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Copperbelt University Directorate of Distance Education and Open Learning Master in Business Administration (Finance) GBS 621: Corporate Finance Assignment #1 Written by Ignatius Kasela Zulu SIN: 20900369 Lecturer: Dr. Izidin El Kalak 07th September 2021 What is the future value of an initial $100 after 3 years if it is invested in an account paying 10% annual interest? Known: Present Value (PV) = $100 Number of periods involved in the analysis (N) = 3 years Interest Rate (R) = 10% Unknown: Future Value (FV) =?? From standardised formulas FV= PV* (1+R) N …………………………………………………eqn 1 Therefore, using equation 1: FV=100*(1+0.1)3 = 100*(1.01)3 = $ 103.03 The future value of an initial $100 after 3 years if it is invested in an account paying 10% annual interest is $ 103.03. What is the present value of $100 to be received in 3 years if the appropriate interest rate is 10%? Knowns: Future Value (FV) = $100 Number of periods involved in the analysis (N) = 3 years Interest Rate (R) = 10% Unknowns: Present Value (PV) = ?? From standardised formula equation 1; FV= PV * (1+R) N PV = FV/ [(1+R) N] ------------------------------------------eqn 2 Therefore: PV= 100/ (1.01)3 = $ 97.09 The present value of $100 to be received in 3 years with an interest rate of 10% is $97.09. We sometimes need to find out how long it will take a sum of money (or anything else) to grow to some specified amount. For example, if a company's sales are growing at a rate of 20% per year, how long will it take sales to double? Taking N =?? Current sales as Present Value (PV) Interest Rate (R) = 20% Future Sales as Future Value (FV) Since we are looking for sales to double, therefore: FV = 2*PV …………………………………………………eqn 3 Using standardised formula eqn 1; FV = PV*(1+R) N FV/PV= (1+R) N Log (FV/PV) = N Log (1+R) N = [Log (2)] / [Log 1.2] = 3.801 years It will take 3 years 9 months to double the sales. If you want an investment to double in 3 years, what interest rate must it earn? Known: N=3 Since we are looking for sales to double, therefore: FV = 2*PV Unknown R =?? Using standardised formula eqn 1: FV = PV*(1+R) N 2PV=PV*(1+R) 3 21/3 = (1+R) 3*1/3 2 1/3 = 1+R R= 2 1/3 – 1 = 1.26 – 1 = 0.26 R = 26% The interest rate to be charged is 26% What is the difference between an ordinary annuity and an annuity due? An annuity is when equal payment are made at fixed intervals. For example, $100 paid at the end of each of the next 3 years is a 3-year annuity. If payment is made at the end of each period, then we have an ordinary (or deferred) annuity. Mortgage payments, car loans and student loans are made at the end of each period and are therefore ordinary annuities. If payment is made at the beginning of each period, then we have an annuity due. Rental fees, life insurance premiums, are examples of annuities due. Refferences: 1. Ehrhardt, M. (2017). Corporate finance: A focused approach (6th Ed.). Boston, MA: Cengage Learning. ISBN 9781305637108