# Exam 2 Study Guide. o o

Size: px
Start display at page:

## Transcription

1 1. LS7a An account was established 7 years ago with an initial deposit. Today the account is credited with annual interest of \$860. The interest rate is 7.7% compounded annually. No other deposits or withdrawals have been made. How much is the end-of-day balance? o o **Note** For some reason the test answers to this question exhibit very large rounding errors. For example, the correct test answer is 12,034. Even the answer that Dr. Downs comes to on his example is about \$10 off from the test answer. I have no explanation for why he does this, but be aware.

2 2. MC5c Here are two future expenses that you want to save for today: \$5,200 payable in 6 years, and \$7,700 payable in 9 years. You make an investment today that perfectly finances the future expenses if the investment earns a target 12.8% average annual rate of return (compounded annually). The investment indeed grows sufficiently to finance your first expense. Unfortunately, for the entire investment horizon your actual annual rate of return falls short of the target by 240 basis points per year. When it is time to pay the second expense, how much money do you lack? First, discount back your two future payments to find out how much you deposited in the account. N = 6 N = 9 I/Y = 12.8 I/Y = 12.8 PV = CPT = -2, PV = CPT = -2, PMT = 0 PMT = 0 FV = 5,200 FV = 7,700 Total Deposit = 2, , = 5, Now you need to see how much your initial deposit actually grew during the first 6 years. N = 6 I/Y = = 10.4 PV = -5, PMT = 0 FV = CPT = 9, Now subtract your first payment and see how much your remaining balance grows over the next 3 years. N = 9 6 = 3 I/Y = = 10.4 PV = (9, ,200) = 4, PMT = 0 FV = CPT = 5, Since you owe 7,700 and you only have 5, your shortfall is 7,700 5, = 2,202.04

3 3.1 ROR1 A venture capitalists provides a company equity financing of \$11.0 million. After 7 years the company repurchases the equity for \$47.4 million. There are no other cash flows between the two. Find the average annual geometric rate of return, and also find the cumulative rate of return. N = 7 I/Y = CPT = = Geometric Return PV = -11 PMT = 0 FV = 47.4 Cumulative Rate of Return 3.2 ROR3c Two years ago you purchased a stock for \$37. One year ago the price had moved to \$10. Today it is at \$49. Which one statement about the annual average rate of return is correct? a) The geometric average return is 17.3% and the arithmetic average return is 158.5%. b) The geometric average return is 17.3% and the arithmetic average return is 137.8%. c) The geometric average return is 13.1% and the arithmetic average return is 158.5%. d) The geometric average return is 15.1% and the arithmetic average return is 137.8%. e) The geometric average return is 15.1% and the arithmetic average return is 158.5%. N = 2 I/Y = CPT = = Geometric Return PV = -37 PMT = 0 FV = 49 Arithmetic Average Return 3.3 LS4c A deposit exactly 14 years ago of \$2,300 earns 9.5% annual interest compounded annually. There have been no other deposits or withdrawals. As of today, how much total interest-on-principal has accumulated?

4 3.4 LS6a A savings account was established with \$36,000 exactly 9 years ago. The account earns 5.3% compounded annually. Otherwise, the account has been left alone. When the annual interest is credited to the account today, how much interest is credited? o N = 9 1 = 8 o I/Y = 5.3 o PV = -36,000 o PMT = 0 o FV = CPT = 54, =

5 4.1 BS38 The Federal Reserve Board of Directors uses three significant tools to influence market activity. Which of these statements is the most accurate description of one of these Fed tools? Accurate Statements The official government "discount rate" is the interest rate charged by Federal Reserve District banks to member public and private banks. The reserve requirement on member bank accounts regulates the amount of loans that banks may lend to business and individual borrowers. Buying and selling currencies and government securities in the global financial marketplace affects supply and demand conditions for capital. 4.2 LS24 You wish to purchase in 10 years an item that today costs \$1,400. The cost is expected to inflate at an annual rate of 4.4%. You make a deposit today that perfectly finances the future purchase. The observed interest rate that your savings earns is 7.6%. Describe the relation between your deposit, inflation, and the discount rate. a) the deposit equals the real cost of \$1400 discounted at the nominal rate 7.6% b) the deposit equals the real cost of \$1400 discounted at the real rate 3.07% c) the real interest rate is 7.6% d) Two choices, A and B, are correct e) None of the A-B-C choices are correct Correct Answer = B The real interest rate is the rate that your purchasing power increases at and can be found by

