If the book value of a certain piece of equipment was $5,000 exactly 5 years ago, what is its present...

Understanding the Question

We need to find: If equipment had a book value of \(\$5,000\) exactly 5 years ago, what is its present book value?

Given Information

• Book value 5 years ago = \(\$5,000\)
• Time elapsed = 5 years
• Need: Present book value

What We Need to Determine

To find a specific present book value, we need to know:

• The depreciation method and rate
• When the equipment was originally purchased
• The original purchase price

The key insight: Knowing the value at one point in time (5 years ago) isn't enough without understanding the equipment's depreciation history.

Analyzing Statement 1

Statement 1: "From the time the piece of equipment was purchased, its book value decreased by 10 percent of its purchase price each year of its life."

What Statement 1 Tells Us

This describes straight-line depreciation where the book value decreases by \(10\%\) of the ORIGINAL PURCHASE PRICE each year (not \(10\%\) of the current value).

The Critical Gap

We know the equipment was worth \(\$5,000\) five years ago, but consider these possibilities:

Example 1: Equipment purchased 10 years ago for \(\$10,000\)

• Annual depreciation = \(\$1,000\) (\(10\%\) of \(\$10,000\))
• Value 5 years ago = \(\$10,000 - (5 \times \$1,000) = \$5,000\) ✓
• Present value = \(\$10,000 - (10 \times \$1,000) = \$0\)

Example 2: Equipment purchased 7 years ago for \(\$7,000\)

• Annual depreciation = \(\$700\) (\(10\%\) of \(\$7,000\))
• Value 5 years ago = \(\$7,000 - (2 \times \$700) = \$5,600\)... Wait, this doesn't equal \(\$5,000\)!

Let's find another example:
Example 2 (revised): Equipment purchased 6.25 years ago for \(\$6,667\)

• Annual depreciation = \(\$667\) (\(10\%\) of \(\$6,667\))
• Value 5 years ago = \(\$6,667 - (1.25 \times \$667) \approx \$5,000\) ✓
• Present value = \(\$6,667 - (6.25 \times \$667) \approx \$2,500\)

Without knowing when the purchase occurred relative to "5 years ago," we get different present values.

Statement 1 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

Important: We now analyze Statement 2 independently, forgetting Statement 1 completely.

Statement 2: "The present book value of another piece of equipment is \(\$2,000\)."

This tells us about a completely different piece of equipment. It provides:

• No information about our equipment's depreciation method
• No information about our equipment's depreciation rate
• No relationship between the two pieces of equipment

Since this tells us nothing about how our equipment's value changed over 5 years, we cannot determine its present value.

Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Statements

Now let's use both statements together.

Combined Information

• Statement 1: Our equipment depreciates by \(10\%\) of its original purchase price per year
• Statement 2: Some other equipment has a present value of \(\$2,000\)

Why Together They're Still Not Sufficient

Even combining both statements, we face the same fundamental problem:

• We still don't know when our equipment was purchased
• We still don't know the original purchase price
• The information about different equipment doesn't help us

The examples from Statement 1 analysis still apply - we could have equipment worth \(\$0\) today or \(\$2,500\) today, both consistent with a value of \(\$5,000\) five years ago.

The statements together are NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice C.

The Answer: E

Neither statement alone nor both together provide enough information to determine:

• When the equipment was originally purchased
• The original purchase price

Without these critical pieces of information, we cannot calculate the present book value.

Answer Choice E: Statements (1) and (2) together are not sufficient.