# Index Numbers ja Consumer Price Index

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1 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 and services between different years. The consumer price index measures also the inflation. Buying power It is the current value of available cash in relation to the quality and quantity of products that can be purchased. When the prices of goods and services increase (inflation) also the earnings should increase relatively as much to remain the same buying power. Assignment 1 The average net earnings of employees in the manufacturing company end of 2008 were 2,100 /month and four years later the net salary, end of 2012, it was 2,500 /month. a) Find the CPI values for years 2008 and 2012 and calculate the inflation from 2008 to 2012 b) What is a real increase in buying power when the inflation is considered? How many euros? How many percent? Assignment 2 Simple Interest I = Cti C = principal i = rate t = time in days The interest rate of the bank account was 3% p.a. The following transactions occurred during the year Balance of the account ,500 Deposit ,500 Withdrawal Withdrawal ,000 a) Find the balance of the account when the earned interest in added to the principal. b) Use Excel graphics to present how interest was earned during the year 2013.

2 Some Essential Financial Functions in Excel 2 Function In Theory FV-function Computes a future value of an investment or a future value of an ordinary annuity PV-function Returns the present value of an investment when the future value is known. Or computes the present value of an ordinary annuity when series of equal future values are known NPV-function Calculates the net present value of an investment by using a discount rate and a series of future payments (negative values) and income (positive values) RATE-function Returns the interest rate per period of an investment æ M ö NPER-function logç Returns the number of periods for an investment based on C t = è ø periodic, constant payments, and a constant interest rate log(1 + i) IRR-function Returns the internal rate of return for a series of cash flows represented by the numbers in values. PMT-function Calculates an annuity based on constant payments and a constant interest rate PPMT- function Returns the payment on the principal for a given period for an investment based on periodic, constant payments and a constant interest rate. IPMT function Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate ISPMT function Calculates the interest paid during a specific period of an investment.

3 3 Compound Interest æ M ö logç C t = è ø log(1 + i) For all the arguments, cash you pay out, such as deposits to savings, is represented by negative numbers; cash you receive, such as dividend checks, is represented by positive numbers. Assignment 3 a) Find the future value, accumulated value of 15,000 for 5 years at 6 % interest compounded annually. What is the total earned interest in 5 years? b) Find the future value, accumulated value of 15,000 for 5 years at 6 % interest compounded monthly. What is the total earned interest in 5 years? c) The investor is considering investing in a project in the end of the year. The future value of the investment in the end of the year 2020 would be 10,000. What would be the present value of the investment if the interest rate is 5 %p.a.? d) The turnover of the company doubled in 7 years. How long does it take to triple the turnover, if the rate of growth would keep up the same relative level? Assignment 4 Mr K made an investment of 20,000 in In ten years,, the value of the investment has increased to 40,000. a) What nominal interest rate does the investment yield? b) What real annual interest rate does the investment yield assuming that the average annual inflation rate during the period has been 2.0 % p.a.? Assignment 5 A company is considering introducing a personnel training project. According to the offer obtained, the initial costs of the training are 100,000. The company estimates that the training would increase productivity so that the company s profit (after taxes) would improve annually as follows: Year 1 Year 2 Year 3 Year 3 40,000 35,000 32,000 30,000 a) Use the NPV-method to investigate if the introduction of the training project is economical based on 10 % p.a interest rate b) Use the IRR-method to investigate if the introduction of the training project is economical based on 10 % p.a interest rate c) Illustrate using Excel graphics Assignment 6 The corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. These costs are: Startup costs: machinery, employee training costs 100,000 (outflow) Operational costs: 5,000 per year (outflow) Cash inflows: expected to be 30,000 per year (inflow) Residual value (how much a fixed asset is worth at the end of its investment period) 20 % of the initial investment. The required rate of interest is 10% p.a. a) Use NPV-method and suggest if the company should invest into the project. b) Use IRR-method and suggest if the company should invest into the project. c) Illustrate using Excel graphics.

