FIN111 Lecture Notes - Lecture 5: Critical Thinking, Time Deposit, Compound Annual Growth Rate

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Week 5 – The Time Value of Money

Time Value of Money

• How does a manager determine the value of a series of future cash flows, whether

paying for an asset or evaluating a project?

• What is the value of the stream of future cash flows today?

• We refer to this value as the time value of money (TVM)

Consuming Today or Tomorrow

• TVM is based on the belief that people prefer to consume goods today rather than

wait to consume similar goods tomorrow

- Positive time preference

• Money has a time value because a dollar today is worth more than a dollar

tomorrow

• Todays dollar a e iested to ear iterest or spet

Generalizations

• Value of a dollar invested (positive interest rate) grows over time

- The further in the future you receive a dollar, the less it is worth today

• Rate of interest determines trade-off between spending today versus saving

- The higher the interest rate the more likely you will invest funds

Timelines as Aids to Problem Solving

• Timelines are an easy way to visualize cash flows associated with investment

decisions → starts at 0 and shows the cash flows as they occur over time

- 0 is often the current point in time (today)

- Cash outflows as negative values

- Cash inflows as positive values

Future Value vs Present Value

• Financial decisions are evaluated either on a future value basis or present value basis

• Future value measures what one or more cash flows are worth at the end of a

specified period.

• Present value measures what one or more cash flows that are to be received in the

future will be worth today (at n=0).

• Discounting is the process of converting future cash flows to their present values

Definitions

• Principal amount is the amount invested

• Simple interest → amount of interest paid on the original principal amount.

• Interest on interest → interest earned on the reinvestment of previous interest

payments

• Compounding → process of earning interest over time.

• Compound interest → both simple interest and interest on interest

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Future Value and Compounding

• The future value of an investment is what the investment will be worth after earning

interest for one or more time periods

• Compounding → converting the initial amount into future values

Single Period Investment

• We can determine the value of an investment at the end of one period if we know

the interest rate to be earned by the investment

• If you invest for one period at an interest rate of i, your investment, or principle, will

grow by (1 + i) per dollar invested

• The term (1+ i) is the future value interest factor, often called simply the future value

interest factor

Two-period Investment

• A two-period investment is simply two single-period investments back-to-back

• After the first period, interest accrues on original investment (principle) and interest

earned in preceding periods

• The principle is the amount of money on which interest is paid

• Simple interest is the amount of interest paid on the original principle amount only

• Compounding interest consists of both simple interest and interest-on-interest

Example:

If you put $100 in a bank savings account that pays interest at 10% a year. How much money will you have in one

year?

FV = Principal + Interest earned

= $100(1 + 0.10)

= $110

Example:

Suppose you want to put your new amount of $110 back in the bank for another year at 10% interest.

How much money will you have at the end of the second year (FV2)?

- Multiply the new principal amount by the future value factor (1 + i)

FV2 = FV1 x (1 + i)

= 100(1 + 0.10)2 * the power of 2 means 2 years

= $121

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The Future Value Equation

• General equation to find the future value after any number of periods

• The term (1 + i)n is the future value factor.

FVn = PV x (1 + i)n

where:

• FVn = future value of investment at the end of period n

• PV = original principle (P0) or present value

• i = the rate of interest per period

• n = the number of periods

• (1 + i)n = the future value factor

What is the total compound interest?

Total compound interest = total simple interest + total interest on interest

• To find the total simple interest you find the simple interest for the first year then

multiply it for the amount of years

• To find the simple interest (SI):

SI = P0 x i

where:

• i = the simple interest for the period

• P0 = the initial principal amount

Example:

Suppose you decide to leave your $100 in the bank at 10% interest for 5 years. How much would you have at the

end of 5 years?

FV5 = $100(1 + 0.10)5

= $161.05

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Document Summary

Week 5 the time value of money. Consuming today or tomorrow: tvm is based on the belief that people prefer to consume goods today rather than wait to consume similar goods tomorrow. Positive time preference: money has a time value because a dollar today is worth more than a dollar tomorrow, today(cid:859)s dollar (cid:272)a(cid:374) (cid:271)e i(cid:374)(cid:448)ested to ear(cid:374) i(cid:374)terest or spe(cid:374)t. Generalizations: value of a dollar invested (positive interest rate) grows over time. The further in the future you receive a dollar, the less it is worth today: rate of interest determines trade-off between spending today versus saving. The higher the interest rate the more likely you will invest funds. Timelines as aids to problem solving: timelines are an easy way to visualize cash flows associated with investment decisions starts at 0 and shows the cash flows as they occur over time. 0 is often the current point in time (today)

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.

We are told that a dollar today is worth more than a dollar tomorrow. This is logical just due to the effects of inflation alone, but there are a multitude of other factors that also play into this phenomenon. The most significant concern among those factors is the issue of risk. Given that any future investment is based on a set of assumptions and educated guesses, we have to factor in the effects of risk as we look at the value of money over time. For this discussion, do the following: Locate at least one online resource (a link, article, or book, for example) pertaining to the application of time value of money and/or risk & return either within a broad industry context or within the healthcare field. In your discussion, examine the content and then share the resource (post your resource and use APA style). Summarize the resource(s) and what you find useful about it.

BUSI 320 Comprehensive Problem 3 SUMMER D

Use what you have learned about the time value of money to analyze each of the following decisions:

Decision #1: Which set of Cash Flows is worth more now?

Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive:

Option A: Receive a one-time gift of $ 9000 today.

Option B: Receive a $1400 gift each year for the next 10 years. The first $1400 gift would be

received 1 year from today.

Option C: Receive a one-time gift of $18,000 10 years from today.

Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect the interest rate to be 7% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect to be able to earn 10% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Decision #2 begins at the top of page 2!

Decision #2: Planning for Retirement

Tom and Tricia are 22, newly married, and ready to embark on the journey of life. They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $1800 per year to prepare for retirement. Tricia just told Tom, though, that she had heard that they would actually have more money the day they retire if they put $1800 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments â then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do). Please help Tom and Tricia make an informed decision:

Assume that all payments are made at the END of the year, and that the rate of return on all yearly investments will be 8% annually.

(Please do NOT ROUND when entering âRatesâ for any of the questions below)

How much money will Tom and Tricia have in 45 years if they do nothing for the next 10 years, then put $1800 per year away for the remaining 35 years?

How much money will Tom and Tricia have in 10 years if they put $1800 per year away for the next 10 years?

b2) How much will the amount you just computed grow to if it remains invested for the remaining

35 years, but without any additional yearly deposits being made?

c)How much money will Tom and Tricia have in 45 years if they put $1800 per year away for each of the next 45 years? (This amount can be referred to as their âretirement nest eggâ)

Using your solution to question C, what is the value in today's dollars, assuming 3% average inflation, of Tom and Tricia's retirement nest egg? (âTodayâ Tom and Tricia are 22 years old. Retirement is 45 years away!)

e)If Tom and Tricia wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years assuming an annual interest rate of 8% in order to have $700,000 saved up on the first day of their retirement 45 years from today?

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FIN111 Lecture Notes - Lecture 5: Critical Thinking, Time Deposit, Compound Annual Growth Rate

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