FINA 3000E Lecture Notes - Lecture 3: Annual Percentage Rate, Cash Flow

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chocolatebeaver78

30 Aug 2016

School

University of Georgia

Department

Finance

Course

FINA 3000E

Professor

Poulsen

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Document Summary

R is the interest rate applied to the present value. The risk attached to the cash flow is captured by r. Venture capital has high risk but bank cd has very low. Compound interest is due not only on the principal but on prior interest also. The amount of interest due each period is the interest rate times the principal amount at the beginning of each period: most finance applications involve compound interest. Present value finds the amount at time zero. As r increases, the future value of the cash flow increases: more interest more interest gets invested. As n increases, the future value of the cash flow increases: time is your friend. How do r and n affect present value: r and n are opposites. Interest may be compounded more frequently than once per year. Compounding more frequently means we are paid interest more frequently. M= how many times interest is compounded per year.

Related Questions

QUESTION 1 The time value of money refers to the issue of: A. what the value of the stream of future cash flows is today. B. why a dollar received tomorrow is worth more than a dollar received today. C. what the time required to double an amount of money. D. why people prefer to consume things at some time in the future rather than today.

QUESTION 2 The process of converting an amount given at the present time into a future value is called: A. annualizing. B. discounting. C. compounding. D. capital budgeting. 2 points

QUESTION 3 Juan Vinson is planning to buy a house in five years. He is looking to invest $25,000 today in an index mutual fund that will provide him a return of 12 percent annually. How much will he have at the end of five years? (Round to the nearest dollar.) A. $45,000 B. $28,000 C. $44,059 D. $28,530 2 points

QUESTION 4 Which of the following statements is true with respect to the present value of a future amount? A. The higher the discount rate, the higher the present value of a single sum for a given time period. B. The relation between present value and time is exponential. C. The greater the time period, the higher the present value of a single sum for a given interest rate. D. The lower the discount rate, the lower the present value of a single sum for a given time period. 2 points

QUESTION 5 Which of the following statements is true of the rule of 72? A. It can be used to determine the amount of time it takes to double an investment. B. It is fairly accurate for interest rates between 25 and 50 percent. C. It states that the time to double your money (TDM) approximately equals 72/i, where i represents the years it takes to double your investment. D. It can be used to estimate approximate compound interest earned for a period of 72 days. 2 points

QUESTION 6 The present value of future cash flows are computed by multiplying future value with the: A. discounting factor. B. compound factor. C. interest rate. D. number of periods. 2 points

QUESTION 7 The present value of multiple cash flows is: A. greater than the sum of the cash flows. B. equal to the sum of all the cash flows. C. less than the sum of the cash flows. D. higher or lower than the cash flows depending on the interest rate. 2 points

QUESTION 8 Cash flows associated with annuities are considered to be: A. an uneven cash flow stream. B. a constant cash flow stream. C. a mix of constant and uneven cash flow streams. D. a cash flow stream with decreasing trend. 2 points

QUESTION 9 The annuity transformation method is used to transform: A. a present value annuity to a future value annuity. B. a present value annuity to an annuity due. C. an ordinary annuity to an annuity due. D. a perpetuity to an annuity. 2 points

QUESTION 10 The true cost of borrowing is the: A. annual percentage rate. B. effective annual rate. C. quoted interest rate. D. periodic rate.

Are my answers correct?

Suppose you invest $10,000 in a savings account earning 2% interest (compounded yearly) with no risk. After 7 years, how much will you have?

Principal = $10,000.00

Rate = 2.00%

Year = 7

Amount (Compound interest) = P x (1 + r/n) ^nt

Where P = Principal

r rate of interest

n = number of time interest is calculated in a year

t = time

Amount after 7 years = 10,000 x (1+0.02) ^7 = $11,486.86

Repeat Question #1, but this time there is an inflation rate of 4%. How does this change your overall return on investment? If you had a chance to invest in an account with a long-term expected rate of 5%, with a 50% chance of earning 0% nominal compound interest and a 50% chance of earning 10% nominal compound interest in each year, would you choose this account, or the savings account? Why?

Effects of inflation on PV = 10,000 x (1/(1+0.04)^7) = $7,599.18

FV Adjusted for inflation = 11,486.86 x (1/(1+0.04)^7) = $ 8,729.07

Overall return on investment will decrease by 1,270.93 = 10,000 â 8,729.07

Repeat #1 with inflation:

Amount after 7 years = 10,000 x ((1+0.02)/(1+0.04)) ^7

10,000 x (0.98) ^7 = $8,729.07.

Safe vs. Risky (not including inflation)

If I get 0%, the amount after 7 years = 10,000 x (1+0.00) ^7 = $10,000.00

If I get 10%, the amount after 7 years = 10,000 x (1+0.10) ^7 = $19,487.17

If I get 5% (expected), amount after 7 years = 10,000 x (1+0.05) ^7 = $14,071.00

I would choose the account with the 5% expected rate of return because it has higher effective annual return over the saving account. There is a higher return, but the risk is higher as compared to the savings account, which provides a certain return.

Suppose you will need $50,000 in 4 years to start up a new business you have planned. With a 5% real interest rate, how much do you have to invest now in order to achieve this goal?

This condition clearly says that we need to calculate the present value of the future earnings and it has to be the present value factor and not annuity.

Therefore, to get 50000 is the future value therefore present value of 50000

Amount to be invested today =PVF@5%,4 *Amount

= .82270 * 50000

= $ 41135.12

Repeat Problem #3, but assume you can contribute an equal amount on a yearly basis. How much would you need to put into the account each year?

Amount to invested each year = Amount /FVAF@5%,4 = 11,600.66

magentajackal745

I. Fill in the blank using a number of terms listed below (@1 point). Annuity due, Asset Mgmt ratio, Call, Comparisons, Comparative ratio analysis, Corporation, Covered, Current Ratio, DSO, Du Pont Equation , Equal, Future performance, Greater, Higher, In-the-money, Less, Liquidity, Lower, Option, Ordinary Annuity, Out-of-the-money, Percentage, Perpetuity, Put, PV, Quick, Reduced, TIE, TATO, Trend Analysis, Writer 11. The payment or receipt of equal amounts, at the end of a series of equal periods, for a specified amount of time is called a(n) _______________. 12. When a loan is amortized over a five year term, the amount of interest paid is ________________ each year. 13. You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases? It will be worth _________________. 14. The more frequent the compounding the _________________ the effective interest rate. 15. More frequent compounding results in _______________ future values and _______________ present values than less frequent compounding at the same nominal interest rate. 16. A(n) _______________ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever). 17. A(n) _________________ is a contract which gives its holder the right to buy(or sell) an asset at some predetermined price within a specified period of time. 18. The seller of an option is called the option __________________. 19. An investor who writes call options against stock held in his or her portfolio is said to be selling _______________ options. 20. When the exercise price exceeds the current stock price, a call option is said to be _____________________; however, when the exercise price is less than the current price of the underlying stock, a call option is _________________. 21. An option which gives you the right to sell a stock at a specified price within some future period is called a(n) ______________ option.

FINA 3000E Lecture Notes - Lecture 3: Annual Percentage Rate, Cash Flow

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