6 5.1 LS14 Today your account was credited with its annual interest of \$5,210. The account was established some time ago with a \$17,150 initial deposit. No other deposits or withdrawals have been made. The account earns 8.7% annual interest. How many years ago was the account established? o o N = CPT = 16 I/Y = 8.7 PV = -17,150 PMT = 0 FV = 65, LS15 Some time ago a \$136,000 initial deposit opened an account. No other deposits or withdrawals have been made. Today the annual interest was credited to the account. Total lifetime interest now equals \$71,210. The account earns 6.2% annual interest. How many years ago was the account established? N = CPT = 7 I/Y = 6.2 PV = -136,000 PMT = 0 FV = 136, ,210 = 207,210

7 6. LS10a In exactly 20 months a bill of \$15,120 is due. Today you deposit money such that if the account earns a target rate of return of 0.84% per month, the bill is perfectly financed. Unfortunately, your account earns 15 basis points less than your target. When the bill is due, how much money do you lack? N = 20 = 20 I/Y = 0.84 = = 0.69 PV = CPT = -12, = -12, PMT = 0 = 0 FV = 15,120 = CPT = 14, Since you owe 15,120 and you only have 14,676.48, you lack 15,120 14, =

8 7. CY10a In exactly 14 years a bill of \$26,040 is due. Today you deposit money such that if the account earns a target rate of return of 6.00% per annum, compounded quarterly, the bill is perfectly financed. No other deposits or withdrawals have been made. Your account actually accumulates \$22,154. What was the actual average annual percentage rate? N = 14 =14 I/Y = 6 = CPT = 4.78 PV = CPT = -11, = -11, PMT = 0 = 0 FV = 26,040 = 22,154

9 8. CY21 Suppliers X and Z are competing to sell your company supplies. The full price of supplies from supplier X is \$1,300 and they offer these payment plans: 4.9% discount if you pay within 10 days, otherwise pay full price within 230 days. The full price with supplier Z is \$1,390 and they offer these payment plans: 5.8% discount if you pay within 25 days, otherwise pay full price within 290 days. Your company financing rate is 7.7% compounded daily. Find the supplier and payment plan that represent the lowest present value of cost. Supplier X Plan 1 Supplier X Plan 2 N = 10 N = 230 I/Y = 7.7/365 = I/Y = 7.7/365 = PV = CPT = 1, PV = CPT = 1, PMT = 0 PMT = 0 FV = 1,300 (1,300 x 0.049) = 1, FV = 1,300 Supplier Z Plan 1 Supplier Z Plan 2 N = 25 N = 290 I/Y = 7.7/365 = I/Y = 7.7/365 = PV = CPT = -1, PV = CPT = 1, PMT = 0 PMT = 0 FV = 1,390 (1,390 x 0.058) =1, FV = 1,390 Supplier X plan 1 has the lowest present value, but if you buy from supplier Z the lowest present value plan is plan 1

10 9.1 FF6 By how many basis points does 4.4% differ from 8.5%? = TR15 What are proper definitions for PVIFA, FVIFA, and the discount rate? Proper Definitions the present value interest factor for an annuity, PVIFA(r,N), equals the initial deposit into an account earning the periodic rate r that perfectly finances a series of N one-dollar withdrawals the future value interest factor for an annuity, FVIFA(r,N), equals the total accumulation in an account earning the periodic rate r that results from a series of N one-dollar deposits the discount rate is the periodic percentage return subtracted from the future cash flow for computing present value 9.3 TR33 From a series of periodic rates of return there are two procedures for computing the average rate of return per period: the arithmetic average and the geometric average. Is the following statement about these two statistics TRUE or FALSE: The geometric average periodic rate of return always is greater than or equal to the arithmetic average periodic rate of return. False TRUE or FALSE: The arithmetic average periodic rate of return always is greater than or equal to the geometric average periodic rate of return. True

11 10.1 FV7 Your parents contribute \$135 monthly to a college savings plan for you that earns 8.00% compounded monthly. The first deposit was exactly 9 years ago. Find the account balance after today's monthly deposit and crediting of monthly interest. N = 9 x 12 = 108 I/Y = 8/12 = PV = -135 PMT = -135 FV = CPT = 21, FV9 An account is today credited with its monthly interest thereby bringing the account balance to \$5,450. The interest rate is 10.10% compounded monthly. You plan to make monthly withdrawals of \$55 each. The first withdrawal is in exactly one month and the last in exactly 12 years. Find the account balance immediately after the last withdrawal. N = 12 x 12 = 144 I/Y = 10.10/12 = PV = -5,450 PMT = 55 FV = CPT = 2,908.44

