Assessing Value Story Problems

Read through the story problems, solve the problems and interpret your findings. On a piece of paper, show the work for your calculations $$ including the formula used. Circle your final answer. Then, write out your interpretation of your solution$($s$).$ Be sure to show all work for full credit. Once you are finished with all problems, take pictures of your hand$-$written calculations and upload to Canvas for this corresponding assignment.

The first story problem solution is provided as an example.

TEV$=$cost of the next$-$best alternative $+$ value of the performance differential

$1.$ Consider a firm trying to sell a new product to the owner of a toy factory that requires an air$-$filtration system. Assume the factory owner faces two choices $$ this seller$$s new product and a well$-$established, next$-$best alternative offered by another firm$$each with the characteristics seen in the table below.

New Product

Next$-$Best Alternative

Probability of system crash

$1\%$ over one year

$20\%$ over one year

Cost of system crash

$$100,000$

$$100,000$

Hours of operation

$2,500$

$2,500$

Operating system cost per hour

$$15$

$$10$

Price

To be determined

$$75,000$

Assume that the system will be used for a single year for a total of $2,500$ hours. In addition, assume the cost to the toymaker of a system failure is $$100,000($because of production downtime during repairs$)$ and that the filtration system supplier will bear the cost of any system crash after the first one. Given this information, we can calculate the TEV for the new product to this potential buyer as follows:

TEV $=$ price of next$-$best alternative $+$ expected system crash savings $$ added operating costs

$=$ $$75,000+((20\%*$ $$100,000)(1\%*$ $$100,000))$

$((2,500$ hours $*$ $$15/$hour$)(2,500$ hours $*$ $$10/$hour$))$

$=$ $$75,000+$ $$19,000-$ $$12,500$

$=$$$81,500$

Thus, the TEV of the new product for this customer is $$81,500$which means that a fully informed, rational buyer with this cost structure should be indifferent between the next$-$best alternative priced at $$75,000$ and the new product priced at $$81,500.$

$2.$ Consider the owner of a tire manufacturer needs a tool charging station. The operating conditions, probability of a system crash, the cost of a system failure, and the system$$s operating costs per hour are shown in the table below.$$

New Product

Next$-$Best Alternative

Probability of system crash

$2\%$ over one year

$23\%$ over one year

Cost of system crash

$$350,000$

$$350,000$

Hours of operation

$2,500$

$2,500$

Operating system cost per hour

$$18$

$$12$

Price

To be determined

$$75,000$

Calculate the TEV of the tool charging station for tire manufacturer.

$3.$ MetaPress manufactures equipment for processing raw metals. The sales team needs to determine the true economic value $($TEV$)$ for a new extrusion press. This machine costs $$20$ per hour to operate. A system crash costs $$500,000$ and the probability that the machine will crash is $5\%.$ The next$-$best alternative has a price of $$150,000,$ and costs $$15$ per hour to operate. The cost of a system crash for the alternate is $$500,000$ and the probability of crash is $15\%.$ The machine will be operating for $2,920$ hours.$$

Calculate the TEV for the extrusion press for MetalPress.