×10\% \\ =\$30,000×\frac{10}{100} \\ =\$3,000 \end{gathered}$$

localid="1648541243546" $$\begin{gathered} \mathrm{Total}\mathrm{expected}\mathrm{value}=\mathrm{Expected}{\mathrm{value}}_1+\mathrm{Expected}{\mathrm{value}}_2 \\ =\$36,000+\$3,000 \\ =\$39,000 \end{gathered}$$

localid="1648541286419" $$\begin{gathered} \mathrm{Total}\mathrm{transaction}\mathrm{price}=\mathrm{Contract}\mathrm{Price}+\mathrm{Total}\mathrm{expected}\mathrm{value}\mathrm{of}\mathrm{bonus} \\ =\$200,000+\$39,000 \\ =\$239,000 \end{gathered}$$

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