ICASL  Business School Programme


 Lee Lawson
 2 years ago
 Views:
Transcription
1 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 venture. When an individual or a company makes an investment in a business, a return in the form of a profit, dividend or interest is expected. Before making an investment, the investor would like to know the return he would receive from such an investment and in what time and whether at regular intervals or at once at the end of a said period. In any investment decision, time is an important factor. The longer an investment continues, the greater will be the return required to the investor. Let us deal with the allimportant form of return known as interest. When an amount of money is invested over a number of years, the interest earned can be dealt with in two ways: 1. Simple interest 2. Compound interest SIMPLE INTEREST Interest is the profit return on investment. If money is invested then interest is paid to the investor. If money is borrowed then the person who borrows the money will have to pay interest to the lender. The money which is invested or borrowed is called the principal. Simple interest is interest earned in equal amounts for fixed periods and it is a given proportion of the principal. With simple interest the principal always stays the same no matter how long the investment lasts. If a sum of money is invested for a given period of time, then the amount of simple interest which accrues depends upon the period of time, the interest rate and the amount invested. To calculate the simple interest the following formula could be used. I = P * n* r Where I Simple interest P Principal n Period r Rate of interest (a proportion) 1
2 Alternative Formula A= P (1+ nr) Where P = the original sum invested r = the interest rate (expressed as proportion, so 10% = 0.1) n = the number of periods (normally years) A = the accrued amount after n periods, consisting of the original capital (P) plus interest earned. Worked Example 1: Rs. 700,000 is invested at 7% per annum. How long will it take for the investment to reach Rs. 798,000? Solution 1: The interest element = Rs. 798,000 Rs. 700,000 = Rs. 98,000 We therefore have P = 700,000, I = 98,000 and r = ,000 = 700,000 * n * 0.07 n = = 2 years Or alternatively A = 798,000, P = 700,000 and r = 0.07 A= P (1+ nr) 798,000 = 700,000 [ n] 1.14 = n n = 0.14/0.07 = 2 years Worked Example 2: Which receives more interest per annum? Rs. 50,000 8% per annum or Rs. 60,000 7% per annum. What is the annual difference? Solution 2: Option 1: P = 50,000, n = 1 and r = 0.08 Interest per annum = 50,000 * 1* 0.08 = 4,000 Option 2: P = 60,000, n = 1 and r = 0.07 Annual difference = Rs200 Interest per annum = 60,000 * 1* 0.07 = 4,200 2
3 COMPOUND INTEREST This is different from simple interest in that the interest earned is added to the principal which also attracts interest. If money is invested at compound interest, the interest due at the end of each period is added to the principal for the next period. For example, if Rs200,000 is invested to earn 10% interest, after one year the original principal plus interest will amount to Rs220,000, which will be the principal for the second year, after two years the principal will become Rs242,000, after three years the total investment will be Rs266,620 and so on. Original investment 200,000 Interest in the first year (10%) 20,000 Total investment at the end of one year 220,000 Interest in the second year (10%) 22,000 Total investment at the end of two years 242,000 Interest in the third year (10%) 24,200 Total investment at the end of three years 266,200 The basic formula for compound interest is A = P (1 + r) n Where P = the original sum invested r = the interest rate, expressed as proportion, (so 12% = 0.12) n = the number of periods A = the accrued amount after n periods. Worked Example 3: Rs. 2,500 invested on 1 January 1995 had grown to be worth Rs. 61,482 on 31 December The equivalent annual compound growth rate (to one decimal place) is A) 23.8% B) 22.6% C) 22.4% D) 24.2% Solution 3: A = Rs61,482 P = Rs2,500 n = 15 years r =? A = 61,482 = 2,500 * = {1 + r} = 1 + r r = (3dp) r = 23.8 % Correct answer  (A) 3
4 Worked Example  4: An investment quadruples in value in eight years. The annual percentage compound interest growth rate is closest to A) 15 B) 19 C) 22 D) 37 Solution: Let the initial investment be Rs. M, and then M becomes 4M in 8 years. P = M, A = 4M n = 8 r =? A = 4M = M * = {1 + r} = 1 + r 1 + r = r = r = 19% (approx.) Correct answer  (B) WITHDRAWALS OF CAPITAL OR INTEREST If an investor takes money out of an investment, it will cease to earn interest. For example, if an investor puts Rs800,000 into a bank deposit account which pays interest at 10% per annum, and makes no withdrawals except at the end of year 2 and 3, when he takes out Rs500,000, and Rs400,000 respectively, what would be the balance in his account after four years? Rs Original investment 800,000 Interest in year 1 (10%) 80,000 Investment at the end of year 1 880,000 Interest in year 2 (10%) 88,000 Investment at the end of year 2 968,000 Less withdrawal 500,000 Net investment at the start of year 3 468,000 Interest in year 3 (10%) 46,800 Investment at the end of year 3 514,800 Less withdrawal 400,000 Net investment at the start of year 4 114,800 Interest in year 4 (10%) 11,480 Investment at the end of year 4 126,280 4
