Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)


 Claud McDowell
 6 years ago
 Views:
Transcription
1 Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for something uncertain tomorrow. 1.2 The uncertainty factor increases with time the distant the cash flows, the more uncertain they become. 1.3 The lower is the compounding period, the higher is the effective rate of interest. 1.4 With high inflation rate, the interest rates tend to increase. 1.5 One of the reasons for attributing time value to money is that individuals prefer future consumption to current consumption. 1.6 The nominal rate of interest is equal to the effective rate of interest when interest is compounded annually. 1.7 The rule of 72 is more precise (provides a better estimate) than the rule of 69 to find the period required to double your initial amount. 1.8 Financial analysis require an explicit consideration of time value of money because most financial problems at corporate and individual level involves cash flows occurring at different points in time. 1.9 Given a principal amount of Rs. 10,000 to be invested for 9 months, it is better to invest in a scheme that offers 12% annual compound interest than investing in a scheme that earns 12% simple interest.
2 1.10 A bank that pays 10% interest compounded annually pays a higher effective rate of interest than a bank that pays 10% interest compounded quarterly The formula for effective rate of interest (re) is re= (1+r/m) n A regular (deferred) annuity is one in which a series of periodic cash flows of equal amount occur at the beginning of each period The rule of 72 is useful in determining the future value of an annuity given the rate of interest Frequency of compounding has no effect on interest earned Maximum benefit of compounding occurs when money is compounded daily Present value of an uneven stream of cash flows can be calculated with the help of present value of annuity table While investing money it is always better to insist on a higher frequency of compounding Increased frequency of compounding means the same thing as decrease in compounding period The benefits from increased compounding frequency decrease with each successive increase in compounding frequency In case of most of banks, fixed deposit money is compounded quarterly Effective rate of interest depends on the compounding period Higher the compounding period, higher is the effective rate of interest.
3 1.23 In simple interest, interest for each year in same The process of determining present value is often called discounting Continuous compounding results in the maximum possible future value for given rate of interest and time period A perpetuity is an annuity that continues for 100 years In perpetuity, the principal amount remains intact The present value of any future sum is inversely related with rate of interest Continuous compounding occurs when interest is compounding daily Sinking fund factor is used to determine the periodic fixed amount that must be invested regularly to accumulate a specified sum at the end of a given period at a given rate of interest When debt(loan) is amortized in periodic fixed installments, the principal component of installment declines over time The compound value of any sum invested today varies directly with rate of interest (r) and time period (n) Money has time value because a sum of money to be received in future is more valuable than the same amount today The process of compounding assumes discounting at same rate An annuity due is one in which periodic cast flows of equal amount occur at the beginning of each period.
4 1.36 Compounding over the same time period, annuity due will have a higher future value than ordinary annuity An amortization schedule tells us about the interest component and principal repayment component of each fixed installment paid by borrower towards loan repayment Annuity tables can be used far all types of cash flows For a given rate of interest(r) and given number of years(n), the present value annuity factor will be greater than future value annuity factor In present value tables, all values are less than Present value of annuity due is equal to present value of ordinary annuity x (1 + r) Future value of annuity due = present value of ordinary annuity x (1 + r) PVAF (Present value Annuity Factor) is knows as capital recovery factors FVAF (Future value Annuity Factor) is known as sinking fund factors The price of any asset today is the present value of all the future cash flows associated with the asset Bond prices vary inversely with the rate of interest An annuity is a stream of constant cash flows occurring at regular intervals of time A perpetuity is an annuity that continues for ever i.e., till infinity.