12 11. FV5 An account is today credited with its annual interest thereby bringing the account balance to \$7,490. The interest rate is 9.10% compounded annually. You plan to make annual withdrawals of \$700 each. The first withdrawal is in exactly one year and the last in exactly 18 years. Find the account balance immediately after the last withdrawal. N = 18 I/Y = 9.10 PV = -7,490 PMT = 700 FV = CPT = 6,722.12

13 12. FV6 Today you inherit an account with a balance of \$7,400. For a while you don't do anything with the account but it continues to accrue interest. Exactly 20 months from today you start an ambitious savings plan and deposit \$200 into the account. You plan to deposit that much each month. Exactly 40 months from today you reconsider your plan, make your last deposit, and make no additional deposits. You nonetheless leave the account alone and it continues to accrue interest at a rate of 8.6% compounded monthly. You finally close the account exactly 7 years from today. How much is the total accumulation? N = 19 = = 21 = (7 x 12) 40 = 44 I/Y = 8.6/12 = = 8.6/12 = = 8.6/12 = PV = -7,400 = -8, = -14, PMT = 0 = -200 = 0 FV = CPT = 8, = CPT = 14, = CPT = 19,663.68

14 13.1 TR3 Suppose two alternative investments promise cash flow streams that possess equal lives. Further, suppose the simple sum of the cash flows for each investment is the same amount. Given a positive interest rate, which investment has the smallest present value? a) an investment that is being discounted by a small discount rate. b) an investment which generates equal cash flows each period. c) an investment which generates most cash flows at the beginning of its life. d) there is no reliable relationship between the distribution of cash flows and present value. e) an investment which generates most cash flows at the end of its life. Answer = E 13.2 TR4 Suppose two alternative investments promise cash flow streams that possess equal lives. Further, suppose the simple sum of the cash flows for each investment is the same amount. Given a positive interest rate, which investment has the biggest present value? a) an investment that is being discounted by a large discount rate. b) an investment which generates equal cash flows each period. c) there is no reliable relationship between the distribution of cash flows and present value. d) an investment which generates most cash flows at the end of its life. e) an investment which generates most cash flows at the beginning of its life. Answer = E 13.3 TR5 Suppose two equal-cost alternative investments promise cash flow streams that possess equal lives. Further, suppose the simple sum of the after-tax cash flows for each investment is the same amount. Given a positive interest rate, which investment has the smallest present value? a) an investment which generates most cash flows at the end of its service life. b) an investment which generates equal cash flows each period. c) an investment that is being discounted by a small discount rate. d) there is no reliable relationship between the distribution of cash flows and present value. e) an investment that has relatively high sales revenues. Answer = A

15 14.1 PV7 A friend received an inheritance 5 years ago and put all funds into an account earning 8.00% compounded quarterly. Exactly one quarter after establishing the account the friend started withdrawing \$1,300 per quarter. Today she'll make another quarterly withdrawal, and quarterly interest will be credited to the account, and then the balance will be \$18,711. How much was the friend's inheritance? N = 5 x 4 = 20 I/Y = 8/4 = 2 PV = CPT = -33, PMT = 1,300 FV = 18, PV9 You might invest in a security that will return after-tax cash flow to you of \$1,100 per year for 7 years (first cash flow one year from now), after which the security likely can be sold immediately for \$7,100. You make an offer to buy the security so that you'll get a 10.30% rate of return (compounded annually). Find the offer price. N = 7 I/Y = 10.3 PV = CPT = -8, PMT = 1,100 FV = 7,100

16 15. PV10b You might invest in an asset that will return after-tax cash flow to you of \$2,200 per month for 40 months (first cash flow one month from now), and after receiving the last cash flow you'll immediately receive after-tax net proceeds from liquidation equal to \$82,500. You make an offer to buy the asset so that you'll get your "target" annual rate of return of 16.80% (compounded monthly). The seller makes a counteroffer that is \$8,300 higher than your offer. Find your annual rate of return if you buy at the counteroffer price and receive the expected cash flows. N = 40 N = 40 I/Y = 16.8/12 = 1.4 I/Y = CPT = x 12 = PV = CPT = -114, PV = -114, ,300 = -122, PMT = 2,200 PMT = 2,200 FV = 82,500 FV = 82,500