5 This can be shown using a table given below: Amount available at the beginning of the year (Rs) Interest receivable (Rs) Withdrawals(Rs) Amount available at the end of year (Rs) 800,000 80, , ,000 88, , , ,000 46, , , ,800 11, ,280 CHANGES IN THE RATE OF INTEREST If the rate interest changes during the period of an investment, the compounding formula must be amended slightly, as follows. A = P (1 + r1) x (1+r2) nx Where r1 = the initial rate of interest x = the number of years in which the interest rate r1 applies r2 = the next rate of interest n  x = the (balancing) number of years in which the interest rate r2 applies. Worked Example  5: An investor places Rs80,000 into an investment for 10 years. The compound rate of interest earned is 8% for the first 4 years and 12% for the last 6 years. At the end of the 10 years the investment is approximately worth A) Rs224,680 B) Rs214,830 C) Rs246,730 D Rs268,120 Solution 5: A = 80,000 A = 80,000 * * A = Rs. 214,830 (approx.) Correct answer  (B) REGULAR INVESTMENTS An investor may be encouraged to add to his investment from time to time when he finds that it is a profitable venture. In this chapter, the problems encountered are based on uniform time intervals. That is, it is assumed that the deposits are of equal amounts and made at regular intervals. 5
6 A person invests Rs. 100,000 now, and a further Rs. 100,000 each year for three more years. How much would the total investment be worth after 3 years if interest is earned at the rate of 10% per annum? In problems such as this, we call now year 0, the time one year from now year 1 and so on. Year 0 The first year s investment will be Rs. 100,000 (1.10) 4 = 146,410 1 The second year s investment will be Rs. 100,000 (1.10) 3 = 133,100 2 The third year s investment will be Rs. 100,000 (1.10) 2 = 121,000 3 The fourth year s investment will be Rs. 100,000 (1.10) = 110, ,510 The amount available of a regular investment at the end of a given period can be calculated using the equations given below: Case  I: (For investment made at the end of the year) If a fixed amount (Rs. A) is invested at the end of each year for a given period (n years) at a given rate of interest (r), the amount available at the end of n years (Rs. S) can be expressed as Where r is the rate of interest expressed as proportion and R = 1 + r Case  II: (For investment made at the beginning of the year) If a fixed amount (Rs A) is invested at the beginning of each year for a given period (n years) at a given rate of interest (r), the amount available at the end of n years ( Rs. S) can be expressed as Where r is the rate of interest expressed as a proportion and R = 1 + r Worked Example  6: Mr. Perera invested 12 annual payments of Rs2000 into an investment fund earning a compound interest of 6% p.a. If the first payment was at year zero calculate the value of the fund at year 12. A) Rs. 38,140 B) Rs. 53,840 C) Rs. 33,140 D) Rs. 35,760 Solution 6: S = Rs. 35,760 Correct answer  (D) 6
7 Worked Example  7: At the end of each year a company sets aside Rs. 100,000 out of its profits to form a reserve fund. This is invested at 10% p.a. compound interest. If the first deposit will be made in one year s time what will be the value of the fund after four years? A) Rs. 356,100 B) Rs. 510,000 C) Rs. 464,100 D) Rs. 484,800 Solution 7: S = Rs. 464,100 AMORTIZATION SCHEDULE (For an agreed amount of repayments) Correct answer  (C) An Amortization Schedule is a statement which shows the outstanding amount of a loan period by period. Our syllabus deals with the loans and mortgages which involve fixed repayments. The amount of repayment can be either calculated in which case every repayment from the first to the final is the same and it covers the principal amount and the interest, or as agreed by the two parties in which case every payment is the same except for the final payment which is the balance due on the loan at the end. And the final repayment would be smaller than the other repayments. The calculation of repayment will be discussed in annuities in detail and here we consider the latter. Example: A customer of your firm has purchased a computer costing Rs. 160,000. The customer has paid a Rs. 60,000 deposit and has agreed to pay off the rest of the purchase price by instalments of Rs. 35,000 per year payable at the end of each year. Interest is charged on the outstanding balance at 17% per year. a) Draw up a schedule of the payments until the debt is paid off, round your interest calculations to the nearest Re. b) How many full payments of Rs. 35,000 are made? c) What is the value of the final payment d) How much is paid in total for the computer? Solution Year Amount outstanding at the beginning Interest payable Repayment 1 100,000 17,000 (35,000) 82, ,000 13,940 (35,000) 60, ,940 10,360 (35,000) 36, ,300 6,171 (35,000) 7, ,471 1,270 (8,741) NIL Amount outstanding at the end 7