5 1.49 The present value of a mixed stream of cash flows is the sum of the present values of the individual cash flows An investment option that comes with specified present value and future value after given period has hidden rate of interest. Solutions : Section I 1.1 T 1.2. T 1.3. T 1.4 T 1.5 F 1.6 T 1.7 F 1.8 T 1.9 F 1.10 F 1.11 F 1.12 F 1.13 F 1.14 F 1.15 F 1.16 F 1.17 T 1.18 T 1.19 T 1.20 T 1.21 T 1.22 F 1.23 T 1.24 T 1.25 T 1.26 F 1.27 T 1.28 T 1.29 F 1.30 T 1.31 F 1.32 T 1.33 F 1.34 T 1.35 T 1.36 T 1.37 T 1.38 F 1.39 F 1.40 T 1.41 T 1.42 F 1.43 T 1.44 T 1.45 T 1.46 T 1.47 T 1.48 T 1.49 T 1.50 T
6 Time Value of Money Work book Section II Fill in the blanks Fill in the blanks with suitable answers 2.1 The process of determining present value is often called... and is the reverse of the... Process. 2.2 A... is an annuity that continues forever. 2.3 An... is a series of cash flows of fixed amount occurring at regular intervals of time. 2.4 A...is the annual deposit or investment of fixed amount that is necessary to accumulate a specified future sum. 2.5 If a loan is to be repaid in equal periodic amounts, it is said to be an Effective annual rate of interest is... to nominal rate of interest, when interest is compounded annually. 2.7 Effective annual rate of interest with halfyearly compounding is... than, with quarterly compounding. 2.8 The formula for effective annual rate of interest (re) is If the repayment of a loan is to start after a gap of few years, it is called an... loan The general formula for intra year compounding is Using the rule of 72 to find doubling period we...72 by...
7 2.12 Annuity (constant annual cash inflow) Rate of interest (r) is the formula to find present value of Lower is the compounding period, the... is the effective annual rate of interest The formula to find the growth of money with continuous compounding is Present or future value of annuity due = present or future value of ordinary annuity x PVAF (present value annuity factor) refers to FVAF (future value annuity factor) refers to When cash flows of constant amount occur at the beginning of each period, the annuity is called an Compound interest is more than simple interest because in... interest is earned on interest compounding results in maximum possible future value at the end of n periods for a given rate of interest. Answers to section II 2.1 Discounting, compounding 2.2 perpetuity 2.3 Annuity 2.4 sinking fund 2.5 amortized loan 2.6 equal 2.7 less 2.8 re = (1 + r/m) m deferred 2.10 FVn= (1 + r/m) mn 2.11 divide, r 2.12 perpetuity 2.13 higher 2.14 FVn = Po. e rn 2.15 (1+r) 2.16 capital recovery factor 2.17 sinking fund factor 2.18 annuity due 2.19 compound interest 2.20 continuous.
8 Time Value of Money Work book Section III Multiple choice questions Mark ( ) the right answer from given alternatives : 3.1 Money has time value because: a. Individuals prefer future consumption to present consumption. b. Money today is more certain than money tomorrow c. Money today is wroth more than money tomorrow in terms of purchasing power. d. There is a possibility of earning risk free return on money invested today. e. (b), (c) and (d) above. 3.2 Given an investment of Rs. 10,000 to be invested for one year; a. It is better to invest in a scheme that pays 10% simple interest. b. It is better to invest in a scheme that pays 10% annual compound interest. c. Both (a) and (b) provide the same return
9 3.3 Given an investment of Rs. 10,000 for a period of one year, it is better to invest in a scheme that pays: a. 12% interest compounded annually b. 12% interest compounded quarterly c. 12% interest compounded monthly d. 12% interest compounded daily 3.4 Given an investment of Rs. 10,000 over a period of two years, it is better to invest in a scheme that pays; a. 10% interest in the first year and 12% in second year. b. 12% interest in the first year and 10% in second year. c. Both (a) and (b) above provide the same return 3.5 The rule of 72 is used to find; a. Approximate doubling period, given the interest rate (r) b. Approximate interest rate, given the doubling period (n) c. Both (a) and (b) above. 3.6 The relation between effective annual rate of interest (re) and nominal rate of interest (r) is best represented by; a. re = (1 + r /m) mn 1 b. re = (1 + r/m) m 1 c. r = (1 + re/m) 1 d. None of the above
