FIN111 Lecture Notes - Lecture 5: Compound Interest, Discount Window, Time Preference

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10 May 2018

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Time value of money:

• The time value of money

• Future value and compounding

• Present value and discounting

• Additional concepts and applications

How does a manager determine the value of a series of future cash flows, whether paying for an

asset or evaluating a project?

Time Value of Money:

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 can be invested to earn interest or spent.

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

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

Timelines as aid to problem solving:

• Timelines are an easy way to visualise cash flows.

Cash outflows as negative values.

Cash inflows as positive values.

E.g. 5 year time line for $10,000 investment

Future value versus 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).

• Compounding is the process of earning interest over time. . It is the process of converting

an amount given at the present time into a future value.

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

Future value and compounding:

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) is per dollar invested.

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

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Document Summary

Future value and compounding: the time value of money, present value and discounting, additional concepts and applications. We refer to this value as the time value of money (tvm) Timelines as aid to problem solving: timelines are an easy way to visualise cash flows. Financial decisions are evaluated either on a future value basis or present value basis. It is the process of converting an amount given at the present time into a future value: discounting is the process of converting future cash flows to their present 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. Simple interest is the amount of interest paid on the original principle amount only. Future value equation (we are not using table, equation only) General equation to find the future value after any number of periods.

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.

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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8. You have saved $250,000 for a cash down payment to buy a house. You are currently prepared to
pay up to $3,000 per month for a 20-year mortgage, and your bank is currently charging 4% p.a.
interest, compounded monthly. What amount is closest to the maximum you can pay for a house?
A) $633,453
B) $745,066
C) $824,204
D) $1,205,365
E) None of the above
9. You have just accepted a job offer, which came with a signing bonus of $5,000 to be paid today
in your retirement account. Your employer will also contribute an extra $10,000 at the end of
each full year (you start work tomorrow!). If this account is expected to earn 10% p.a.
compounded semi-annually, which number is closest to the amount of money will you have in
that account after five years? (including the payment for that year).
A) $59,500
B) $65,500
C) $69,500
D) $72,500
E) None of the above
10. Which of the following is/are an advantage of being a publicly listed company?
A) Access to capital markets
B) Limited liability
C) Unlimited life
D) All of the above
E) None of the above
11. A bond with 15 years to maturity is paying 6% coupons semi-annually, and the last coupon has
just been paid. The face value is $1,000 and the yield to maturity is 8% p.a.
What is the price today closest to:
A) $827.08
B) $932.95
C) $1,000.00
D) $1,324.32
E) None of the above
12. Company HDE is expected to pay an interim dividend of $1.00 six months from now and a final
dividend of $2.10 one year from now. HDE is then expected to repeat the same pattern every year
for the foreseeable future with no growth in dividends. Given that the appropriate effective
discount rate is 7.0% p.a., what is the stock price of HDE closest to today?
A) $30
B) $35
C) $40
D) $45
E) None of the above
13. Which of the following statements is FALSE?
A) The process of moving a value or cash flow forward in time is known as compounding.
B) The effect of earning interest on interest is known as compound interest.
C) It is only possible to compare or combine values at the same point in time.
D) A dollar in the future is worth more than a dollar today.
E) Interest paid only on the principal is simple interest.
14. Consider the following four alternatives:
1. $132 received in two years.
2. $160 received in five years.
3. $200 received in eight years.
4. $220 received in ten years.
The ranking of the four alternatives from most valuable to least valuable if the interest rate is
7% per year would be:
A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 3, 4, 2, 1
D) 3, 1, 2, 4
E) 3, 1 = 2, 4

FIN111 Lecture Notes - Lecture 5: Compound Interest, Discount Window, Time Preference

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