# Kế toán doanh nghiệp - Chapter 6: Time value of money concepts

The future value of a single amount is the amount of money that a dollar will grow to at some point in the future. Assume we deposit \$1,000 for three years that earns 6% interest compounded annually. Writing in a more efficient way, we can say the future value is \$1,000 times 1.06 to the 3rd power. In fact, the future value of any invested amount can be determined using the concise formula shown on the screen: The Present Value (PV) times 1 plus the interest rate raised to the power of the number of compounding periods.

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Time Value of Money ConceptsChapter 6Future Value of a Single AmountThe future value of a single amount is the amount of money that a dollar will grow to at some point in the future. Assume we deposit \$1,000 for three years that earns 6% interest compounded annually.\$1,000.00 × 1.06 = \$1,060.00and\$1,060.00 × 1.06 = \$1,123.60and\$1,123.60 × 1.06 = \$1,191.02Future Value of a Single AmountWriting in a more efficient way, we can say . . . . \$1,191.02 = \$1,000 × [1.06]3FV = PV × (1 + i)nFutureValueAmount Invested at the Beginning of the PeriodInterestRateNumberof Compounding PeriodsUsing the Future Value of \$1 Table, we find the factor for 6% and 3 periods is 1.19102. So, we can solve our problem like this. . . FV = \$1,000 × 1.19102FV = \$1,191.02Future Value of a Single AmountPresent Value of a Single AmountInstead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a known future amount. This is a present value question.Present value of a single amount is today’s equivalent to a particular amount in the future.Present Value of a Single AmountAssume you plan to buy a new car in 5 years and you think it will cost \$20,000 at that time.What amount must you invest today in order to accumulate \$20,000 in 5 years, if you can earn 8% interest compounded annually?Present Value of a Single AmountIf you deposit \$13,611.60 now, at 8% annual interest, you will have \$20,000 at the end of 5 years.i = .08, n = 5Present Value Factor = .68058 \$20,000 × .68058 = \$13,611.60Present Value of \$1 Table Statement of Financial Accounting Concepts No. 7“Using Cash Flow Information and Present Value in Accounting Measurements”The objective of valuing an asset or liability using present value is to approximate the fair value of that asset or liability.Expected Cash Flow ApproachThe present value factor is obtained using the company’s credit-adjusted risk-free rate of interest. An annuity with payments at the end of the period is known as an ordinary annuity.Ordinary AnnuityEnd of year 1\$10,000\$10,000\$10,000\$10,0001234TodayEnd of year 2End of year 3End of year 4Annuity DueAn annuity with payments at the beginning of the period is known as an annuity due.Beginning of year 1\$10,000\$10,000\$10,000\$10,0001234TodayBeginning of year 2Beginning of year 3Beginning of year 4Future Value of an Ordinary AnnuityWe plan to invest \$2,500 at the end of each of the next 10 years. We can earn 8%, compounded interest annually, on all invested funds. What will be the fund balance at the end of 10 years?Future Value of an Annuity DueCompute the future value of \$10,000 invested at the beginning of each of the next four years with interest at 6% compounded annually.Present Value of an Annuity DueCompute the present value of \$10,000 received at the beginning of each of the next four years with interest at 6% compounded annually.Present Value of a Deferred AnnuityIn a deferred annuity, the first cash flow is expected to occur more than one period after the date of the agreement.Present Value of a Deferred Annuity1/1/1312/31/1312/31/1412/31/1512/31/1612/31/17Present Value?\$12,500\$12,5001234On January 1, 2013, you are considering an investment that will pay \$12,500 a year for 2 years beginning on December 31, 2015. If you require a 12% return on your investments, how much are you willing to pay for this investment?Valuation of Long-term BondsCalculate the Present Value of the Lump-sum Maturity Payment (Face Value)Calculate the Present Value of the Annuity Payments (Interest)On June 30, 2013, Ebsen Electric issued 10% stated rate bonds with a face value of \$1 million. The bonds mature in 5 years. The market rate of interest for similar issues was 12%. Interest is paid semiannually beginning on December 31, 2013. What was the price of the bond issue?Valuation of Long-term LeasesCertain long-term leases require the recording of an asset and corresponding liability at the present value of future lease payments.Valuation of Pension ObligationsSome pension plans create obligations during employees’ service periods that must be paid during their retirement periods. The amounts contributed during the employment period are determined using present value computations of the estimate of the future amount to be paid during retirement. End of Chapter 6
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