10 3.7 To find the present value of a sum of Rs. 10,000 to be received at the end of each year for the next 5 years at 10% rate, we use: a. Present value of a single cash flow table b. Present value of annuity table. c. Future value of a single cash flow table d. Future value of annuity table 3.8 Sinking fund factor is the reciprocal of : a. Present value interest factor of a single cash flow. b. Present value interest factor of an annuity. c. Future value interest factor of a single cash flow. d. Future value interest factor of an annuity. 3.9 According to the 'Rule of 69' doubling period of an investment at an interest rate of 15% is : a. 4.6 years b. 4.2 years c years d years 3.10 If the effective rate of interest compounded quarterly is 16%, then the nominal rate of interest is : a. 14.6% b. 15% c. 14.8% d %
11 3.11 If the interest rate on a loan is 1% per month, the effective annual rate of interest is : a. 12% b % c % d % 3.12 If a loan of Rs. 30,000 is to be paid in 5 annual installments with interest rate of 12% p.a. then the equal annual installment will be; a. Rs b. Rs c. Rs 7812 d. Rs X took a housing loan of Rs. 25,00,000. The loan is to be redeemed in 120 monthly installments of Rs. 31,000 each to be paid at the end of each month. What is the implied interest rate per annum. a. 8.50% b. 8.1% c. 7.70% d. 9.12%
12 3.14 The difference between effective annual rate of interest with monthly and quarterly compounding, when nominal rate of interest is 10% is; a. 0.10% b. 0.14% c. 0.21% d. 0.09% 3.15 A bond has a face value of Rs and a coupon rate of 10%. It will be redeemed after 4 years at 10% premium. Find the present value of bond at a required rate of 12% : a. Rs b. Rs c. Rs d. Rs Axis bank offers 10% nominal interest for a three year fixed deposit to senior citizens. If the compounding is done quarterly, then effective annual rate of interest is : a % b % c % d %
13 3.17 X deposits Rs at the end of every month in a bank for 5 years. If the interest rate offered by bank is 8% p.a. compounded monthly, the accumulated sum X will get after 5 years will be: a. Rs. 1,76,802 b. Rs. 1,83,692 c. Rs. 1,91,507 d. Rs. 1,94, You invest Rs at the end of year one and Rs at the end of second year and Rs each year from third to tenth. Find the present value of stream at discount rate of 10% a. Rs. 25,062 b. Rs. 24,712 c. Rs. 26,502 d. Rs. 24, If you take a loan of Rs 1,00,000 today and return Rs. 1,51,807 after 4 years to clear off the loan, what effective annual interest rate is paid by you: a. 12% b. 13% c. 11% d. 12.4%
14 3.20 In how much period Rs. 1 becomes Rs. 3 at 12% rate of interest compounded annually. a. 12 years b. 8 years c years d years 3.21 Which of the following statements is true? a. Frequency of compounding, has no effect on rate of interest. b. An annuity is a series of cash flows of variable amount. c. The nominal rate of interest is equal to or more than the effective rate of interest. d. Cash flows occurring in different time periods cannot be compared unless they are discounted to a common date If a 12% loan is to be paid back after 10 years, the sinking fund factor will be equal to: a b c d Mr X has decided to deposit Rs. 70,000 per year in his public provident fund account for next 15 years. At 8% interest compounded annually, how much money will accumulate in his accounts? a. Rs. 19,00,648 b. Rs. 20,14,340 c. Rs. 16,05,151 d. Rs. 19,91, 243
15 3.24 If a bank offers to double your money in 8 years, what is the effective rate of interest? a. 8.9% b. 9.7% c. 10.2% d. 9.05% 3.25 An investment of Rs.5000 in a deep discount bond will return Rs. 1,00,000 in 20 years. Find the interest rate implicit in the offer? a % b % c % d % 3.26 A machine is to be replaced after 5 years, when it is expected to cost Rs. 10,00,000. How much equal sum should be set aside and invested, at the end of each year at 12% p.a. to accumulate the desired sum? a. Rs. 1,62,416 b. Rs. 1,57,410 c. Rs.1,75,115 d. Rs.1,53,429 Answer to Section III 3.1 e 3.2 c 3.3 d 3.4 c 3.5 c 3.6 b 3.7 b 3.8 d 3.9 c 3.10 d 3.11 c 3.12 d 3.13 a 3.14 d 3.15 a 3.16 b 3.17 b 3.18 a 3.19 c 3.20 d 3.21 d 3.22 b 3.23 a 3.24 d 3.25 d 3.26 b
