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Time Value of Money

Managerial Accounting

Prepared by Diane TannerUniversity of North Florida

Chapter 14

The Tools to Evaluate Investment Opportunities

Acquisition of long-term assets require more than one year to recover the cost The value of money over time is considered a

significant factor i.e., time value of money

Money is worth more today than tomorrow Present value concepts determine the value

of money to be received in the future at today’s dollars

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American’s Got Talent

• Winners have two options– $25,000 a year for 40 years

before taxes• Present value at 4%

interest is $484,819– A lump cash payment of

$208,289 at 4% (again, before taxes)

Which is the better choice?

Winner is awarded a $1,000,000 prize!

Present Value Calculating present value

Remove the interest cost from cash flows expected to be received in the future

Interest formula I = PRT where P = Principal amount

R = Annual interest rateT = Time period (portion of a year)

Value to be received in the future i.e., future value

P + I = FV or P + PRT = FV

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Present Value Example Assume you want to accumulate $500 at the end

of one year in a bank account that pays 4% interest

FV = P + I = 500P + [P x 4% x 1 year] = 500 Present value = $480.77

Interest cost = FV ― PV I = $500.00 ― $480.77 = $19.23

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Present value $480.77+ Interest for one year (480.77 x 4% x 1) 19.23Future value $500.00

Tools to Determine TVM Amounts

• A financial calculator (BAII Plus Professional) • Excel® financial functions• Mathematical formulas

• Tredious• Trial and error calculations

• Tedious• Present value tables

• Limited

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Assumptions of the Timing of Cash Flows

1. Assume annual operating periods. Group cash flows in annual periods

2. Assume all revenues are received in cash in the same year as earned.

Eliminates adjustment for receivables and unearned revenues

2. Assume all expenses are paid in cash in the same period as incurred.

Eliminates the need to adjust for accrued expenses and deferred costs such as prepaids

3. Assume operating cash flows occur at the end of each year.

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Cash Flow Time Lines• Used to identify the point in time in which the

cash flows occur• Operating cash flows

– Occur every year as net inflows– Inflation and other budgeting issues may

cause differences in amounts each year• Investing cash flows

– Occur at time 0 as an outflow when the asset is to be purchased

– Occur at the end of the useful life as an inflow from sale of asset for its salvage value

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Using Cash Flow Time Lines

Label time periods as 0, 1, 2, 3 etc. stopping at the end of the useful life of the proposed acquisition

Post operating activity amounts on the time line based on when the cash flow is expected to occur, beginning with year 1

Post the investing cash flow for the acquisition cost at time 0 Show as negative amount since an outflow

If the investment has a salvage value Post as an investing cash flow at end of useful life Show as positive amount since an inflow

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Using Cash Flow Time Lines

Purchased a $5,000 machine with an estimated

salvage value of $500 and a 4-year estimated life.

Operating cash flows are expected to be $2,200 per

year.

0 1 2 3 4

(5,000) 2,200 2,200 2,200 2,700

Operating $2,200 + Investing $500

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The End