4 4 Annuities An annuity Is a series of equal payments, made at regular interval of time. When the payments are made at the end of the payment interval (period), the annuity is called ordinary annuity. Future value of ordinary annuities The future value at compound annual rate i at time n is denoted by snei and is given by: Assignment 7 The manager of the Royal Greeting Card Company decides that he will need two new printers in 5 years. He estimates that total cost of both printers will be about \$12,000. How much he should pay every three months to the ordinary sinking fund to be able to purchase the printers? The interest rate is 2 % annual rate compounded quarterly. Present value of ordinary annuities Assignment 8 A female student who was 25 years old in 2013 will retire after working 40 years. The future is very unpredictable and the welfare system could be very different and old age pension may no longer be as good as today. This means that people will either have keep working or fund their own retirement. Your task in this investigation is to plan so that the student will be financially independent in her retirement. The following estimations are needed for the calculations: The interest rate of the pension scheme is estimated to be average 4 % p.a. in the future The average life expectancy for women is estimated to be 87 years If a person would retire in 2013 the comfortable additional pension would be 25,000 /year. a) Find the yearly pension in 2053 if the inflation is predicted to be average 2 % annual rate in the future b) Calculate the total sum needed in 2053 for the future pensions (you may assume that pension is fixed ) c) How much the student will require to deposit yearly into pension scheme in in order to achieve the total sum needed to save? d) How much is the total interest earned in euros during 40 years?

5 5 Annuity loan - Amortization schedule Assignment 9 Choosing a mortgage You are working as a financial adviser, and have been asked by a client to help her decide which of a number of mortgages she should choose, in order to purchase a house costing 125,000 at a start of. She can afford to put down deposit of 20,000, and wishes to pay off the mortgage over 20 years. The mortgages on offer are the follows: Bank A Offers a fixed rate of 8.5% p.a. for the whole period. Create an amortization schedule for the offer and find out the total interest paid in 20 years. Bank B Offers a fixed rate of 7 % p.a. for five years, after which you estimate that the rate is likely to rise to 9 % p.a. for the remainder of the period. Create an amortization schedule for the offer and find out the total interest paid in 20 years. Advise the client on her best option. Assignment 10 Two years ago, a person took out a 5-year loan to buy a new car. The amount of loan taken was 20,000 at 5.25% p.a. with monthly annuity payments. Now he has inherited some money and wants to pay off of the whole loan. Find the current balance of the loan and calculate how much he needs to pay.

6 6 Leasing Assignment 11 Financial company offers leasing contract by the following terms: Leasing period 36 months Lease payment is paid monthly in the beginning of month Residual value (how much a fixed asset is worth at the end of its lease) is accounted to be 20 % purchase price. a) A client of the company would like to lease a car which purchasing price is 30,000. Determine the monthly lease payment when the financing company uses 7.5 % annual interest rate for running the business. b) Another client would like to lease a car and pay maximum 500 monthly lease payment. What is the maximum purchasing price of the car for the customer?

7 7 Extra exercises Assignment 12 A firm is considering purchasing of one of two machines. The first, costing 1,700, is expected to bring revenue of 1,000, 800 and 500 respectively in three years which it will operative, while the second, which costs 2,000, produces revenues of 1,200, 900 and 600, and has the same lifetime. An interest rate of 20 % p.a. has been suggested as appropriate. a) Using NPV-method advise the firm as to the financial wisdom of purchasing one or the other of these machines b) Calculating internal rate of return for both machine investments advise the firm as to the financial wisdom of purchasing one or the other of these machines Assignment 13 A company is planning t.o modernize their production line. The purchase price of the new production line would be 1,200,000 and other start-up costs would be 300,000. The investment is estimated to have life of 5 years. The annual operational costs are estimated to be 200,000 and the annual return (inflow) is estimated to be 600,000. The company owners require the annual interest rate of company investments to be at least 8 % p.a. Should the product line investment approved based on this requirement? Assignment 14 Three alternative projects have been proposed with initial costs and revenues (1000 ) for the next five years as shown below: Project Initial cost Net revenue in each year A B C If the company has enough resources to start only one project suggest the best using Internal rate of return method for different alternatives. Assignment 15 Study the structure of the following Excel functions and present also a numerical example when the function is used: PPMT- function IPMT function

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