16
17 Time Value of money Work book Section IV Practical Sums Based on Future (compound) Value and Present (Discount) Value Equation : 4.1 If you invest Rs. 10,000 today for a period of 5 years, what will be its maturity value if the interest rate p.a. is: (a) 8% (b) 10% (c) 12% (d) 15% 4.2 If you invest Rs today at interest rate of 10% p.a., what will be its maturity value after 100 years under: (a) Simple interest (b) Compound interest 4.3 How many years will it take for Rs invested today at 12% p.a. rate of interest to grow to Rs. 160,000? Use rule of In how much period your Rs. 10,000 becomes Rs. 20,000 at 15% rate of interest, using (a) Rule of 72, (b) Rule of How much a deposit of Rs. 50,000 grows at the end of 5 years if the nominal rate of interest is 12% p.a. and money is quarterly compounded? Compare this with the amount you get with annual compounding. 4.6 Nominal rate of interest is 12% p.a. Find the effective annual rate of interest when the money is compounded: (a) Annually (b) Semiannually (c) Quarterly (d) Monthly (e) Daily
18 4.7 Find the growth rate of sales from 1998 to 2004 from given data: Year Sales (in million of Rs.) A company currently pays a dividend of Rs. 1 per share which is expected to grow to Rs. 3 per share in 10 years. Find the average annual compound growth rate? 4.9 You invest Rs today and get Rs. 10,000 after 6 years. What is the implicit interest rate in this? 4.10 If you are given a choice between Rs today and Rs. 15,000 after 10 years. Which one will you choose and what your choice implies? 4.11 Find, how much Rs. 10,000 will grow at 8% p.a. nominal rate of interest after 3 years when compounding is done: (a) monthly (b) annually (c) perpetually ( continuously) What is the present value of Rs. 1,00,000 to be received 10 years from now if rate of interest is 12% p.a.? 4.13 What is the present value of Rs. 50,000 receivable 40 years from now if rate of interest (r) is 8% p.a.? 4.14 What is the present value of following cash flow stream at 10% p.a. rate of interest. Year Cash flows (in rupees) 10,
19 Answer to section IV 4.1 (a) Rs (b) Rs (c) Rs (d) Rs (a) Rs (b) Rs. 1,37,80, years 4.4 (a) 4.8 years (b) 4.95 years 4.5 Rs , Rs (a) 12% (b) 12.36% (c) 12.55% (d) 12.68% (e) 12.75% % % % % 4.11 (a) Rs (b) Rs (c) Rs Rs Rs Rs
20 Time Value of Money Workbook Section V Questions based on Annuities Future value and Present value of Annuities 5.1 Mr. X deposits Rs. 10,000 at the end of every year for 5 years in his savings account paying 5% p.a. interest. How much money he will get at the end of 5 years? 5.2 Mr. X is planning to buy a car after 5 years when it is expected to cost Rs. 5 Lakh. How much he should save annually to reach his target if his savings earn a compound annual interest rate of 12%? 5.3 A machine is to be replaced after 10 years when it is expected to cost Rs. 10,00,000. How much money should be set aside and invested in a sinking fund at 12% interest p.a. to accumulate the funds needed for replacement? 5.4 X Ltd has Rs. 10,00,000 worth of debentures outstanding. They are to be redeemed 5 years from now. If the interest rate is 12% p.a., how much money should be set aside and invested each year in a sinking fund to accumulate the funds needed for redemption? 5.5 A finance company advertises that it will pay Rs. 1,00,000 at the end of 5 th year to any person, who deposits Rs. 16,000 at the end of every year for 5 years. What interest rate is implicit in this offer? 5.6 A travel operator announces that it can take anybody on a world tour at a price of Rs. 2,00,000. I wish to avail this offer. I can save Rs. 25,000 annually and my savings earn 10% p.a. compound interest. How long I will have to wall?