17 16. FV17 Today you open an account with a \$8,800 deposit that earns 8.70% compounded annually. You've set a target for the account so that in exactly 6 years its balance will be \$11,500. To reach the target you'll adjust the balance annually; each year's adjustment will be exactly the same amount and the first adjustment occurs exactly one year from now. After the last annual adjustment in exactly 6 years, and crediting of that year's interest, the account balance exactly equals the target. Describe the annual adjustment that you make each year. N = 6 I/Y = 8.7 PV = -8,800 PMT = CPT = FV = 11,500 Each year you make a withdrawal of

18 17.1 TR1 Which statement describes the "rule of 72"? a) The approximate number of years required for a deposit to double equals 72 divided by the percentage interest rate. b) The number of months required for a deposit to double equals the decimal interest rate divided by 72. c) The simple sum of cash flows required for an investment to earn a positive rate of return equals the investment cost divided by 72. d) The number of months required for a deposit to double equals the decimal interest rate times 72. e) The simple sum of cash flows required for an investment to earn a positive rate of return equals the investment cost times 72. Answer = A 17.2 TR2 For the simple time value lump-sum relation with monthly compounding find the most accurate statement. For all cases, hold everything constant except the stated variables. Accurate Statements When the interest rate doubles then the total interest more than doubles. When the term doubles then the total interest more than doubles. When the beginning wealth doubles then the total interest exactly doubles TR27 Banks advertise loans so that you'll borrow money from them and pay them interest. They also advertise deposits so that you'll open an account with them and they'll pay you interest. Which statement below most likely describes the relation between the effective annual rate ("EAR") and annual percentage rate ("APR"). Accurate Statements The EAR generally is bigger than the APR. The APR generally is smaller than the EAR. When banks advertise for loans they likely quote the APR. When banks advertise for deposits they likely quote the EAR.

19 18. TS1b You wish to establish an endowment fund that will provide student financial aid awards every semiannum, perpetually. To finance the scholarships you will make a series of equal deposits into a savings account. The deposits will be made semiannually equal to \$2,200 each, with the first one today and the final one in 7 years. The first award is to be granted one semiannum after the last deposit. The savings rate is 6.30% compounded semiannually. How much is each award? N = 7 x 2 = 14 I/Y = 6.3/2 = 3.15 PV = -2,200 PMT = -2,200 FV = CPT = 41,370.46

20 19. AM3d The Company borrowed \$174,000 at 9.60% to be repaid monthly over 15 years. They just remitted payment number 83. How much interest-to date has been paid? N = 15 x 12 = 180 = 83 I/Y = 9.6/12 = 0.8 = 9.6/12 = 0.8 PV = 174,000 = 174,000 PMT = CPT = -1, = -1, FV = 0 = CPT = -122, ( ) ( ) ( )

21 20.1 AM5a Your friend is taking out a mortgage for \$127,000 at 8.70% repayable with monthly payments over 25 years. She respects your financial expertise and asks "how many payments will I have to make before I reduce the principal balance by half its original amount." You pull out your calculator, and tell her the number of payments she'll make to reduce the balance by half is: N = 25 x 12 = 300 N = CPT = 219 I/Y = 8.7/12 = I/Y = 8.7/12 = PV = 127,000 PV = 127,000 PMT = CPT = -1, PMT = -1, FV = 0 FV = -127,000/2 = -63, AM9c You have just bought a house by borrowing \$220,000 at a 8.70% annual interest rate (compounded monthly) repayable with fixed payments over 25 years. When finally in the far-off future you make your last payment, how much of that last payment will be principal? N = 25 x 12 = 300 N = (25 x 12) 1 = 299 I/Y = 8.7/12 = I/Y = 8.7/12 = PV = 220,000 PV = 220,000 PMT = CPT = -1, PMT = -1, FV = 0 FV = CPT = 1,788.28

