Financial management time value of money questions and answers

FIN 701, PRACTICAL APPLICATION 1, SUMMER 2020 AP1 This assignment is an opportunity to further practice your time value of money calculation skills and to help reinforce the concepts from this module. Being able to work a wide variety of problem types, and For each problem, you need to show your work in order to receive credit. A correct answer with no work shown gets half credit (which means you fail the assignment). An incorrect answer with no work receives 0 credit. With time value of money (TVM) problems, that means showing your inputs for the financial calculator. Make your final answer very clear for the graders. Please don’t make them hunt for your answer. If in doubt, look at my solutions for the practice problems. For example, on 1a, I would show: N = 4; I/Y = 7.5; PV = -1200; PMT = 0, Calc FV = _______ For uneven cash flows, show CF0 = xx, CF1 = xx F01 = x; CF2 = xx F02 = x, etc. Show all dollar and percentage values to two decimals ($xxx.xx) and percentage values to x.xx% (be sure to have enough decimals showing on your calculator). Rounded answers will receive point deductions. In some cases, an equation will be easier than using the TVM keys, show your equation if that is the case. If you use Excel, show what the equation and inputs used. As with all TVM problems, assume annual compounding unless otherwise specified. Further, assume “regular” annuities (end of period payments) unless specified as “annuities due” (beginning of period payments). This is an individual assignment, not group work. The assignment is worth a total of 30 points problems with differing setups is important. 1. (a) If you deposit $1,200 in the bank today, what is its future value at the end of four years if it is invested in an account paying 7.5% annual interest, assuming annual compounding? (1 point) (b) What is the present value of $1,200 to be received in four years if the appropriate interest rate is 7.5% (annual compounding)? (1 point) 2. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. (a) For example, if a company’s sales are growing at a rate of 7.5% per year, approximately how long will it take sales to triple? Show your answer to 2 decimals (x.xx years) (1 point) (b) If you want an investment to double in 6 years, what interest rate must it earn? Show your answer to 2 decimals (x.xx%) (1 point) 3. (a) What is the difference between an ordinary annuity and an annuity due? (2 points) (b) What type of annuity is shown in the following cash flow timeline? (1 point) (c) How would you change it to the other type of annuity? (Think about the cash flows) (1 point) 4. (a) What is the future value of a 4-year ordinary annuity (recall that ordinary annuities have end of year cash flows) of $1,200 if the appropriate interest rate is 7.5%? (1 point) (b) What is the present value of the annuity? (1 point) (c) What would the future and present values be if this annuity were an annuity due (beginning of year cash flows)? Hint, set your calculator to BGN, there is a video in M2 that shows you how to do this. Don’t forget to reset to “END” after you work an annuity due problem. (1 pt) PV = (1 pt) FV = Note: Look at the difference between an annuity vs. annuity due for the respective PVs and FVs. This relationship is something you will want to remember. 5. What is the present value of the following uneven cash flow stream? The appropriate interest rate is 7.5%, compounded annually. Note that the final cash flow represents a project where there may be reclamation or other “end of project” costs which are greater than any final income and/or salvage value. (1 point) 0 1 2 3 4 155 285 -125 425 6. What annual interest rate will cause $1,200 to grow to $1,652 in 5 years? Show your answer to 2 decimals (x.xx%) (1 point) 7. (a) Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually — holding the stated interest rate constant? Explain your answer. (2 points) As a cross-check, compare your answer in 1a to 7b-1 below. (b-1) What is the future value of $1,200 after four years under 7.5% semiannual compounding? (1 point) (b-2) What is the effective annual rate for 7.5% interest with semiannual compounding? Be sure to show your EAR answer to 2 decimals, that is xx.xx% (1 point) Hint: Go to practice problem 26 and review the problem and solution. Also note in Moodle: “Video, how to work Practice Problems #26 & 27). This provides a “click by click” solution for EAR problems using the BAII Plus with the equation. • • • There are multiple ways to calculate EAR, whichever method you use, you need to show your inputs. If using equation: EAR = ( 1 + APR/m)^m, identify APR and m If using the financial calculator’s “ICONV” function, identify NOM, and C/Y If using Excel’s “effect” function, identify your inputs and how the equation would look in Excel. (c-1) What is the future value of $1,200 after four years under 7.5% quarterly compounding? (1 point) (c-2) What is the effective annual rate (EAR) for 7.5% interest with quarterly compounding? (1 point) (d-1) What is the future value of $1,200 after four years under 7.5% daily compounding? Assume 365 day years and do not do any interim rounding.