8 a) 4 full payments of Rs. 35,000 have been made. b) Final payment would be Rs8,741 c) Total amount paid for the computer = Rs. 60, x (Rs. 35,000) + Rs. 8,741 = Rs. 208,741 Practice Questions 1. Sarah invested Rs. 5,000 in a bank deposit account, which pays interest of 9% per annum, added to the account at the end of the year. She made one withdrawal of Rs1,500 at the end of 3 years. What was the account (to the nearest Re) at the end of 5 years A) Rs. 9,511 B) Rs. 5,992 C) Rs. 5,119 D) Rs. 5, After 15 years an investment of Rs. 60,000 has grown to Rs. 674,000. What annual rate (to one decimal place) of compound interest has been applied? A) 17.5% B) 19.2% C) 20.5% D) 17.8% 3. Perera invests Rs700 on 1 January each year starting in Compound interest of 10% has been credited on 31 December each year. To the nearest Re, the credit of his investment on 31 December 2019 will be A) Rs. 12,972 B) Rs. 11,156 C) Rs. 10,456 D) Rs. 2, An item of equipment currently costs Rs. 4,000,000. The rate of inflation for 3 years is expected to be 8% per annum then 10% per annum for the following 2 years. The price of equipment is expected to increase in line with the inflation. The price (to the nearest Rs000) after 5 years will be A) 6,907,000 B) 6,156,000 C) 6,097,000 D) 7,906,000 DISCOUNTING Discounting is the reverse of compounding. As defined in the previous chapter, compounding can be stated as if we invest rupees P now for n years at the rate of r per annum, we should obtain P (1+r) n in n years time. Discounting is, therefore can be stated as if we wish to have rupees A in n years time, how much we need to invest now (at year 0) at an interest rate of r in order to obtain the required sum of money in the future. 8
9 The formula for discounting is P = A (DCF) Where DCF = * The rate r is sometimes called a cost of capital. A is the sum to be received after n time periods P is the present value of that sum r is the rate of return, expressed as a proportion n is the number of time periods (usually years) Note: For given rate of discount and period of time, the DCF value can be obtained either by using the formula or obtained from the DCF Table. INVESTMENT APPRAISAL OR PROJECT EVALUATION A project should be evaluated before it is undertaken. That is, the expenses to be incurred by the project and the return from the project are studied carefully and then whether the project makes a profit or not, is analysed. This analysis is known as project evaluation. The expenses incurred for the project at various points of time are known as cash outflows and the return from the project when considered in terms of cash are known as cash inflows. The cash outflows and inflows are converted to one point of time (year 0) since the rupee value now is not the same as in the future. They are usually converted to present values (or today s rupee value). The difference between the two is calculated. This is known as Net Present Value, denoted by NPV. Interpretation of NPV 1. If the NPV of a project is positive, the project is in profits and hence it is considered to be acceptable. 2. If the NPV of a project is negative, the project makes a loss and hence it is considered to be unacceptable. Note: If the present value of all cash inflows equals that of the cash outflows then the project makes neither profits nor losses. This position is known as breakeven situation. Example: A company purchased a machine now for Rs. 1,000,000. The accountant of the firm estimates that the machine would contribute Rs. 250,000 per annum to profits for next five years, after which point of time it can be disposed of, for Rs. 50,000. Determine the NPV of the machine if the rate of discount is 10% per annum. 9
10 You may assume, for ease of calculations that all inflows occur at yearends. The NPV calculations are usually shown in tabular form as shown below: Year Cash flows Discount factor Present value Rs Obtained from table A 0 1,000, ,000, , , , , , , , , , ,200 Rs NPV = 121,700 THE INTERNAL RATE OF RETURN METHOD The internal rate of return method (IRR) of evaluating a project is an alternative to the net present value method. With the NPV method, the net present value of a project at a given rate of discount is calculated to see whether the project is viable or not. If the NPV is zero, then it indicates that the return from the project is equal to the rate used for discounting. The internal rate of return of a project is the rate of interest at which the NPV of the project is zero. It is the rate at which a project makes neither profits nor losses. It is obtained generally by a trial and error method as follows: 1. Determine a discount rate at which NPV is small and positive; 2. Determine another (larger) discount rate at which NPV is small and negative; There is no precise formula for calculating the IRR of a given project. However, it can be calculated (using a linear interpolation technique) either a) by formula b) graphically Estimation of IRR by formula The exact formula equivalent of the graphical linear interpolation method is given below: If a project makes NPVs of N 1 and N 2 at discount rates of r 1 and r 2 respectively, the IRR of the project would be 10
11 IRR = Or IRR = Where N 1 is the NPV at the rate of r 1 % N 2 is the NPV at the rate of r 2 % Graphical estimation of IRR In order to estimate the IRR of a project graphically:  scale the vertical axis to include both NPVs  scale the horizontal axis to include both discount rates  plot the two points on the graph and join them with a straight line  identify the estimate of the IRR where this line cuts the horizontal axis Worked Example  1: A client of yours has asked for your advice to choose one of the two contracts awarded to him. The first contract generates net cash inflows of an initial Rs10 million at the start of the contract and then Rs1 million at the end of each of the 4 years of the contract. The second contract also lasts for four years and generates net cash inflows of Rs4 million at the end of each year. The client s current rate of interest is 8% per annum. a) Which contract would you advise the company to choose? b) The rate of interest is forecast to fall to 5% before either of the contracts is due to start. How would this affect your advice? Solution  1 Cash flows with Contract  1 Year Net cash inflows (Rs million) DCF (8%) Present value NPV