21 5.7 You expect to receive Rs. 10,000 annually for 3 years at the end of each year. What is its present value at 10% rate? 5.8 You can afford to pay Rs. 10,000 per month for 3 years to a finance company for a housing loan. Finance company charges 1% interest per month. How much I can borrow? 5.9 You have borrowed Rs. 10,00,000 from HDFC to finance a house. It charges 1.25% per month. You can pay Rs. 15,000 per month. What will be the maturity period of loan? 5.10 Your father deposits Rs. 3,00,000 on retirement in a bank which pays 10% p.a. interest compounded annually. How much fixed amount (annuity) he can withdraw annually at the end of every year for 10 years? 5.11 If you deposit Rs. 1,00,000 today, a bank promises to pay you annually Rs. 20,000 for 6 years. What interest rate is implicit in this offer? 5.12 Firm X borrows Rs. 1,000,000 at 15% p.a. interest. The loan is to be paid back in 5 equal annual installments at the end of each year. Find the amount of each equated installment and also make amortization schedule. Answers to Section V 5.1 Rs Rs Rs Rs. 1,57, % years 5.7 Rs Rs. 3,01, months 5.10 Rs % 5.12 Rs
22 Time Value of Money Workbook Section VI Advance problems on time value of money 6.1 You invest Rs a year for 3 years and Rs a year for 7 years thereafter at interest rate of 12% p.a. What will be the maturity value at the end of 10 years?. 6.2 A company is offering to pay Rs. 10,000 annually for a period of 10 years, if you deposit Rs 50,000 now. What is implied interest rate in this offer? 6.3 Mr. X receives Rs a year for the first 8 years and Rs a year forever thereafter. Calculate the PV if interest rate is 12% p.a. 6.4 You invest Rs at the end of year 1, Rs 20,000 at the end of year 2 and Rs 50,000 at the end of each year from 3 rd year to 10 th. Calculate the PV of this stream if the discount rate is 10%. 6.5 Sunil is due to retire 20 years from now. He wants to invest a lump sum now so as to be able to withdraw Rs. 10,000 every year, beginning from the end of the 20 th year. How much he should invest now if r = 12%? 6.6 Sunil has deposited Rs 2,00,000 in a bank which pays 8% p.a. How much can he withdraw at the end of every year for a period of 25 years, so that there is no balance left in the end?
23 6.7 Mr X is going to retire soon. His employer gives him two options; (a) an annual pension of Rs 8000 for as long as he lives, and (b) a lump sum amount of Rs 50,000. If he expects to live for 20 years and his time preference rate is 10%, which option is better for X? 6.8 How much do you need to invest now at interest rate of 10% p.a. to have a perpetual income of Rs 20,000 from the beginning of the 15 th year? 6.9 In order to accumulate Rs at the end of 10 th year, how much you should invest at the beginning of each year if r = 10%? 6.10 You require Rs 10,000 at the beginning of each year from 10 th to 14 th year. How much you should invest at the end of each year from 1 st to 5 th year if interest rate is 10% p.a.? 6.11 Calculate the PV of an annuity of Rs. 5,000 receivable for 35 years, if the first receipt occurs after 15 years. Take discount rate as 12% Akshay takes a bank loan of Rs 10,000 to purchase a scooter. He has to pay an installment of Rs 500 p.m. for next 2 years. What is the implied interest rate? 6.13 As a potential investor you are considering the purchase of a bond that pays 10% per year on face value of Rs The bond will mature in 5 years at a premium of 5%. What price you should be willing to pay if you require 12% rate of return You deposit a sum of Rs 10,000 with a bank at 12%. If you want to withdraw Rs 1,500 every year, for how long can you do this?
24 6.15 A Rs 20,00,000 plant expansion is to be financed as follows; 15% down payment and remainder is borrowed at 9% interest. The loan is to be repaid in 8 equal installments starting 4 years from now. Find the amount of each equal annual installment Ten years from now Mr. X will start receiving a pension of Rs 3,000 a year. The payment will continue for 16 years. How much is the pension worth now at 10%? 6.17 You deposit Rs. 4,500 per year at the end of each year for next 25 years in an account that yields 10% p.a. How much you could withdraw at the end of each of the next twenty years following your last deposit? 6.18 A finance company makes an offer that if you deposit Rs 10,000 today, you can receive annual return of Rs 1,100 perpetually, starting from 5 th year. Should this offer be accepted if the rate of interest preference is 8% p.a.? 6.19 A deposit is made in a bank that earns 10% compounded half yearly. It is desired to withdraw Rs 50,000 three years from now and Rs. 70,000 five years from now. What is the size of initial deposit? 6.20 A loan of Rs 1,00,000 is taken on which interest is 10%. The repayment is to start at the end of 3 rd year from now. What should be the annual payment if loan is to be repaid in 6 equal annual installments?
