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

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5 May 2018

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Week 5

Fin111 Lecture Notes

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!

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!

-Todays dollar can be invested to earn interest or spent!

-Value of a dollar invested (at a positive interest rate) grows over time!

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

Timelines As Aids To Problem Solving!

-Timelines are an easy way to visualise cash ﬂows!

•Cash outﬂows as negative values!

•Cash inﬂows as positive values!

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)!

-is the process of earning interest over time!

-is the process of converting future cash ﬂows to their present values!

Future Value And Compounding!

Single Period Investment!

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Week 5

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

what 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 factor!

Two Period Investing!

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

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

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!

The Future Value Equation!

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

-The term (1+i)squared is the future value factor!

-Investing for a single period!

•Suppose you invest $100 for one year at 10% i per year, What is the future

value in one year?!

•Interest = 100(0.1) = $10!

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Document Summary

We refer to this value as the time value of money. 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. Todays dollar can be invested to earn interest or spent. Value of a dollar invested (at a positive interest rate) grows over time. Rate of interest determines trade o between spending today versus saving. Timelines are an easy way to visualise cash ows: cash out ows as negative values, cash in ows as positive values. Financial decisions are evaluated either on a future value basis or present value basis. Future value measures what one or more cash ows are worth at the end of a speci ed period.

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.

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

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: Time Preference, Compound Interest, Interest

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