12 Note: Since the cash flows from year 1 to year 4 are the same the NPV could be obtained using the shortcut method discussed below: NPV = Initial cash inflow now + annual cash inflow Cum DCF (8%, 4 years) (The cumulative DCF could be obtained from Table B of Mathematical Tables of ICASL) NPV = 10 + ( ) = Rs million Similarly the NPV of Contract 2 would be given as follows NPV = Annual cash inflow Cum DCF (8%, 4 years) NPV = = Rs million Hence, Contract1 would be more profitable. If the rate of interest changes only the DCF will get changed cash flows remain the same. At 5% rate of discount NPV of Contract 1 = Initial cash inflow now + annual cash inflow Cum DCF (5%, 4 years) NPV = 10 + ( ) = Rs million NPV of Contract 2 would be = Annual cash inflow Cum DCF (5%, 4 years) NPV = = Rs million Hence the decision would be reversed. Worked Example  2: The Finance Division of a company has been asked to evaluate the following proposals for the maintenance of a new Central Air Conditioning System with a life of six years. Proposal 1: The supplier of the air conditioner will make a charge of Rs. 180,000 per year on a six year contract. Proposal 2: The company will carry out its own maintenance estimated at Rs. 100,000 per annum now, rising at 10% per annum with a major overhaul at the end of year 4 costing an additional Rs. 300,
13 The discount rate is 12%, and all payments are assumed to be made at year ends. a) Calculate the maintenance cost for each year, if the company provides its own maintenance b) Calculate the present value of the cost of maintenance, if the company carries out its own maintenance c) Calculate the present value of the supplier s maintenance contract d) Recommend, with reasons, which proposal should be adopted Solution  2: If the company provides its own maintenance, the present value of cost maintenance would be as follows: Year Maintenance cost DCF (12%) Present Value 1 (110,000) = (110,000) (98,230) 2 (121,000) = (121,000) (96,437) 3 (133,100) = (133,100) (94,767) 4 (146,410) + (300,000) = (446,410) (283,917) 5 (161,051) = (161,051) (91,316) 6 (177,156) = (177,156) (89,818) Present value of cost of maintenance (754,485) If the supplier provides maintenance, the present value of cost of maintenance would be Year Maintenance cost 1 (180,000) 2 (180,000) 3 (180,000) 4 (180,000) 5 (180,000) 6 (180,000) Since the cash flows are the same the present value of the maintenance could be obtained using the cumulative DCF table (Table B of Mathematical Tables of ICASL) Present value = 180,000 Cum DCF (12%, 6 years) = 180, = Rs. 739,980 If we compare the two options given above, Proposal  1 (supplier s maintenance contract) is more economical and hence it is recommended. 13
14 ANNUITIES An annuity is a sequence of fixed equal payments (or receipts) made over uniform time intervals without any interruption. It is an agreement whereby a person pays (or receives) a fixed amount at the end (or beginning) of each period. Examples:  Weekly wages,  Monthly salaries,  Pension scheme,  Insurance premiums,  Housepurchase mortgage payments,  Hirepurchase payments Annuities may be paid  at the end of payment intervals Or PV of an annuity This is the most common form of annuity. It is known as an ordinary annuity. This is where the amounts are payable (or receivable) in arrears.  at the beginning of payment intervals This form of annuity can be observed in certain types of investment or insurance premiums where it will not be deemed to have started until the first deposit or payment has been made. Case 1: An ordinary annuity Consider an ordinary annuity of Rs. A, payable at the end of each year, for n years. If the rate of interest is r%, the present value (or cost) of the annuity would be as follows: An ordinary annuity starts from year 1 and it goes on till year  n Year Cash flows 1 A 2 A 3 A n A 14
15 To calculate the present value of a fixed annual cash flow, we can multiply the annual cash flows by the sum of the DCF factors for the relevant years. This total factor could either be obtained from the Table PV = annual amount Cumulative DCF (r%, n years) Where Cum. DCF = Worked Example 3: The present value of a 5year annuity receivable which begins in one year s time at 5% per annum compound interest is Rs. 60,000. The annual amount of the annuity, to the nearest Re, is A) Rs. 12, 000 B) Rs. 13, 860 C) Rs. 25, 976 D) Rs. 300, 000 Solution  3 PV = annual amount Cum DCF (5%, 5) 60,000 = A A = 60,000/ = Rs. 13,860 Correct answer  (B) Case 2: A due annuity Consider a due annuity of Rs. A, payable at the beginning of each year, for n years. If the rate of interest is r%, the present value (or cost) of the annuity would be as follows: A due annuity starts from year 0 and it goes on till year (n1) Year Cash flows 0 A 1 A 2 A n  1 A PV = amount at year 0 + annual amount Cumulative DCF (r%, n1 years) PV = annual amount [1 + Cumulative DCF (r%, n1 years)] 15
