time. Invest:NPV>0 Present Value of Annuities: V0=CF1- 11+knk=CF[PVIFAk;n] = Present Value of Perpetuities:V0=CFk 1k=PVIFAk‚n≡Annuity‚ n→∞ Future Values of Annuities:Vn=V0*FVIFk‚n=CF*PVIFAk;n*FVIFk;n=CF*FVIFA(k;n) FVIFAk;n=1+kn-1k Annuities Due: PVIFAduek;n=1-11+knk(1+k)‚ FVIFAduek;n=1+kn-1k(1+k) Growing Annuity:V0=CF1*1-1+gn1+knk-g≡Annuity at g=0‚ CF2=CF1(1+g) Growing Perpetuity:V0=CF1k-g≡Prep at g=0 Amortized Loans: V0=CF*PVIFA(k;n)
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more that what they earn‚ so they pay with credit cards or take out loans which have to be paid off at some point in the future. In this paper we will discuss the present value of money‚ the future value of money‚ compounding effect of money‚ and annuities. Knowledge of this basic time value of money principles and calculations is crucial for making sound financial decisions in business as well as in our personal lives. Looking at the borrowing transaction from the borrower’s perspective‚ there are
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retirement plan are addressed at the end. CASE STUDY SOLUTION Question 1: Choosing a Discount Rate on debt securities. Given a discount rate i%‚ it is straightforward to convert a stream of cash flows into a present value‚ a FV (FV)‚ or an annuity. For example‚ the present value of a sum of
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at year 5 than option A given a zero rate of return. e. Option A is preferable because it is an annuity due. Answer: b Difficulty level: Medium Topic: UNEVEN CASH FLOWS AND PRESENT VALUE 3. You are comparing two annuities with equal present values. The applicable discount rate is 7.5 percent. One annuity pays $5‚000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year? a. $4‚651 b. $5‚075 c. $5
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Chapter 5: Time Value of Money Multiple Choice Questions 1. What is the total amount accumulated after three years if someone invests $1‚000 today with a simple annual interest rate of 5 percent? With a compound annual interest rate of 5 percent? A. $1‚150‚ $1‚103 B. $1‚110‚ $1‚158 C. $1‚150‚ $1‚158 D. $1‚110‚ $1‚103 Level of difficulty: Easy Solution: C. Simple interest rate: $1‚000 + ($1‚000)(5%)(3) = $1‚150 Compound interest rate: $1‚000(1.05)3 = $1‚158 2
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Importance of Compounding There are many important features of compounding. One valuable feature of compounding is that it makes money grow‚ and grow fast‚ especially when compounding an annuity. An annuity is a series of installments‚ usually yearly‚ in an account that bears interest. Once interest is earned‚ an annuity allows that interest to be compounded setting the way for an investor to earn interest on interest. Another important feature of compounding is time. The longer money is left in an
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learn them from the owner’s manual. (There is one example of using these functions in red below.) If your calculator is showing a comma where there should be a decimal point: [GOLD] [./‚] To switch from end mode (for ordinary annuity calculations) to begin mode (for annuities due): [GOLD] [BEG/END] You want to be in END mode for most calculations. If you use begin mode‚ you MUST change back to end mode after finishing your calculations in begin mode. Time Value of Money calculations: FV of a Lump
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8 years from now discounted back to the present at 3 percent 1000/(1.03)^8 = 789.41 d. $1‚000 to be received 8 years from now discounted back to the present at 20 percent 1000/(1.2)^8 = 232.56 (Present value of an annuity) what is the present value of the following annuities? a. $2‚500 a year for 10 years discounted back to the present at 7 percent 2500 x {1-(1/1.07)10}/.07 = 2500 x 7.02 =17550 b. $70 a year for 3 years discounted back to the present at
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00 9.4% Yr 5 2 =(250‚0 00*2/21 )=23‚81 0 126‚190. 00 138‚095. 00 9.0% Yr 6 1 =(250‚0 00*1/21 )=11‚90 5 138‚095. 00 0 8.6% 2.a. Explain the mechanism of calculating the present value of cash flows.What is annuity due? How can you calculate the present and future values of an annuity due? Illustrate Ans. Money has time value: e.g. Rs 1‚000 received today is not the same after year Present value of cash flow: It shows the value of expected amount at current value. Discount rate = Inflation
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Lottery Winnings – Looks Can Be Deceptive! State-sponsored lotteries are extremely popular and highly successful methods by which state governments in many countries raise much needed funds for financing public expenses‚ especially education. In Michigan alone‚ during the year 2000‚ Michigan Lottery reported annual sales of $1.69 billion in fiscal 2000‚ and generated $618.5 million in net revenue for the state School Aid Fund‚ supporting public education (K-12) programs throughout the state. Retailers
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