Chapter 1, Problem 10CACQ

To determine

(a)

To calculate:

The accounting profits.

Answer to Problem 10CACQ

The total accounting profit is $240,000.

Explanation of Solution

The accounting profits at the end of each of three years for the owner of the building as follows:

$\text{Accounting}\text{profit}=\text{Total}\text{revenue}-\text{Explicit}\text{costs}$

Given,

The annual rent earned by leasing the building is $120,000, and

The annual explicit cost of maintaining the building is $40,000.

Calculate the accounting value as follows:

$\begin{array}{c}\text{Accounting}\text{Profit}=\text{Total}\text{Revenue}-\text{Explicit}\text{Cost}\\ =\$\text{120,000}-\$\text{40,000}\\ =\$\text{80,000}\end{array}$

Thus, annual accounting profits for the building owner is $80,000.

Since the building owner is considering leasing it for three years and the rent and the costs are identical at the end of each year, her accounting profits will also be identical at the end of each year.

Calculate the total accounting profit as follows:

$\begin{array}{c}\text{Total}\text{accounting}\text{Profit}=\text{Accounting}\text{profit}\times \text{Number}\text{of}\text{leasing}\text{years}\\ =\text{\$80,000}\times \text{3}\\ =\text{\$240,000}\end{array}$

Thus, the total accounting profit is $240,000.

Present value of the stream of accounting profits:

Use the following equations to find the present value of the accounting profits:

$PV=\frac{F{V}_1}{{(1+i)}^1}+\frac{F{V}_2}{{(1+i)}^2}+\frac{F{V}_3}{{(1+i)}^3}$

Where,

PV is the present value of the accounting profit from the building.

FV₁ is the accounting profits at the end of the first year.

FV₂ is the accounting profit at the end of second year, and

FV₃ is the accounting profits at the end of third year.

In this case,

FV₁is $80,000,

FV₂is $80,000 and

FV₃is $80,000.

Calculate the present worth as follows:

$\begin{array}{c}\text{Present}\text{value}=\$23,810+\$22,675.737+\$21,595.94\\ =\$68,081\end{array}$

$\begin{array}{c}\text{PV}=\frac{80,000}{{(1.05)}^1}+\frac{80,000}{(1.103)}+\frac{80,000}{(1.157)}\\ =76,190.48+72,562.36+69,107.01\\ =\$217,859.84\end{array}$

Thus, although the building owner will earn a total accounting profit of $240,000 in the next three years, the present value of these accounting profits is $217,859.84 only.

Economics Concept Introduction

Explicit cost:

Explicit cost is the cost incurred by a firm and is paid exclusively and recorded in books of accounts. For example, wages paid to workers.

Implicit cost:

Implicit cost is the cost incurred by a firm which is imputed and is not recorded in books of accounts. For example, the rent, salaries which owner foregoes as he employs his own resources.

To determine

(b)

To calculate:

The economic profits.

Answer to Problem 10CACQ

The economic profit is $75,000.

Explanation of Solution

The economic profits at the end of each of three years for the owner of the building as follows:

$\text{Economic}\text{profit}=\text{Total}\text{revenue}-\text{Explicit}\text{costs}-\text{Opportunity}\text{costs}$

Given,

The annual rent earned by leasing the building is $120,000.

The annual explicit cost of maintaining the building is $40,000.

The annual implicit cost of maintaining the building is $55,000.

The annual rent earned by leasing the building is $120,000.

The annual explicit cost of maintain the building is $40,000 and

The annual cost of maintain the building is $55,000.

Economic profit is as follows:

$\begin{array}{c}\text{Economic}\text{Profit}=\text{Total}\text{Revenue}-\text{Explicit}\text{Cost}-\text{Implict}\text{Cost}\\ =\$120,000-\$40,000-\$55,000\\ =\$25,000\end{array}$

Since the building owner is considering leasing it for 3 years and the rent and costs are identical at the end of each year, her economic profit will be identical at the end of each year.

$\begin{array}{c}\text{Total}\text{economic}\text{profit}=\text{Economic}\text{Profit}\times \text{Number}\text{of}\text{leasing}\text{years}\\ =\$\text{25,000×3}\\ =\text{\$75,000}\end{array}$

Thus, the economic profit is $75,000.

Present Value of the stream of economic profits:

Present Value of the economic profits from the building over three years is as follows:

$PV=\frac{F{V}_1}{{(1+i)}^1}+\frac{F{V}_2}{{(1+i)}^2}+\frac{F{V}_3}{{(1+i)}^3}$

Here,

PV is the present value of the accounting profit from the building,

FV₁ is the accounting profits at the end of the first year,

FV₂ is the accounting profit at the end of second year, and

FV₃ is the accounting profits at the end of third year.

In this case,

FV₁is $25,000

FV₂is $25,000

FV₃is $25,000.

Calculate the present worth as follows:

$\begin{array}{c}PV=\frac{F{V}_1}{{(1+i)}^1}+\frac{F{V}_2}{{(1+i)}^2}+\frac{F{V}_3}{{(1+i)}^3}\\ =\frac{25,000}{{(1+0.05)}^1}+\frac{25,000}{{(1+0.05)}^2}+\frac{25,000}{{(1+0.05)}^3}\end{array}$

$\begin{array}{c}\text{PV}=\frac{25,000}{{(1.05)}^1}+\frac{25,000}{(1.103)}+\frac{25,000}{(1.157)}\\ =\$23,810+\$22,675.737+\$21,595.94\\ =\$68,081\end{array}$

Thus, although the building owner will earn a total economic profit of $75,000 in the next three years, the present value of these economic profits is $68,081 only.

Economics Concept Introduction

Economic profit:

The opportunity costs and explicit costs when deducted from the earned revenues gives economic profit. The economic profit is that profit which is earned after exceeding the opportunity costs.