16 Worked Example 4: A farmer is to lease a field for 6 years at an annual rent of Rs. 50,000, the rentals being paid at the beginning of each year. What is the present value of the lease at 7%? A) Rs. 190,000 B) Rs. 200,000 C) Rs. 238,300 D) Rs. 255,000 Solution 4: PV = annual amount [1 + Cumulative DCF (r%, n1 years)] PV = 50,000 [1 + Cum DCF (7%, 5)] PV = 50,000 [ ] PV = Rs. 255,000 Correct answer  (D) PERPETUITY A Perpetuity is the same as an annuity except that payments go on forever. The present value (or cost) of an annuity for every year in perpetuity can be expressed as PV = Where r is the cost of capital as a proportion Worked Example 5: AB Ltd wants to undertake a project which costs Rs. 2 million now and generates an annual cash flow of Rs. 250,000per annum for every year in perpetuity. If the rate of discount is 12% is the project viable? Solution 5: Year Cash flows DCF (12%) PV 0 (2,000,000) ,000, , = ,083,333 (approx.) Hence, the project is viable at 12% rate of discount. NPV = 83,333 16
17 MORTGAGES AND LOANS Though the two terms, mortgage and loan are treated alike for calculation purposes, there is a difference between the two in commerce and business. A mortgage is a method of using property as security for the payment of debt. That is, it is a type of loan that is secured with real estate or personal property. If an amount of money is borrowed over a period of time, one way of amortizing the debt is by paying a fixed amount at uniform time intervals. This fixed amount includes both repayment of capital and interest. Generally the bank mortgages or loans are of this type. There are several ways of calculating the amount of repayments of a mortgage; the following methods are the ones which could be understood easily. To explain the methods a simple example is shown below: Example: A company obtains a loan of Rs50,000 at 6% interest per annum repayable in equal annual instalments at every yearend over the next 5 years. Calculate the annual payment necessary to amortize the debt and prepare the amortization schedule? Method 1: Using the DCF Table Year Amount borrowed Amount settled DCF (6%) Present Value Loan Repayments 0 50, ,000 1 A 2 A 3 A Cum DCF 4 A = A 5 A A = 50,000 A = Rs. 11,871 (approx.) , A ===== ====== 17
18 Method 2: Using a formula. A = Where A Repayment amount L Loan amount n Period r Rate of interest (a proportion) and R = 1 + r A = A = Rs. 11,870 (approx.) Note: A difference of Re1 is due to rounding off. Amortization Schedule Year Amount outstanding at the beginning Interest payable Repayment Amount outstanding at the end 1 50,000 3,000 11,870 41, ,130 2,468 11,870 31, ,728 1,904 11,870 21, ,762 1,306 11,870 11, , ,870 NIL Worked Example 6: A mortgage of Rs. 100,000 is arranged now for 5 years at a rate of interest of 11%. Interest is compounded on the balance outstanding at the end of each year. The loan is to be repaid by 5 annual instalments, the first being due after the end of one complete year. a) Find the gross annual instalments b) Find the amount outstanding after two complete years c) If the rate of interest changes to 13% after two complete years, find the revised annual instalments. 18
19 Solution  6 (a) A = A = Rs. 27,057 (approx.) (b) Year Amount outstanding at the beginning Interest payable Repayment Amount outstanding at the end 1 100,000 11,000 27,057 83, ,943 9,234 27,057 66,120 (c) A = A = Rs. 28,003 (approx.) 1. The present value of Rs. 50,000 receivable 3 years from now, assuming a rate of discount of 9%, is A) Rs. 38,600 B) Rs. 42,000 C) Rs. 63,500 D) Rs. 64, An investment has a net present value of Rs. 4,000 at 10% and one of Rs. 2,000 at 15%. What is the approximate IRR? 3. A job carries a monthly salary of Rs. 10,000, payable in arrears. The net present value of next year s salary, assuming an annual rate of interest of 12% is A) Rs. 89, 000 B) Rs. 94,700 C) Rs. 103,700 D) Rs. 112, The annual rent of a building is Rs. 120,000 payable in advance at the beginning of each year. At an interest rate of 14%, the present value of the rental payments is Rs. 531,960. The length of the lease is A) 3 years B) 4 years C) 5 years D) 6 years 5. A fixedinterest Rs. 200,000 mortgage with annual interest compounded at 6% each year, is to be repaid by 15 equal annual payments. The annual repayment will be closest to A) Rs. 14,133 B) Rs. 20,593 C) Rs. 31,954 D) Rs. 83,400 19
20 6. A company needs to have a balance of Rs. 500,000 in exactly three years from now. It plans to achieve this by putting 12 equal quarterly sums into a Fund. The first sum will be deposited in three months from now. The fund attracts compound interest of 2.5% each quarter. a) Calculate the size of the quarterly sum required for the Fund. b) Demonstrate simply why your answer is reasonable. 7. A small company is faced with 3 options. OPTION 1: To trade in the existing computer for Rs. 25,000 and buy a new computer priced at Rs. 95,000, paying the difference of Rs. 70,000. OPTION 2: To upgrade the existing computer at a cost of Rs. 30,000. OPTION 3: To continue with the existing computer as at present for another four years. OPTION Initial cost (Rs.) Market Value at the end of 4 years (Rs.) Annual maintenance & repair cost payable in advance (Rs.). 1 70,000 25,000 15, ,000 12,000 20, ,000 a) Determine the most economical option based on net present value criterion using a discount rate of 12% per annum. b) What other nonfinancial factors should be taken into consideration before making a decision? 8. S Ltd has developed a vehicle security device and is considering manufacturing marketing the new product. The project will require a Rs20 million investment. The following estimates of costs and revenues for the product over the 5 years have been made. Sales forecast: Year Quantities sold (units sold) Selling price (Rs per unit) 1 5,000 2, ,000 2, ,000 2, ,000 2, ,000 2,000 New plant and machinery will be purchased at a cost of Rs20 million; this will have a resale value of Rs1.5million at the end of 5 years. Labour cost will be Rs400 per unit in year 1, rising by Rs20 per unit in each succeeding year. 20
