Time Value of Money
Apply the present value of one dollar to accounting-related recording issues and problems
1. A company issues a five-year zero-interest-bearing note for a new vehicle Equipment is exchanged for a noninterest-bearing note. Payment of $20,000
it purchased for $25,000. The market rate of interest at the time the note on the note is to be made in one year. The market rate for notes of similar
was issued is 4%. Assuming an annual interest rate of 4% for five years is risk is 5%. Assuming an annual interest rate of 5% is appropriate, the present
appropriate, the present value of the principal is $25,000 × 0.82193 = value of the principal is $20,000 × 0.95238 = $19,048. Assuming that a
$20,548. Assuming an annual interest rate of 5% for 4 years is semiannual interest rate of 2.5% is appropriate, the present value of the
appropriate, the present value of the principal is $25,000 × 0.82270 = principal is ($20,000/2) × 1.92742 = $19,274.
$20,568.
What amount should be recorded for the purchase of this equipment?
What amount should be recorded for the cost of the vehicle?
2. Company A sells land to Company B for $100,000. Company A takes a Company A sells a parcel of land to Company B in exchange for a note
note from Company B that is due in two years. Assuming an annual receivable. The terms of the note require Company B to make a single
interest rate of 5% is appropriate, the implied annual interest is $100,000 payment of $600,000 in two years. Using a 10% interest rate, the implied
× 0.05 = $5,000, and the present value of the note is $100,000 × 0.90703 annual interest is $600,000 × 0.10 = $60,000, and the present value of the
= $90,703. note is $600,000 × 0.82645 = $495,870.
What amount should Company A record for the sale? What amount must Company A consider as proceeds from the sale of the
land in order to calculate gross profit or gain/loss on the sale, and be in
accordance with generally accepted accounting principles (GAAP)?
3. A company performs services for a customer in exchange for a A customer signs a noninterest-bearing note, promising to pay the company
noninterest-bearing note. The customer agrees to make a payment of $11,664 in two years. The payment amount is based on an annual interest
$100,000 in three years. Using a 5% interest rate, the implied annual rate of 8%, which the company believes is appropriate, resulting in the
interest is $100,000 × 0.05 = $5,000, and the present value of the note is present value of the note of $11,664 × 0.85734 = $10,000.
$100,000 × 0.86384 = $86,384.
Which amount should the company record as sales revenue from this
Which amount should the company record as service revenue from this transaction to be in accordance with generally accepted accounting
transaction to be in accordance with generally accepted accounting principles (GAAP)?
principles (GAAP)?
Apply the present value of one dollar to accounting-related recording issues and problems
4. A company requires $8,000 cash in a savings account earning 2% interest A company collects $1,500 of rent from a tenant at the end of the year. The
at the end of the year. Assuming an annual interest rate of 2% is company invests the rent money in an investment earning 4% interest per
, appropriate, the implied annual interest is $8,000 × 0.02 = $160, and the year. Assuming a 4% annual interest rate is appropriate, the implied annual
present value of the savings is $8,000 × 0.98039 = $7,843. interest is $1,500 × 0.04 = $60, and the present value of the rent is $1,500 ×
0.96154 = $1,442.
What amount should be deposited into the savings account at the
beginning of the year? What is the discounted value of this rent at the beginning of Year 1?
5. A company expects to incur $1,000,000 in environmental remediation A person opens a savings account at a bank that earns 5% interest,
costs in 10 years to restore land at one of the production sites it is compounded annually. Four years after depositing a principal sum into the
currently operating. Using an 8% interest rate, the implied annual interest account, the account contains exactly $5,000. Assuming a 5% annual interest
is $1,000,000 × 0.08 = $80,000, and the present value of the remediation rate is appropriate, the implied annual interest is $5,000 × 0.05 = $250, and
cost is $1,000,000 × 0.46319 = $463,190. the present value of the savings is $5,000 × 0.82270 = $4,114.
What amount must the company record today as an asset retirement How much principal did the person deposit?
obligation (ARO) to be in accordance with generally accepted accounting
principles (GAAP)?
6. A company needs to have $70,000 in cash at the end of four years. The
company can invest the cash now in a money market account that will
return 6% interest compounded annually. Using a 6% interest rate, the
implied annual interest is $70,000 × 0.06 = $4,200.
The following information is given:
•Assuming an annual interest rate of 4% for 6 years is appropriate, the
present value of the deposit is $70,000 × 0.79031 = $55,322.
•Assuming an annual interest rate of 6% for 4 years is appropriate, the
present value of the deposit is $70,000 × 0.79209 = $55,446.
•Assuming an annual interest rate of 6% for 6 years is appropriate, the
present value of the deposit is $70,000 × 0.70946 = $49,662.
How much does this company need to deposit today?
