IE2140 Engineering Economy Tutorial 3 (Lab 1) Using Excel Financial Functions for Project Evaluation

Transcription

1 IE2140 Engineering Economy Tutorial 3 (Lab 1) Using Excel Financial Functions for Project Evaluation 1. Objectives and Overview Solutions Guide by Hong Lanqing, Wang Xin and Mei Wenjie The objective of Lab 1 is to learn how to use the various Excel financial functions to solve problems and project proposals involving cash flows and time value of money. At the end of this lab session, you should be able to use the following functions in Excel: (i) PV, PMT, FV, RATE, NPER (ii) NPV (iii) IRR, MIRR. 2 Review of Excel Financial Functions The following is a quick review of the descriptions of the essential Excel financial functions. See Appendix A, Chapter 3 of Lecture Notes for examples of their applications. 2.1 PV (Present Value) Function The PV function computes the negative of the equivalent Present Value of a uniform series cash flows and a single cash flow in the end of last period, at a specific constant interest rate. =PV (rate, nper, pmt, fv, [ type]) rate = interest rate per period nper = total number of periods pmt = uniform cash flow per period fv = cash flow at end of period Nz 0 end of periods uniform cash flows (default) type = 1 beginning of period uniform cash flows type = 0 type = PMT (Payments) Function The PMT function computes the negative of the equivalent uniform series cash flow of a single cash flow at time zero and a single cash flow at end of period N, at a specific constant interest rate. =PMT (rate, N, P, F, [ type ]) rate = interest rate per period N = total number of periods P = cash flow at time zero F = cash flow at end of period N 0 end of periods uniform cash flows (default) type = 1 beginning of period uniform cash flows type = 0 type = 1 soln-tut3-lab1-1

2 2.3 FV (Future Value) Function The FV function computes the negative of the equivalent Future Value of a single cash flow at time zero, and a uniform series of cash flows, at a specific constant interest rate. type = 0 =FV (rate, N, A, P, [ type] ) rate = interest rate per period N = total number of periods A = uniform cash flow per period P = cash flow at time zero. 0 end of periods uniform cash flows (default) type = 1 beginning of period uniform cash flows type = RATE Function The RATE function computes the interest rate that makes the PW or NPV of a set of cash flows comprising a uniform series over N periods, a single sum at time zero, and a single sum at time N, equals to zero. type = 0 =RATE (N, A, P, [F], [ type], [guess] ) rate = interest rate per period N = total number of periods A = uniform cash flow per period P = cash flow at time zero. F = cash flow at time N 0 end of periods uniform cash flows (default) type = 1 beginning of period uniform cash flows guess = an initial value for iterative computation of RATE. type = NPER (Number of Periods) Function The NPER function computes the number of periods N that makes PW or NPV of a set of cash flows comprising a uniform series of cash flows over N periods, a single cash flow at time zero, and a single cash flow at time N, equal to zero at a specific interest rate. type = 0 =NPER (rate, A, P, [F], [ type ] ) rate = interest rate per period A = uniform cash flow per period P = cash flow at time zero. F = cash flow at time Nper 0 end of periods uniform cash flows (default) type = 1 beginning of period uniform cash flows type = 1 soln-tut3-lab1-2

3 2.6 NPV (Net Present Value) Function The NPV function computes the net present value or present worth of a series of cash flows starting at time 1, at a specific constant interest rate. =NPV (rate, series) rate = interest rate per period series = series of cash flow in a range of cells starting from time 1. NPV (i, series) = FF 1 (1+ii) + FF 2 (1+ii) FF NN 1 + FF NN (1+ii) NN 1 (1+ii) NN series = {F1, F2,, FN} Note that the series starts at EoY 1. Any initial cash flow at EoY 0 must be added outside the formula, i.e., PW(i%) = F o + NPV( i, {F 1, F 2,, F N} ). 2.7 IRR (Internal Rate of Return) Function The IRR function compute the internal rate of return of a series of cash flows starting at time zero. =IRR (values, guess) values = a series of cash flows starting at time zero with at least one positive and one negative, in a range of cells. guess = an initial guess value. 2.8 MIRR (Modified IRR) Function The MIRR computes the modified internal rate of return of a series of cash flows starting at time zero. NN =MIRR (values, r 1, r 2) = FFFF(all+ve net CFs,r 2) 1 PPPP(all ve net CFs,r 1 ) values = array or series of net cash flows r 1 = finance rate for the net cash outflows r 2 = reinvestment rate for the net cash inflows Note that ERR is a special case of MIRR with r 1 = r 2 = εε = reinvestment rate. Hence the ERR of a series of net CFs at reinvestment rate εε can be computed as MIRR (values, εε, εε) soln-tut3-lab1-3