21 Material costs will be Rs800 per unit for the first two years of production rising by 10% in year 3 and by a further Rs60 in each of years 4 and 5. Other variable costs will be Rs100 per unit and are expected to remain at that level for the duration of the project. Fixed costs of the production will be Rs2 million for the first two years rising by 10% in year 3 and by a further 5% in each of years 4 and 5. The cost of capital to the company is 12%. Calculate the net present value of the project and comment on whether the investment should be initiated? 9. A Rs100,000 mortgage is arranged now for 5 years at a rate of interest of 11%. Interest is compounded on the balance outstanding at the end of each year. The loan is to be repaid by 5 annual instalments, the first being due after the end of one complete year. 1) Find the gross annual instalments 2) Find the amount outstanding after two complete years 3) If the rate of interest changes to 13% after two complete years, find the revised annual instalments. 10. An oil well is currently producing annual (yearend) cash flows of Rs50 million. The best geological evidence suggests that the well has reserves that will last for another 10 years, at the present rate of extraction. A special pump could be installed, at a cost of Rs75 million, that could double the rate of extraction but halve the life of the well. After the well had been exhausted, this special pump could be sold for Rs1 million. The immediate introduction of the special pump is now being considered. Last year s earnings have just been distributed and the existing equipment has no resale value. You are required I. to tabulate the annual effect on earnings over the next 10 years of introducing the special pump; II. to compare the net present value of the options if the cost of capital to the company is 8% p.a.; III. to find whether the pump should be installed if the cost of capital were to be 12%. 21
Statistical 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 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 informationCalculation Guide Estate Master DF Summary Report Performance Indicators. August 2012
Calculation Guide Estate Master DF Summary Report Performance Indicators August 2012 Table of Contents Introduction... 3 Summary Report  Performance Indicators... 4 1. Gross Development Profit... 4 2.
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
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
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 informationFinal Course Paper 2 Strategic Financial Management Chapter 2 Part 6 CA. Anurag Singal
Final Course Paper 2 Strategic Financial Management Chapter 2 Part 6 CA. Anurag Singal Replacement Decision Replacement decision is one of the most important classifications of capital budgeting. Replacement
More informationThe 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 informationCHAPTER 25. P.25.16 The following data are furnished by the Hypothetical Leasing Ltd (HLL):
CHAPTER 25 Solved Problems P.25.16 The following data are furnished by the Hypothetical Leasing Ltd (HLL): Investment cost Rs 500 lakh Primary lease term 5 years Estimated residual value after the primary
More informationInvestment Appraisal INTRODUCTION
8 Investment Appraisal INTRODUCTION After reading the chapter, you should: understand what is meant by the time value of money; be able to carry out a discounted cash flow analysis to assess the viability
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 informationIf Alfred s endowment was payable in five years time what sum should be payable to make both of equal value?
FUTURE VALUE OF A SINGLE SUM Question 1 Alfred and George are brothers. They have both been given an endowment of 5,000 by Great Uncle Edward. George will receive his money immediately whilst Alfred must
More informationThe 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.
More information3. 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
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 information3. Time value of money
1 Simple interest 2 3. 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 informationLeasing Decisions CHAPTER 3
CHAPTER 3 Leasing Decisions BASIC CONCEPTS AND FORMULAE 1. Introduction Lease can be defined as a right to use an equipment or capital goods on payment of periodical amount. Two principal parties to any
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 information10.SHORTTERM DECISIONS & CAPITAL INVESTMENT APPRAISAL
INDUSTRIAL UNIVERSITY OF HO CHI MINH CITY AUDITING ACCOUNTING FACULTY 10.SHORTTERM DECISIONS & CAPITAL INVESTMENT APPRAISAL 4 Topic List INDUSTRIAL UNIVERSITY OF HO CHI MINH CITY AUDITING ACCOUNTING FACULTY
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 informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
More informationCalculator and QuickCalc USA
Investit Software Inc. www.investitsoftware.com. Calculator and QuickCalc USA TABLE OF CONTENTS Steps in Using the Calculator Time Value on Money Calculator Is used for compound interest calculations involving
More informationCompound 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.
