5.1 Time Value of Money

Time value of money: a dollar today is worth more than a dollar in the future.
Focus on present value (PV) and future value (FV) techniques.
PV techniques are used in accounting to value assets and liabilities on financial statements.
Affects revenue and expense recognition on the income statement.
PV and FV techniques are valuable for determining fair value, evaluating long-term investment proposals, and measuring impairment losses.

Long-term notes receivables.
Long-term debt (notes payable, bonds payable, mortgage payable).
Capital leases (valuation of both the leased asset and the lease liability).
Long-term investments in bonds held to maturity.
Sinking funds (funds set aside to retire debt).
Environmental liabilities.
Pension and post-retirement benefits.
In accounting, long-term receivables and payables are reported at present value on the balance sheet.
This helps end-users evaluate the cash flow needed to retire debt or the cash flow the company would receive if a note receivable were extinguished.

When assessing investment or borrowing options, compare today's dollar and tomorrow's cash flow on the same basis.
Present value (PV) is the equivalent value today of a future cash flow, discounted back to the present.
Discounting eliminates the compounding of interest over time.
$PV$ means the dollar today, the equivalent value of receiving a dollar today minus the interest of a cash flow that could be received in the future.

Measurement: Determining the dollar amount to record for a transaction or report in financial statements.
Example: Long-term contracts with customers who finance purchases over time.
Customers make installment payments over several years for services delivered today.
Future cash flows are not equivalent to what would be accepted today minus the interest.
Sales revenues should be recorded when earned.
Understand how notes receivable or payable change over time, affecting the balance sheet.

Single lump sum: A one-time cash flow that exists now or will in the future.
Series of equal payments (annuity): Equal dollar amounts paid or received periodically, such as installment loans or cost savings.
Annuity: A series of equal payments spaced equally in time.

Single cash flow that occurs at the end of the period.
Scenario: Desert Company needs $25,000 in three years to retire a note payable. How much must Desert invest today in an account earning 6% interest?
The goal is to determine the equivalent value today, which will grow to $25,000 at the end of year three with 6% interest.

Using the present value of a dollar table, the factor for 6% for three compounding periods is $0.8396$ .
This factor eliminates three years of interest compounding at 6%.
Formula: Future Value × Present Value Factor = Present Value
$25,000
eqimes 0.8396 = $20,990
Desert Company needs to invest $20,990 today to have $25,000 at the end of year three.
Interest eliminated: $25,000 - $20,990 = $4,010

Business decisions often involve a series of equal payments.
Annuity: Series of equal periodic payments spaced equally in time.
Determine whether it is an ordinary annuity or an annuity due, based on the timing of cash flows.

Payments occur at the end of the period (year, month, quarter).
Abbreviated as $PVOA$ (Present Value of Ordinary Annuity).
Cash flows:
- End of year one: Payment
- End of year two: Payment
- End of year three: Payment
- End of year four: Payment
Use a present value of an ordinary annuity factor to solve.

Payments occur at the beginning of the period.
Abbreviated as $PVAD$ (Present Value of Annuity Due).
Cash flows:
- Beginning of year one: Payment (principal only, no interest)
- Beginning of year two: Payment (principal and interest)
- Beginning of year three: Payment (principal and interest)
Use a present value of an annuity due factor to solve.
The first cash flow is made today, so no interest has accrued.

To solve for the present value of an annuity, take the cash flow (payment) and use the appropriate factor (PVOA or PVAD).
The factor eliminates the compounding of interest from each cash flow, giving the equivalent value today.

Scenario: Sparky Consulting performed services for ABC Company and accepted a five-year note receivable.
Five equal annual payments of principal and interest in the amount of $10,000
Customer's normal borrowing cost is 6%.
Question: How much revenue can Sparky recognize on January 1 if the first payment is due on December 31 of year one?

The first payment of $10,000 is received at the end of year one.
Labeled as a PVOA.
Use the factor for 6% for five compounding periods from the present value of an ordinary annuity table which is $4.2124$ .
Cash flows sum to $50,000 , but the equivalent value today is different because of interest.
Solve for present value:
- PV = Payment
  eqimes Ordinary Annuity Factor
- PV = $10,000
  eqimes 4.2124 = $42,124
Sparky would record service revenue of $42,124 , the cash equivalent value of what they would have accepted today.

Debit Note Receivable: $42,124
Credit Service Revenue: $42,124
The difference between $50,000 and $42,124 ( $7,876 ) will be recognized as interest revenue over time.
Revenue is recognized after it has been earned.

Payment remains $10,000
Use an annuity due factor.
Get factor from the table for the present value of an annuity due at 6% for five compounding periods, which is $4.4651$ .
PV = Payment eqimes Annuity Due Factor
- PV = $10,000
  eqimes 4.4651 = $44,651
The equivalent value today is $44,651 .

Cash flows received in the future (either a single sum or a series of equal payments) are not the same as a dollar today.
In order to make an informed decision, compare them in present value terms.