Apply the present value of an ordinary annuity due of one dollar to accounting-related recording issues and problems
7. A company will receive payments of $10,000 at the beginning of each A company is leasing a machine for ten years. The annual payments of
Apply the present value of one dollar to accounting-related recording issues and problems
1. A company issues a five-year zero-interest-bearing note for a new vehicle Equipment is exchanged for a noninterest-bearing note. Payment of $20,000
it purchased for $25,000. The market rate of interest at the time the note on the note is to be made in one year. The market rate for notes of similar
was issued is 4%. Assuming an annual interest rate of 4% for five years is risk is 5%. Assuming an annual interest rate of 5% is appropriate, the present
appropriate, the present value of the principal is $25,000 × 0.82193 = value of the principal is $20,000 × 0.95238 = $19,048. Assuming that a
$20,548. Assuming an annual interest rate of 5% for 4 years is semiannual interest rate of 2.5% is appropriate, the present value of the
appropriate, the present value of the principal is $25,000 × 0.82270 = principal is ($20,000/2) × 1.92742 = $19,274.
$20,568.
What amount should be recorded for the purchase of this equipment?
What amount should be recorded for the cost of the vehicle?
2. Company A sells land to Company B for $100,000. Company A takes a Company A sells a parcel of land to Company B in exchange for a note
note from Company B that is due in two years. Assuming an annual receivable. The terms of the note require Company B to make a single
interest rate of 5% is appropriate, the implied annual interest is $100,000 payment of $600,000 in two years. Using a 10% interest rate, the implied
× 0.05 = $5,000, and the present value of the note is $100,000 × 0.90703 annual interest is $600,000 × 0.10 = $60,000, and the present value of the
= $90,703. note is $600,000 × 0.82645 = $495,870.
What amount should Company A record for the sale? What amount must Company A consider as proceeds from the sale of the
land in order to calculate gross profit or gain/loss on the sale, and be in
accordance with generally accepted accounting principles (GAAP)?
3. A company performs services for a customer in exchange for a A customer signs a noninterest-bearing note, promising to pay the company
noninterest-bearing note. The customer agrees to make a payment of $11,664 in two years. The payment amount is based on an annual interest
$100,000 in three years. Using a 5% interest rate, the implied annual rate of 8%, which the company believes is appropriate, resulting in the
interest is $100,000 × 0.05 = $5,000, and the present value of the note is present value of the note of $11,664 × 0.85734 = $10,000.
$100,000 × 0.86384 = $86,384.
Which amount should the company record as sales revenue from this
Which amount should the company record as service revenue from this transaction to be in accordance with generally accepted accounting
transaction to be in accordance with generally accepted accounting principles (GAAP)?
principles (GAAP)?
Apply the present value of one dollar to accounting-related recording issues and problems
4. A company requires $8,000 cash in a savings account earning 2% interest A company collects $1,500 of rent from a tenant at the end of the year. The
at the end of the year. Assuming an annual interest rate of 2% is company invests the rent money in an investment earning 4% interest per
, appropriate, the implied annual interest is $8,000 × 0.02 = $160, and the year. Assuming a 4% annual interest rate is appropriate, the implied annual
present value of the savings is $8,000 × 0.98039 = $7,843. interest is $1,500 × 0.04 = $60, and the present value of the rent is $1,500 ×
0.96154 = $1,442.
What amount should be deposited into the savings account at the
beginning of the year? What is the discounted value of this rent at the beginning of Year 1?
5. A company expects to incur $1,000,000 in environmental remediation A person opens a savings account at a bank that earns 5% interest,
costs in 10 years to restore land at one of the production sites it is compounded annually. Four years after depositing a principal sum into the
currently operating. Using an 8% interest rate, the implied annual interest account, the account contains exactly $5,000. Assuming a 5% annual interest
is $1,000,000 × 0.08 = $80,000, and the present value of the remediation rate is appropriate, the implied annual interest is $5,000 × 0.05 = $250, and
cost is $1,000,000 × 0.46319 = $463,190. the present value of the savings is $5,000 × 0.82270 = $4,114.
What amount must the company record today as an asset retirement How much principal did the person deposit?
obligation (ARO) to be in accordance with generally accepted accounting
principles (GAAP)?
6. A company needs to have $70,000 in cash at the end of four years. The
company can invest the cash now in a money market account that will
return 6% interest compounded annually. Using a 6% interest rate, the
implied annual interest is $70,000 × 0.06 = $4,200.
The following information is given:
•Assuming an annual interest rate of 4% for 6 years is appropriate, the
present value of the deposit is $70,000 × 0.79031 = $55,322.
•Assuming an annual interest rate of 6% for 4 years is appropriate, the
present value of the deposit is $70,000 × 0.79209 = $55,446.
•Assuming an annual interest rate of 6% for 6 years is appropriate, the
present value of the deposit is $70,000 × 0.70946 = $49,662.
How much does this company need to deposit today?
Apply the present value of an ordinary annuity due of one dollar to accounting-related recording issues and problems
7. A company will receive payments of $10,000 at the beginning of each A company is leasing a machine for ten years. The annual payments of