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 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 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 informationStatements MAKEorBREAK Sample Questions
Castle 2.3 Statements Got the answer? Be the first to stand with your group s flag. Got it correct? MAKE or BREAK a castle, yours or any other group s. The group with the most castles wins. Enjoy! Question
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 information1.1 Introduction. Chapter 1: Feasibility Studies: An Overview
Chapter 1: Introduction 1.1 Introduction Every long term decision the firm makes is a capital budgeting decision whenever it changes the company s cash flows. Consider launching a new product. This involves
More information1 (a) Net present value of investment in new machinery Year 1 2 3 4 5 $000 $000 $000 $000 $000 Sales income 6,084 6,327 6,580 6,844
Answers Fundamentals Level Skills Module, Paper F9 Financial Management June 2013 Answers 1 (a) Net present value of investment in new machinery Year 1 2 3 4 5 $000 $000 $000 $000 $000 Sales income 6,084
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
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 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 informationCertified Actuarial An nalyst Resource guide Module 1
Certified Actuarial Resource guide Analyst Module 1 2015/2016 CAA Resource guide: Module 0 May 2016 1 Contents The Certified Actuarial Analyst qualification... 2 Assessment of the Module 1 exam... 3 Studying
More informationMidterm exam financiering/finance. <Front page>
Midterm exam financiering/finance Question 1 An agency problem can be alleviated by: A) requiring all organizations to be sole proprietorships. B) compensating managers in such a way that
More information14 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?
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 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 information6 Investment Decisions
6 Investment Decisions BASIC CONCEPTS AND FORMULAE 1. Capital Budgeting Capital budgeting is the process of evaluating and selecting longterm investments that are in line with the goal of investor s wealth
More informationP2 Performance Management
DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. Performance Pillar P2 Performance Management Instructions to candidates Thursday 28 August 2014 You are allowed three hours to answer this question
More informationExam 2 Study Guide. o o
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
More informationFinal Paper 2 Strategic Financial Management Chapter 2 Part 4 CA. Anurag Singal
Final Paper 2 Strategic Financial Management Chapter 2 Part 4 CA. Anurag Singal Capital Budgeting under Capital Rationing Standard Deviation Capital Budgeting Under Inflation Availability of funds may
More informationTIME VALUE OF MONEY PROBLEM #8: NET PRESENT VALUE Professor Peter Harris Mathematics by Sharon Petrushka
TIME VALUE OF MONEY PROBLEM #8: NET PRESENT VALUE Professor Peter Harris Mathematics by Sharon Petrushka Introduction Creativity Unlimited Corporation is contemplating buying a machine for $100,000, which
More informationFinancial Pillar. F2 Financial Management. 20 November 2014 Thursday Afternoon Session
DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. Financial Pillar F2 Financial Management 20 November 2014 Thursday Afternoon Session Instructions to candidates You are allowed three hours
More informationEXAM 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
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, 7
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 2. Use of
More informationINSTITUTE AND FACULTY OF ACTUARIES EXAMINATION
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 12 April 2016 (am) Subject CT1 Financial Mathematics Core
More informationTime Value of Money 1
Time Value of Money 1 This topic introduces you to the analysis of tradeoffs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households
More informationChapter 2 Balance sheets  what a company owns and what it owes
Chapter 2 Balance sheets  what a company owns and what it owes SharePad is packed full of useful financial data. This data holds the key to understanding the financial health and value of any company
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 information9. Himal Trading has EBIT of Rs 80,000, interest expense of Rs 12,000, and preferred
Set A Fundamentals of Financial Management Model Questions 2072 Program: BBS Time: 3 Hours Part: III F.M.: 100 Code: MGT 215 P.M.: 35 The objective of the model questions is to give an overview of the
More informationBank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.
ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return
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 informationModule 2: Preparing for Capital Venture Financing Financial Forecasting Methods TABLE OF CONTENTS
Module 2: Preparing for Capital Venture Financing Financial Forecasting Methods Module 2: Preparing for Capital Venture Financing Financial Forecasting Methods 1.0 FINANCIAL FORECASTING METHODS 1.01 Introduction
More informationThe Basics of Interest Theory
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
More information2.1 Introduction. 2.2 Interest. Learning Objectives
CHAPTER 2 SIMPLE INTEREST 23 Learning Objectives By the end of this chapter, you should be able to explain the concept of simple interest; use the simple interest formula to calculate interest, interest
More informationAFM 271 Practice Problem Set #1 Spring 2005
AFM 271 Practice Problem Set #1 Spring 2005 1. Text problems: Chapter 1 1, 3, 4 Chapter 2 5 Chapter 3 2, 6, 7 Chapter 4 2, 6, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 38, 40, 46, 48 Chapter 5 2, 4,
More informationChapter 9. Year Revenue COGS Depreciation S&A Taxable Income Aftertax Operating Income 1 $20.60 $12.36 $1.00 $2.06 $5.18 $3.11
Chapter 9 91 We assume that revenues and selling & administrative expenses will increase at the rate of inflation. Year Revenue COGS Depreciation S&A Taxable Income Aftertax Operating Income 1 $20.60
More informationLCCI International Qualifications
LCCI International Qualifications Level 2 Certificate in Business Calculations Syllabus Effective from 1 st October 2001 For further information contact us: Tel. +44 (0) 8707 202909 Email. enquiries@ediplc.com
More informationENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure
ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure Chapter 9 Valuation Questions and Problems 1. You are considering purchasing shares of DeltaCad Inc. for $40/share. Your analysis of the company
More informationTime value of money. appendix B NATURE OF INTEREST
appendix B Time value of money LEARNING OBJECTIVES After studying this appendix, you should be able to: Distinguish between simple and compound interest. Solve for future value of a single amount. Solve
More informationChapter. Discounted Cash Flow Valuation. CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG.
