Question

An owner can leave her building for \(120,000 per year for three years. The explicit cost of maintaining the building is \)40,000, and the implicit cost is $55,000. All revenues are received, and costs borne, at the end of each year. If the interest rate is 5 percent, determine the present value of the stream of (a) Accounting profits. (b) Economic profits.

Short answer

1. The present value of the stream of the accounting profits of the building owner is $217,859.94.

2. The present value of the stream of the economic profits of the building owner is $25,000.

Step-by-step solution

(a) Determining the Accounting profits.

To find the present value of the stream of accounting profits, we calculate first the annual accounting profit for the building owner using the following equation:

Accounting profit=Total revenue – Explicit cost.

Given: Total revenue =$120,000, and explicit cost =$40,000.

Then,

: Accounting profit= Total revenue – Explicit cost

$$\begin{gathered} =\$120,000-\$40,000 \\ =\$80,000 \end{gathered}$$

Since the owner can lease the building for three years and the revenues will be received at the end of each year, so the revenues will be identical. Same goes with the owner’s accounting profit, it will also be identical.

Total accounting profit=Accounting profit .Number of leasing years.

Therefore, total accounting profit

$$\begin{gathered} \$80,000\times 3 \\ =\$240,000. \end{gathered}$$

To find the present value of stream of the accounting profit, we use the formula:

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

Where PV is the present value, FV is the future value and I is the interest rate.

Given: FV=$80,000 and i=5%=0.05

By substituting the given numbers, we get

$PV=\frac{80,000}{(1+0.05{)}^1}+\frac{80,000}{(1+0.05{)}^2}+\frac{80,000}{(1+0.05{)}^3}$

$PV=\frac{80,000}{(1.05)}+\frac{80,000}{(1.103)}+\frac{80,000}{(1.175)}$

$PV=76,190.94+72,562.36+69,107.01$

$\mathrm{PV}=\$271,859.84$

Therefore, the present value stream of the accounting profit is $271,859.84.

(b) Determining the economic profits

The owner can lease the building for three years and the revenues will be received at the end of each year, so the revenues will be identical. So, same goes with the owner’s economic profits, it will also be identical.

To find the total economic profits, we use the equation:

Total Economic profit = Economic profit – Number of leasing years

$$\begin{gathered} =\$25,000\times 3 \\ =\$75,000. \end{gathered}$$

Therefore, the total economic profit of the owner’s building is $75,000.

To find the present value stream of the economic profit, use the formula:

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

Given: FV=$25,000 and i=5%=0.05.

We substitute the given numbers to the equation:

$PV=\frac{25,000}{{\left(1+0.05\right)}^1}+\frac{25,000}{{\left(1+0.05\right)}^2}+\frac{25,000}{{\left(1+0.05\right)}^3}$

$PV=\frac{25,000}{\left(1.05\right)}+\frac{25,000}{\left(1.103\right)}+\frac{25,000}{\left(1.158\right)}$
$PV=23,810+22,675.74+21,595.94$
$PV=68,081.84$

Therefore, the present value stream of the economic profit is $68,081.68.