4 3. Hands on Exercises and Solutions Question 1. 1(a) Solve Tutorial 1, Question 5 Using Goal Seek and RATE function. On January 1, 2005, a person s savings account was worth $200,000. Every month thereafter, this person makes a cash contribution of $676 to the account. If the fund is expected to be worth $400,000 on January 1, 2010, what monthly rate of interest is being earned on this fund? N 60 P $200, A $ F -$400, i? The objective of this question is to find i such that PW = 0, that is, PP (1+ii) NN AA + ii FF (1+ii) NN = 0 (1) 1) Solution using Goal Seek by solve the PW=0 with general formula First, we input all the related values mentioned in the question in Excel, which is already done in the templates. Then, we set the initial value of i as 10%, and input the formula (1) to calculate PW. input formula (1) in B12 to calculate PW initial value of i soln-tut3-lab1-4

5 To find the i such that PW = 0, we use the Goal Sick in Excel: DATA What-If Analysis Goal Seek Set PW equals to zero by changing i, then click OK, we get i = %. objective value of i 2) Solution using RATE function We can also use the RATE function to solve this problem. The RATE function computes the interest rate that makes the PW or NPV of a set of cash flows comprising a uniform series over N periods, a single sum at time zero, and a single sum at time N, equal to zero. =RATE (N, A, P, [F], [ type ], [guess]). We first input the RATE function in B24. Here we set the value of guest as 0.1. After the calculation, we get the objective value of i = %, which is the same as the previous one. input RATE function, = RATE (nper, pmt, pv, [fv], [type], [guest]) objective value of i soln-tut3-lab1-5

6 Note that in Excel, while we are inputting the RATE function, we could refer to the hint offered by Excel. hint 1(b) Tutorial 1, Question 5 Using NPER function. If the account pays interests at 2% per month, use Excel s NPER function to determine how long it would take to achieve the same final amount if the initial amount and monthly contributions remain the same. N? P $200, A $ F -$400, i 2.00% The NPER function computes the number of periods N that makes PW or NPV of a set of cash flows comprising a uniform series of cash flows over N periods, a single cash flow at time zero, and a single cash flow at time N, equal to zero at a specific interest rate. In this question, i is fixed while N is unknown. We need to find an N such that PW = 0, so we apply the NPER function = NPER (rate, A, P, [F], [ type ] ). input the NPER function, = NPER (rate, pmt, pv, [fv], [type]) objective value of N soln-tut3-lab1-6

7 Question 2. Solve Tutorial 2, Question 1 Using PV, NPV function. Evaluate a combined cycle power plant on the basis of the PW method when the MARR is 12% per year. Pertinent cost data are as follows: Cash Flow Initial investment -$13, Expected life (year) 15 Market Value $3, Annual Operating Expenses -$1, Overhaul cost EoY 5 -$ Overhaul cost EoY 10 -$ MARR % In this question, the objective is to calculate the PW of the given cash flow. First, we input all the related value in Excel, which is showed in Excel Sheet named Lab Q2. 1) Using PV function The PV function computes the negative of the equivalent Present Value of a uniform series cash flows and a single cash flow in the end of last period, at a specific constant interest rate. =PV (rate, N, A, F, [ type ] ), In this question, since the PV function does not include the initial cash flow at EoY 0, we need to add the initial value outside the PV function, which is B6 in the Excel Sheet. Then we classify the cash flows into three groups: (i) The first group is the -$1000 and $3000 cash flow. Its rate is 12.00%, NPER is 15, PMT is -$1000, fv is $3000, and type is 0. That is, PV 1= -PV (B12, B7, B9, B8, 0). (ii) The second group is the -$200 cash flow occurs in the fifth year, whose NPER is 5, PMT is $0, fv is -$200, and type is 0. That is, PV 2 = -PV (B12, 5, 0, B19, 0). (iii) The third group is the -$550 cash flow occurs in the tenth year. Its NPER is 10, PMT is 0, fv is - $550, and type is 0. That is, PV 3 = -PV (B12, 10, 0, B11, 0). Therefore, we could input the initial cash flow plus the PV function, and obtain the PW = -$19, initial cash flow + PV functions objective value of PW soln-tut3-lab1-7

8 2) Using NPV function The NPV function computes the net present value or present worth of a series of cash flows starting at time 1, at a specific constant interest rate. However, note that the series starts at EoY 1. Therefore, any initial cash flow at EoY 0 must be added outside the formula. In this question, we use the NPV function to compute NPV from year 1 to year 15, i.e., B21:B35, and then add the initial cash flow B20. Finally, we get the same PW = -$19, initial cash flow + NPV function cash flow in each year objective value of PW soln-tut3-lab1-8

