Question

A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a monthly service charge of $20. Plan A has a cost of $.45 a minute for daytime calls and $.20 a minute for evening calls. Plan B has a charge of $.55 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 200 minutes of calls allowed per month and a charge of $.40 per minute beyond that, day or evening

. a. Determine the total charge under each plan for this case: 120 minutes of day calls and 40 minutes of evening calls in a month. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Cost for Plan A $ Cost for Plan B $ Cost for Plan C $

c. If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (Round each answer to the nearest whole number.Include the indifference point itself in each answer.) Plan A is optimal from zero to minutes. Plan C is optimal from minutes onward.

d. Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans A and B? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places. Omit the "%" sign in your response.) Point percent daytime minutes

Answer 1

Concepts and reason

Relevant Costing: It is a method by which the process of decision making is simplified by ignoring the avoidable costs that are not relevant to the decision that is required to be taken. An example of a managerial decision in which relevant cost plays an important role is Make vs. Buy decisions.

Fundamentals

Fixed Costs: It is the cost which does not change with increase or decrease in the production output level. It remains constant throughout the production. It is a part of the total cost to run a business along with the variable cost.

Variable Costs: It is a cost which changes with an increase or decrease in production output level. It changes with the company’s production volume. When production increases, the variable cost also increases and vice-versa.

Full Cost per plan: It is the sum of all the cost related to the plan. It is calculated by the sum of Variable Cost and Fixed Cost.

Service charge: It is the fixed part of the total cost. It is that charge that the company charges for rendering services to the customers.

Daytime call rate: It refers to per minute rate for calls made during the day.

Night time call rate: it refers to per minute rate for calls made during the night.

Flat call rate: It refers to the charge which remains fixed for up to a certain number of calls or minutes.

a.1

Compute the total cost for plan A using the equation as shown below:

$\begin{array}{c}\\{\rm{Total cost}} = \left( \begin{array}{l}\\{\rm{Fixed service charge}} + \\\\\left( {{\rm{Daytime charge}} \times {\rm{Daytime calls}}} \right) + \\\\\left( {{\rm{Night time charge}} \times {\rm{Night time calls}}} \right)\\\end{array} \right)\\\\ = \left( \begin{array}{l}\\\$ 20 + \left( {\$ 0.45 \times 120{\rm{ minutes}}} \right) + \\\\\left( {{\rm{\$ 0}}{\rm{.20}} \times {\rm{40 minutes}}} \right)\\\end{array} \right)\\\\ = \$ 82\\\end{array}$

a.2

Compute the total cost for plan B using the equation as shown below:

$\begin{array}{c}\\{\rm{Total cost}} = \left( \begin{array}{l}\\{\rm{Fixed service charge}} + \\\\\left( {{\rm{Daytime charge}} \times {\rm{Daytime calls}}} \right) + \\\\\left( {{\rm{Night time charge}} \times {\rm{Night time calls}}} \right)\\\end{array} \right)\\\\ = \left( \begin{array}{l}\\\$ 20 + \left( {\$ 0.55 \times 120{\rm{ minutes}}} \right) + \\\\\left( {{\rm{\$ 0}}{\rm{.15}} \times {\rm{40 minutes}}} \right)\\\end{array} \right)\\\\ = \$ 92\\\end{array}$

a.3

Compute the total cost for plan C using the equation as shown below:

$\begin{array}{c}\\{\rm{Total cost}} = \left( \begin{array}{l}\\{\rm{Fixed service charge}} + \\\\{\rm{Cost upto }}200{\rm{ minutes}}\\\end{array} \right)\\\\ = \$ 20 + \$ 80\\\\ = \$ 100\\\end{array}$

c.

Compute a total number of daytime calls under plan A for the flat rate of plan C using the equation as shown below:

$\begin{array}{c}\\{\rm{Total number of daytime calls}} = \frac{{{\rm{Flat rate under plan C for 200 minutes}}}}{{{\rm{Daytime rate per minute under plan A}}}}\\\\ = \frac{{\$ 80}}{{\$ 0.45}}\\\\ = 178{\rm{ calls}}\\\end{array}$

d.

Compute the percent daytime minutes by equating the plan A and plan B.

$\begin{array}{c}\\{\rm{Total cost equation for plan A}} = {\rm{Total cost equation for plan B}}\\\\\left( {\left( {0.25 \times {\rm{Day call minutes}}} \right) + 20} \right) = \left( {\left( {0.40 \times {\rm{Day call minutes}}} \right) + 15} \right)\\\\0.1{\rm{5 Day call minutes}} = 20\\\\{\rm{Day call minutes}} = 33.33\\\end{array}$

Hence, the percent of day call minutes is 33.33.

Working notes:

Compute the total cost equation for plan A as shown below:

$\begin{array}{c}\\{\rm{Total cost for plan A}} = \left( \begin{array}{l}\\\left( {{\rm{Daytime rate of plan A}} \times {\rm{Day call minutes}}} \right) + \\\\\left( \begin{array}{l}\\{\rm{Night time rate of plan A}} \times \\\\\left( {{\rm{Total call minutes}} - {\rm{Day call minutes}}} \right)\\\end{array} \right)\\\end{array} \right)\\\\ = \left( \begin{array}{l}\\\left( {0.45 \times {\rm{Day call minutes}}} \right) + \\\\0.20\left( {100 - {\rm{Day call minutes}}} \right)\\\end{array} \right)\\\\ = \left( {\left( {0.25 \times {\rm{Day call minutes}}} \right) + 20} \right)\\\end{array}$

Hence, the total cost equation for plan A is ((0.25× Daytime calls) + 20).

Compute the total cost equation for plan B as shown below:

$\begin{array}{c}\\{\rm{Total cost for plan B}} = \left( \begin{array}{l}\\\left( {{\rm{Daytime rate of plan B}} \times {\rm{Day call minutes}}} \right) + \\\\\left( \begin{array}{l}\\{\rm{Night time rate of plan B}} \times \\\\\left( {{\rm{Total call minutes}} - {\rm{Day call minutes}}} \right)\\\end{array} \right)\\\end{array} \right)\\\\ = \left( \begin{array}{l}\\\left( {0.55 \times {\rm{Day call minutes}}} \right) + \\\\0.15\left( {100 - {\rm{Day call minutes}}} \right)\\\end{array} \right)\\\\ = \left( {\left( {0.40 \times {\rm{Day call minutes}}} \right) + 15} \right)\\\end{array}$

Hence, the total cost equation for plan B is ((0.40× Daytime calls) + 15).

Ans: Part a.1

The total cost for plan A is $82.

Part a.2

The total cost for plan B is $92.

Part a.3

The total cost for plan C is $100.

Part c

Plan A is optimal from zero to 178 minutes; beyond that plan C is optimal.

Part d

The percent of day call minutes is 33.33.