22 21. CB2a Consider the following cash flows for two mutually exclusive investments: at time 0: CF A = (\$780) and CF B = (\$1,050) at time 1: CF A = \$547 and CF B = \$117 at time 2: CF A = \$319 and CF B = \$327 at time 3: CF A = \$124 and CF B = \$950 Which statement is true? a) if the financing rate is 16.8% then project A is the better of the two b) if the financing rate is 5.8% then project A is the better of the two c) if the financing rate is 8.52% then projects A and B create the same amount of wealth d) if the financing rate is 11.6% then project B is the better of the two e) if the financing rate is 14.2% then project B is the better of the two Use CF Function on calculator Project A Project B CF ,050 C C C Project A NPV Project B NPV 16.8% % % % % Answer = A

23 22. CB8 The bank issued a \$138, year mortgage (monthly payments) with an annual interest rate of 8.20%. They just received payment number 110 and have decided to sell the loan. The buyer of the loan expects to receive an annual rate of return equal to 10.20%. For the original bank that issued the loan, what was the internal rate of return? N = 25 x 12 = 300 = (25 x 12) 110 = 190 = 110 I/Y = 8.2/12 = = 10.2/12 = 0.85 = CPT = x 12 = PV = -138,000 = CPT = -101, = -138,000 PMT = CPT = 1, = 1, = 1, FV = 0 = 0 = 101,939.95

24 23.1 FF23 The payback period assesses the quality of a cash flow stream. What are some general advantages and/or disadvantages of this assessment measure? the payback period ignores the time value of money a short payback period is better than a long payback period the payback period ignores cash flows occurring after the payback point is reached 23.2 TR32 What factors are relevant for a household choosing between borrowing with a 15-year versus a 30-year loan (assume that fees, interest rates, and all else are equal). Correct Answers Total lifetime interest definitely is less with a 15-year loan but that doesn't mean it is a better choice. Total lifetime interest definitely is more with a 30-year loan but that doesn't mean it is a worse choice. When the household expects short-run liquidity problems as their careers commence but for the long-run they expect high income growth then borrowing with a 30-year loan may be advantageous. When the household expects that in the short-run their uses for money will have low utility but that in the long-run their uses for money will have higher utility then borrowing with a 15-year loan may be advantageous. When the household expects that in the short-run their uses for money will have high utility but that in the long-run their uses for money will have lower utility then borrowing with a 30-year loan may be advantageous TR36 Which statement is most consistent with the Net present value (NPV) and Internal rate of return concepts? Consistent Statements The IRR for a project is the financing rate at which the project's NPV is zero. The NPV for a project is the amount of capitalized economic profit that a project creates. When the project's actual financing rate is less than the IRR then the NPV is positive. When the project's actual financing rate exceeds the IRR then the NPV is negative. When a project's NPV is positive then the actual financing rate is less than the IRR.

25 24. CB10a Your company is analyzing purchase of a machine costing \$8,700 today. The investment promises to add \$9,000 to sales one year from today, \$12,500 two years from today, and \$15,000 three years from today. Incremental cash costs should consume 50% of the incremental sales. The tax rate is 35% and the company's financing rate is 15.8%. The investment cost is depreciated to zero over a 3-year straight-line schedule. Find the project's net present value and internal rate of return. What is important is not the increase in sales but the increase in profits, so for cash flows you have to remove costs and taxes, but you also have to add in the tax benefit from depreciation. [ ( ) ( )] ( ) [ ( ) ( )] ( ) [ ( ) ( )] ( ) NPV = 2, IRR = 30.12%

26 25. CB3c You took out a 30-year mortgage (monthly payments) for \$125,000 at 8.90% and payment number 31 is due today. You are deciding whether you should refinance the outstanding principal by borrowing at today's lower rate of 5.90% an amount that pays off the old loan. The new loan is for 30 years as of today. The total fees for getting the new loan equal 3.6% of the original loan's outstanding principal. The first payment for the new loan would be due one month from today. Suppose you pay the fees today with funds from your savings account. What is the net present value of the refinancing venture if your "personal discount rate" is 15%? N = 30 x 12 = 360 = 31 = 360 I/Y = 8.9/12 = = 8.9/12 = = 5.9/12 = PV = 125,000 = 125,000 = 122, PMT = CPT = = = CPT = FV = 0 = CPT = -122, = 0 Now use the Cash Flow Function CF0 = -122, x = -4, C01 = = F01 = = 329 C02 = F02 = 31 NPV = 16,491.10

### EXAM 2 OVERVIEW. Binay Adhikari

EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing

### FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY

FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY 1. (3 points) BS16 What is a 401k plan Most U.S. households single largest lifetime source of savings is

### Chapter 28 Time Value of Money

Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit \$100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:

### Review Solutions FV = 4000*(1+.08/4) 5 = \$4416.32

Review Solutions 1. Planning to use the money to finish your last year in school, you deposit \$4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen

### 3. Time value of money. We will review some tools for discounting cash flows.

1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

### Compound Interest. Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate:

Compound Interest Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate: Table 1 Development of Nominal Payments and the Terminal Value, S.