Chapter 6 Discounted Cash Flow Valuation CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG. Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute
More informationVilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis
Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................
More informationReal Estate. Refinancing
Introduction This Solutions Handbook has been designed to supplement the HP2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or stepbystep keystroke procedures
More informationWorkbook 2 Overheads
Contents Highlights... 2 Quick Practice Session on Overheads... 2 Financial Quiz 2  Overheads... 3 Learning Zone Overheads... 3 Fixed and Variable costs and Breakeven analysis explained... 3 Fixed Costs...
More informationPaper F9. Financial Management. Friday 6 December 2013. Fundamentals Level Skills Module. The Association of Chartered Certified Accountants
Fundamentals Level Skills Module Financial Management Friday 6 December 2013 Time allowed Reading and planning: Writing: 15 minutes 3 hours ALL FOUR questions are compulsory and MUST be attempted. Formulae
More informationNote: There are fewer problems in the actual Midterm Exam!
HEC Paris Practice Midterm Exam Questions Version with Solutions Financial Markets BS Fall 200 Note: There are fewer problems in the actual Midterm Exam! Problem. Is the following statement True, False
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 informationC02Fundamentals of financial accounting
Sample Exam Paper Question 1 The difference between an income statement and an income and expenditure account is that: A. An income and expenditure account is an international term for an Income statement.
More informationChapter 13. The annuity mortgage Interest discrete versus continuous compounding. Reading material for this chapter: none recommended
Chapter 13 The annuity mortgage Reading material for this chapter: none recommended We formulate a mathematical model for the simplest possible mortgage, the annuity mortgage. We assume that interest is
More informationFin 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
More informationChapter 4 Discounted Cash Flow Valuation
University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute
More informationUnderstanding Cash Flow Statements
Understanding Cash Flow Statements 2014 Level I Financial Reporting and Analysis IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Components and Format of the Cash Flow Statement... 3 3. The
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 informationThe application of linear programming to management accounting
The application of linear programming to management accounting Solutions to Chapter 26 questions Question 26.16 (a) M F Contribution per unit 96 110 Litres of material P required 8 10 Contribution per
More informationManagement Accounting Financial Strategy
PAPER P9 Management Accounting Financial Strategy The Examiner provides a short study guide, for all candidates revising for this paper, to some first principles of finance and financial management Based
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 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 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 informationTopic Overview. Strategies and Management E4: Resources Management Simple interest, Compound Interests & Time
Resources for the TEKLA curriculum at Junior Secondary Topic 6 Simple & Compound Interests and TVM Strategies and Management Extension Learning Element Module E4 Resources Management Topic Level Duration
More informationMODULE 2. Capital Budgeting
MODULE 2 Capital Budgeting Capital Budgeting is a project selection exercise performed by the business enterprise. Capital budgeting uses the concept of present value to select the projects. Capital budgeting
More informationHow will the firm's total aftertax cash flows change if the new project is accepted?
NPV and Capital Budgeting: A Short Note on Estimation of Project Cash Flows (Relevant to AAT Examination Paper 4 Business Economics and Financial Mathematics) KC Chow The most important valuedriving decisions
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 informationNPV calculation. Academic Resource Center
NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year
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 information( ) ( )( ) ( ) 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
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 informationTime 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
More informationCHAPTER 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
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission
2007. M55 Coimisiún na Scrúduithe Stáit State Examinations Commission LEAVING CERTIFICATE EXAMINATION, 2007 A C C O U N T I N G  H I G H E R L E V E L (400 marks) This paper is divided into 3 Sections:
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 informationPreparing cash budgets
3 Preparing cash budgets this chapter covers... In this chapter we will examine in detail how a cash budget is prepared. This is an important part of your studies, and you will need to be able to prepare
More informationConstruction Economics & Finance. Module 6. Lecture1
Construction Economics & Finance Module 6 Lecture1 Financial management: Financial management involves planning, allocation and control of financial resources of a company. Financial management is essential
More informationRate of Return Analysis
Basics Along with the PW and AW criteria, the third primary measure of worth is rate of return Mostly preferred over PW and AW criteria. Ex: an alternative s worth can be reported as: 15% rate of return
More informationB Com (H) III Year. Paper 3.4HA
B Com (H) III Year Paper 3.4HA FINANCIAL MANAGEMENT Module 1 UNIT 1 : INTRODUCTION 1. Give an idea about the Wealth Maximisation objective of Financial Management. 2. Discuss the various functions of Financial
More informationPutting a business idea into practice
Putting a business idea into practice Objectives when starting up What is an objective? An objective is what the business is trying to achieve eg make profit Why do entrepreneurs start a business? There
More informationST334 ACTUARIAL METHODS
ST334 ACTUARIAL METHODS version 214/3 These notes are for ST334 Actuarial Methods. The course covers Actuarial CT1 and some related financial topics. Actuarial CT1 which is called Financial Mathematics
More informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
More informationProblems on Time value of money January 22, 2015
Investment Planning Problems on Time value of money January 22, 2015 Vandana Srivastava SENSEX closing value on Tuesday: closing value on Wednesday: opening value on Thursday: Top news of any financial
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 information