9 Question 3. Solve Tutorial 2, Question 2 Using FV function Determine the FW of the following engineering project when the MARR is 15% per year. Is the project acceptable? Proposal A Cash Flow Investment Cost -$10, Expected life (year) 5 Market Value -$1, Annual Receipts $8, Annual Expenses -$4, MARR % FV function computes the negative of the equivalent Future Value of a single cash flow at time zero, and a uniform series of cash flows, at a specific constant interest rate. =FV(rate, N, A, P, [ type] ) The objective of this question is to calculate the FV, then we apply the FV function in Excel. The interest rate is B10, the period is B6, the income is annual receipts and annual expenses, i.e., B8+B9, and the present value is the investment cost B5, and the type is 0, end of year cash flow. Since the FV function does not contain the Market value in last year, we need to add B7 to the formula. Then we obtain the objective value of FW. Market value + FV function objective value of FW We could also apply the RATE function to find the IRR such that PW = 0. objective value of IRR soln-tut3-lab1-9

10 Question 4. Solve Tutorial 2, Question 3 Using PMT function A company is considering constructing a plant to manufacture a proposed new product. The land costs $300,000, the building costs $600,000, the equipment costs $250,000 and $100,000 additional working capital is required. It is expected that the product will result in sales of $750,000 per year for 10 years, at which time the land can be sold for $400,000, the building for $350,000, and the equipment for $50,000. All of the working capital would be recovered at the EoY 10. The annual expenses for labor, materials, and all other items are estimated to total $475,000. If the company requires a MARR of 15% per year on projects of comparable risk, determine if it should invest in the new product line. Use the AW method. Summary of information: Capital investments Land cost = $300,000 Building cost = $600,000 Equipment cost = $250 Working capital = $100,000 Total Capital Investment = $1,250,000 Annual Revenue & Expenses Annual revenue = $750,000 Annual expense = $475,000 Annual Net Income = $275,000 Salvage values at EoY10 Land = $400,000 Building = $350,000 Equipment = $50,000 Working capital =$100,000 (all recovered at EoY 10) Total Salvage Values = $800, ,000 = $900,000 The objective of this question is to calculate the annual worth, we apply the PMT function. The PMT function computes the negative of the equivalent uniform series cash flow of a single cash flow at time zero and a single cash flow at end of period N, at a specific constant interest rate. =PMT (rate, N, P, F, [ type ]) soln-tut3-lab1-10

11 First, we calculate the total capital investment, annual net income and total salvage values by summing up related cash flows: Total Capital Investment = SUM (B7: B10), Annual Net Income = SUM (B14: B15), Total Salvage Values = SUM (B19: B22) The PMT function could calculate the AW of P (Total Capital Investment, B11), and F (Salvage Values of EoY 10, B23), the rate is 15% (B3), and the period is 10 (B4). Then, we add the Annual Net Income (B16) into the calculation and obtain the total AW. Annual Net Income + PMT (rate, nper, pv, [fv], [type]) objective value of AW We could also use the RATE function to calculate the IRR such that PW = 0. soln-tut3-lab1-11

12 Question 5. Solve Tutorial 2, Question 5 The International Parcel Service has installed a new radio frequency identification (RFID) system to help reduce the number of packages that are incorrectly delivered. The capital investment in the system is $65,000, and the project annual savings are tabled bellow. The system s market value at the EOY five is negligible, and the MARR is 18% per year. (a) What is the FW of this investment? (b) What the IRR of the system? (c) What is the MIRR of this investment if the financing rate is12% and reinvestment rate is 18%? End of Year Savings 1 $25, , , , ,000 First, we calculate the present value up to year k. Here, after inputting the formula in C5, we could put the mouse at the lower right corner of C5 and obtain the formula of C5 ~ C9. Note that since we need to keep the value in B4, B11, B5 fixed as we drag down, so we press F4 to fix these values. For example, after pressing F4, B4 changes to $B$4, which means that both the 4 th row and B th column are fixed. formula to calculate the PW up to EoY k Then, we calculate the objective FW in two steps using first NPV and then FV. drag down and get the formula of C6 ~ C9 PW = initial cash flow + NPV (rate, value1, value 2, ) FV (rate, nper, pmt, [pv], [type]) soln-tut3-lab1-12

13 The IRR function computes the internal rate of return of a series of cash flows starting at time zero. It could deal with irregular cash flow. Here, we input cash flow up to k year (B4: B9), set the value of guest as 0.1, and apply the IRR function to compute the objective IRR directly. IRR (values, [guest]) The MIRR computes the modified internal rate of return of a series of cash flows starting at time zero. Here we apply the MIRR function. MIRR (values, finance_rate, reinvest_rate) soln-tut3-lab1-13