### DISCOUNTED 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

### 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%?

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

### Chapter 5 Time Value of Money

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 of Cash Flows 7. Other Compounding

### Key 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

### Problem 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

### Time-Value-of-Money and Amortization Worksheets

2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability

### Chapter 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

### Chapter 5 & 6 Financial Calculator and Examples

Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get

### The 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

### Finding 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.

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### FinQuiz 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.

### Chapter 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

### Time Value of Money Practice Questions Irfanullah.co

1. You are trying to estimate the required rate of return for a particular investment. Which of the following premiums are you least likely to consider? A. Inflation premium B. Maturity premium C. Nominal

### ICASL - 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

### Chapter 4 Time Value of Money

Chapter 4 Time Value of Money Solutions to Problems P4-1. LG 1: Using a Time Line Basic (a), (b), and (c) Compounding Future Value \$25,000 \$3,000 \$6,000 \$6,000 \$10,000 \$8,000 \$7,000 > 0 1 2 3 4 5 6 End

### THE 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

### CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are

### Chapter 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

### CHAPTER 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)

### CHAPTER 2. Time Value of Money 2-1

CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3

### Discounted 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

### Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 P5-1. 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

### Time 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

### 380.760: Corporate Finance. Financial Decision Making

380.760: Corporate Finance Lecture 2: Time Value of Money and Net Present Value Gordon Bodnar, 2009 Professor Gordon Bodnar 2009 Financial Decision Making Finance decision making is about evaluating costs

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### LO.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

### Solutions to Time value of money practice problems

Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if \$2,500 is deposited today and the account earns 4% interest,

### Time 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

### Time Value of Money 1

Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households

### CHAPTER 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

### ( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100

Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded

### CHAPTER 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

### Chapter 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

### CAPITAL BUDGETING. Net Present Value and Other Investment Criteria

CAPITAL BUDGETING Net Present Value and Other Investment Criteria Net Present Value (NPV) Net present value is the difference between an investment s market value (in today s dollars) and its cost (also

### APPENDIX. 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

### Fin 5413 CHAPTER FOUR

Slide 1 Interest Due Slide 2 Fin 5413 CHAPTER FOUR FIXED RATE MORTGAGE LOANS Interest Due is the mirror image of interest earned In previous finance course you learned that interest earned is: Interest

### Why Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of

1 Why Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of Return Problems with the IRR Approach The Profitability

### Capital Budgeting OVERVIEW

WSG12 7/7/03 4:25 PM Page 191 12 Capital Budgeting OVERVIEW This chapter concentrates on the long-term, strategic considerations and focuses primarily on the firm s investment opportunities. The discussions

### Solutions Manual. Corporate Finance. Ross, Westerfield, and Jaffe 9 th edition

Solutions Manual Corporate Finance Ross, Westerfield, and Jaffe 9 th edition 1 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions 1. In the corporate form of ownership, the shareholders

### Chapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1

Chapter 3 Understanding The Time Value of Money Prentice-Hall, 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,

### FinQuiz 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.

### Oklahoma State University Spears School of Business. Time Value of Money

Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a sign-in bonus for your new job? 1. \$15,000 cash upon signing the

### Topics Covered. Compounding and Discounting Single Sums. Ch. 4 - The Time Value of Money. The Time Value of Money

Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate Inflation & Time Value The Time Value of Money

### CHAPTER 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

University of Virginia - math1140: Financial Mathematics Fall 2011 Exam 1 7:00-9:00 pm, 26 Sep 2011 Honor Policy. For this exam, you must work alone. No resources may be used during the quiz. The only

### Chapter 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

### Chapter 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)

### Future 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

### MBA Financial Management and Markets Exam 1 Spring 2009

MBA Financial Management and Markets Exam 1 Spring 2009 The following questions are designed to test your knowledge of the fundamental concepts of financial management structure [chapter 1], financial

### Chapter 02 How to Calculate Present Values

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

### Topics. 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

### CHAPTER 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

### Main TVM functions of a BAII Plus Financial Calculator

Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

### Chapter 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

### Chapter 4. Time Value of Money

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

### APPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value

1 2 TIME VALUE OF MONEY APPENDIX 3 The simplest tools in finance are often the most powerful. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications.