25 6.21 You want to buy a house costing Rs. 20 lakh. You approach a housing finance company and finance 50% of cost. Finance company charges 1% per month. You can pay Rs. 12,000 per month towards loan amortization. Calculate maturity period of loan. For installment No. 72, calculate interest portion and principal portion Expected cash flows of a project are as follows : Year Cash flows (in rupees) 10, Calculate the present value and future value of the above cash flows at 10%. Also calculate the implicit rate of return Abhijeet borrows Rs. 80,000 for a music system at a monthly interest rate of 1.25%. The loan is to be repaid in 24 equal monthly installments, payable at the beginning of each month. Calculate the amount of each installment? 6.24 Using a discount rate of 10% calculate present value of given cash flows: Year Stream A Stream B 10, Stream C 5, You deposited Rs. 70,000 in your Public Provident Fund A/C for 15 years at 8% interest. How much you will get on maturity.
26 6.26 You bought a share for Rs. 96 today. After one year, you received a dividend of Rs. 5 on it and sold it for Rs What is your return on share over a period of one year? 6.27 A finance company offers to triple your money in 10 years. What is the effective rate of interest implicit in the offer? 6.28 To buy your dream car, you can afford to pay Rs. 10,000 per month for 5 years. You call a finance company for loan. It is ready to offer finance over this period at 1% interest per month. How much you can borrow? 6.29 A Russian company has advertised that it can take any person to moon at a cost of $10 million. I can save $5 lakhs every year. How long I will have to wait if my savings earn 12% p.a. The cost is not likely to change in monetary terms Mr.X borrows Rs. 1,00,000 at 8% interest. Equal annual payments are to be made for 6 years. However at the time of 4 th payment, X decides to pay off the entire loan. Find equal annual installment. Also calculate the amount to be paid at the end of 4 th year. Answers to Section VI 6.1 Rs % 6.3. Rs Rs Rs Rs option A 6.8 Rs Rs Rs Rs % 6.13 Rs years 6.15 Rs Rs Rs Yes 6.19 Rs Rs months, Rs.7964, Rs Rs , Rs.4156, 18.69% 6.23 Rs Rs.17631, Rs.35921, Rs Rs.19,00, % % 6.28 Rs years 6.30 Rs , Rs.60206
The Institute of Chartered Accountants of India
CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able
More information2 Time Value of Money
2 Time Value of Money BASIC CONCEPTS AND FORMULAE 1. Time Value of Money 2. Simple Interest 3. Compound Interest 4. Present Value of a Sum of Money 5. Future Value It means money has time value. A rupee
More informationFinQuiz Notes 2 0 1 4
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
More informationINSTITUTE OF ACTUARIES OF INDIA
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please
More informationHow to calculate present values
How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance
More informationFinQuiz Notes 2 0 1 5
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
More informationIndex Numbers ja Consumer Price Index
1 Excel and Mathematics of Finance Index Numbers ja Consumer Price Index The consumer Price index measures differences in the price of goods and services and calculates a change for a fixed basket of goods
More informationTime Value of Money PAPER 3A: COST ACCOUNTING CHAPTER 2 BY: CA KAPILESHWAR BHALLA
Time Value of Money 1 PAPER 3A: COST ACCOUNTING CHAPTER 2 BY: CA KAPILESHWAR BHALLA Learning objectives 2 Understand the Concept of time value of money. Understand the relationship between present and
More informationHow To Calculate The Value Of A Project
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationICASL  Business School Programme
ICASL  Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business
More informationThe Time Value of Money
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
More informationHow To Read The Book \"Financial Planning\"
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More informationExercise 1 for Time Value of Money
Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
More informationUnderstanding Types of Returns & Time Value of Money Using Excel. July 2012
Understanding Types of Returns & Time Value of Money Using Excel July 2012 Annualized Returns Annualized Return It is a method of arriving at a comparable oneyear return (annual return) for investments
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM0905. January 14, 2014: Questions and solutions 58 60 were
More informationMODULE 2. Finance An Introduction
MODULE 2 Finance An Introduction The functions of finance in an organization is interlinked with other managerial responsibilities and in many instances, the finance manager could also done the role of
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM0905. April 28, 2014: Question and solutions 61 were added. January 14, 2014:
More informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationHow To Value Cash Flow
Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value
More informationCompound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
More informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More information1.21.3 Time Value of Money and Discounted Cash Flows
1.1.3 ime Value of Money and Discounted ash Flows ime Value of Money (VM)  the Intuition A cash flow today is worth more than a cash flow in the future since: Individuals prefer present consumption to
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationTHE TIME VALUE OF MONEY
QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost
More informationCalculations for Time Value of Money
KEATMX01_p001008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
More informationTopics. Chapter 5. Future Value. Future Value  Compounding. Time Value of Money. 0 r = 5% 1
Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series
More informationChapter 3 Present Value
Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
More informationMGT201 Lecture No. 07
MGT201 Lecture No. 07 Learning Objectives: After going through this lecture, you would be able to have an understanding of the following concepts. Discounted Cash Flows (DCF Analysis) Annuities Perpetuity
More informationInternational Financial Strategies Time Value of Money
International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value
More informationChapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS
Chapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS 71 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 $10,000(1.10) 5 $10,000(FVIF 10%, 5 ) $10,000(1.6105) $16,105. Alternatively, with a financial calculator enter the
More informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equalsized
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationTopics Covered. Ch. 4  The Time Value of Money. The Time Value of Money Compounding and Discounting Single Sums
Ch. 4  The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation
More informationLO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.
LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationModule 5: Interest concepts of future and present value
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
More informationBond valuation. Present value of a bond = present value of interest payments + present value of maturity value
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of longterm debt securities 2. Issues 3. Summary 1. Valuation of longterm debt securities Debt securities are obligations
More informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
More informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More informationThe Time Value of Money (contd.)
The Time Value of Money (contd.) February 11, 2004 Time Value Equivalence Factors (Discrete compounding, discrete payments) Factor Name Factor Notation Formula Cash Flow Diagram Future worth factor (compound
More informationNote: The paid up value would be payable only on due maturity of the policy.
Section II Question 6 The earning member of a family aged 35 years expects to earn till next 25 years. He expects an annual growth of 8% in his existing net income of Rs. 5 lakh p.a. If he considers an
More informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationBasic Concept of Time Value of Money
Basic Concept of Time Value of Money CHAPTER 1 1.1 INTRODUCTION Money has time value. A rupee today is more valuable than a year hence. It is on this concept the time value of money is based. The recognition
More informationChapter 03  Basic Annuities
31 Chapter 03  Basic Annuities Section 7.0  Sum of a Geometric Sequence The form for the sum of a geometric sequence is: Sum(n) a + ar + ar 2 + ar 3 + + ar n 1 Here a = (the first term) n = (the number
More informationApplications of Geometric Se to Financ Content Course 4.3 & 4.4
pplications of Geometric Se to Financ Content Course 4.3 & 4.4 Name: School: pplications of Geometric Series to Finance Question 1 ER before DIRT Using one of the brochures for NTM State Savings products,
More informationChapter 4: Time Value of Money
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
More informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationE INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is
E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective
More informationSolutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.
Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at
More informationFinite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan
Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:
More informationUSING THE SHARP EL 738 FINANCIAL CALCULATOR
USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial
More informationPresent Value and Annuities. Chapter 3 Cont d
Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationAPPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
More informationMODULE: PRINCIPLES OF FINANCE
Programme: BSc (Hons) Financial Services with Law BSc (Hons) Accounting with Finance BSc (Hons) Banking and International Finance BSc (Hons) Management Cohort: BFSL/13/FT Aug BACF/13/PT Aug BACF/13/FT
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More informationChapter 1: Time Value of Money
1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting
More informationEcon 330 Exam 1 Name ID Section Number
Econ 330 Exam 1 Name ID Section Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If during the past decade the average rate of monetary growth
More informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C 1
C Time Value of Money C 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationThe Time Value of Money
The Time Value of Money Future Value  Amount to which an investment will grow after earning interest. Compound Interest  Interest earned on interest. Simple Interest  Interest earned only on the original
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
More informationWeek 4. Chonga Zangpo, DFB
Week 4 Time Value of Money Chonga Zangpo, DFB What is time value of money? It is based on the belief that people have a positive time preference for consumption. It reflects the notion that people prefer
More information