### BUSINESS FINANCE (FIN 312) Spring 2009

BUSINESS FINANCE (FIN 31) Spring 009 Assignment Instructions: please read carefully You can either do the assignment by yourself or work in a group of no more than two. You should show your work how to

### Finance 445 Practice Exam Chapters 1, 2, 5, and part of Chapter 6. Part One. Multiple Choice Questions.

Finance 445 Practice Exam Chapters 1, 2, 5, and part of Chapter 6 Part One. Multiple Choice Questions. 1. Similar to the example given in class, assume that a corporation has \$500 of cash revenue and \$300

### 5. 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

### SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions

### Present 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

### The 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

### CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantial

### 14 ARITHMETIC OF FINANCE

4 ARITHMETI OF FINANE Introduction Definitions Present Value of a Future Amount Perpetuity - Growing Perpetuity Annuities ompounding Agreement ontinuous ompounding - Lump Sum - Annuity ompounding Magic?

### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### Real Estate. Refinancing

Introduction This Solutions Handbook has been designed to supplement the HP-2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures

### Chapter 2 Applying Time Value Concepts

Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the

### 5.1 Simple and Compound Interest

5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

### 3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the

### CHAPTER 3. Arbitrage and Financial Decision Making. Chapter Synopsis

CHAPTER 3 Arbitrage and Financial Decision Making Chapter Synopsis 3.1 Valuing Decisions When considering an investment opportunity, a financial manager must systematically compare the costs and benefits

### Exercise 6 Find the annual interest rate if the amount after 6 years is 3 times bigger than the initial investment (3 cases).

Exercise 1 At what rate of simple interest will \$500 accumulate to \$615 in 2.5 years? In how many years will \$500 accumulate to \$630 at 7.8% simple interest? (9,2%,3 1 3 years) Exercise 2 It is known that

### CARMEN VENTER COPYRIGHT www.futurefinance.co.za 0828807192 1

Carmen Venter CFP WORKSHOPS FINANCIAL CALCULATIONS presented by Geoff Brittain Q 5.3.1 Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) 5.3.2 Calculate the capital

### Time Value of Money. Appendix

1 Appendix Time Value of Money After studying Appendix 1, you should be able to: 1 Explain how compound interest works. 2 Use future value and present value tables to apply compound interest to accounting

### 1.4 Interest-Rate calculations and returns

.4 Interest-Rate calculations and returns Effective Annual Rate (EAR) The Effective Annual Rate (EAR) is the actual rate paid (or received) after accounting for compounding that occurs during the year

### Chapter Review Problems

Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute

### Chapter Review Problems

Chapter Review Problems Use 2 decimal places for all answers. Unit 13.1 Home ownership and mortgage payments 1. Your personal residence is considered personal property rather than real estate because you

### Essential Learning for CTP Candidates TEXPO Conference 2016 Session #03

TEXPO Conference 2016: Essential Learning for CTP Candidates Session #3 (Mon.1:45 3:00 pm) Overview of Basic CTP Math from ETM4 Chap 07: Earnings Credits Chap 09: Working Capital Chap 18: Fin. Statements

### Solutions to Problems

Solutions to Problems P4-1. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,

Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation

### Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e

Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,

### 1. % of workers age 55 and up have saved less than \$50,000 for retirement (not including the value of a primary residence).

Toward Quantitative Literacy: Interesting Problems in Finance 2008 AMATYC Conference, Washington, D.C., Saturday, November 22, 2008 http://www.delta.edu/jaham Fill in the blanks. 1. % of workers age 55

### The Time Value of Money Guide

The Time Value of Money Guide Institute of Financial Planning CFP Certification Global Excellence in Financial Planning TM Page 1 Contents Page Introduction 4 1. The Principles of Compound Interest 5 2.

### Finance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.

Chapter 1 Finance 331 What is finance? - Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: -

### Discounted Cash Flow Valuation

BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?

### Chapter 2 Present Value

Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest

### FIN 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

### Integrated Case. 5-42 First National Bank Time Value of Money Analysis

Integrated Case 5-42 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

### USING 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