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Running head: TEXTBOOK PROBLEMS 1 TEXTBOOK PROBLEMS (U04A2) Nafanua Valdez BUS4070- Foundations in Finance May 6, 2022

TEXTBOOK PROBLEMS 2 TEXTBOOK PROBLEMS (U04A2) 5-9 PRESENT AND FUTURE VALUES FOR DIFFERENT PERIODS a) Future Value = Present Value *(1+Rate)^Number of Periods =$600*(1+6%)^1 =$600*1.06 =636 b) FV = Future Value = ? Rate = 6% Nper = 2 years PMT = 0 PV = 600 = FV (6%, 2, 0, -600) = $674.16 c) PV = C/ (1 +R )^ N = 600 600/(1+0.06)^2 = $566.03 d) PV = C/ (1 + R) ^ N = 600/ (1 + 0.06) ^ 2 = 600/ (1.06) ^2 =600/ 1.1236 =$534 5-14 FUTURE VALUE OF AN ANNUITY a) Annual Payments = $500

TEXTBOOK PROBLEMS 3 Number of Payments = 8 Interest Rate = 14% FV= 500 *1.14 ^ 7 + 500*1.14^6 + 500*1.14^5 +…… 500*1.14 = 500 * (1.14 ^ 8 – 1) / 0.14 = 500*13.232760 = $6,616.38 b) Annual Payments = 250 Number of Payments = 4 Interest Rate = 7% FV= 250 * 1.07^3 + 250*1.07^2 + 250*1.07 + 250 = 250 * (1.07^4 – 1) / 0.07 = 250 * 4.439943 = $1,109.99 c) Annual Payments = 700 Number of Payments= 4 Interest Rate = 0 FV = 700 + 700 + 700 + 700 =700 * 4 = $2,800 d) Annuity 1: Annual Payments= 500 Number of Payments= 8 Interest Rate = 14

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TEXTBOOK PROBLEMS 4 FV= 500*1.14^8 + 500*1.14^8 + 500*1.14^7 + 500*1.14^6 + 500*1.14^5 + 500*1.14^4 + 500*1.14^3 + 500*1.14^2 + 500*1.14 =500 * 1.14 * (1.14^8 – 1) / 0.14 =500 * 15.085347 = $7,542.67 Annuity 2: Annual Payments= 250 Number of Payments= 4 Interest Rate= 7% FV= 250*1.07^4 + 250*1^3 + 250*1.07^2 + 250*1.07 =250 * 1.07 * (1.07^4 – 1) / 0.07 =250 * 4.750739 = $1,187.68 Annuity 3: Annual Payments= 700 Number of Payments= 4 Interest Rate= 0 FV= 700 + 700 + 700 + 700 =700 *4 = $2,800 5-15 PRESENT VALUE OF ANNUITY a) Annual Payments = 600 Number of Payments= 12

TEXTBOOK PROBLEMS 5 Interest Rate= 8 FV= 600*1.08^12 + 600*1.08^11 + 600*1.08^10 + 600*1.08^9 + 600*1.08^8 + 600*1.08^7 + ……600*1.08 = 600*12 = $4,521.65 b) Annual Payments 300 Number of Payments 6 Interest Rate= 4% FV= 300*1.04^6 + 300*1.04^5 + 300*1.04^4 + 300*1.04^3 + 300*1.04^2 + 300*1.04 = 300 * 6 = $1,572.64 c) Annual Payments= 500 Number of Payments= 6 Interest Rate= 0% FV= 500 + 500 + 500 + 500 + 500 = 500 = 500*6 = $3,000 d) Annuity 1: a) Annual Payments: 600 Number of Payments= 12 Interest Rate= 8 PV= PMT + PMT*((1-1+i)^-(N-1)/i)

TEXTBOOK PROBLEMS 6 = 600 * 7.5361*1.08 = $4,883.39 Annuity 2: b) Annual Payments= 300 Number of Payments= 6 Interest Rate= 4% PV= PMT+PMT *((1-(1 + i)^-(n-1)/i) =300*5.2421*1.06 =$1,666.98 Annuity 3: c) Annual Payments= 500 Number of Payments= 6 Interest Rate= 0% PV= PMT*N*(1+i) = 500*6*1 = $3,000 5-16 PRESENT VALUE OF A PERPETUITY PVP= D/i = $600/5% = $12,000 PVP= D/i = $600/10% = $6,000

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TEXTBOOK PROBLEMS 7 5-18 UNEVEN CASH FLOW STREAM a) Stream A PV= (0/1+0.05)^0 + (150/1+0.05)^1 + (450/1+0.05)^2 + (450/1+0.05)^3 + (450/1+0.05)^4 + (250/1+0.05)^5 = 0 + 157.50 + 472.50 + 472.50 + 472.50 + 262.50 = $1,837.50 Stream B PV= (0/1+0.05) ^0 + (250/1+0.05)^1 + (450/1+0.05)^2 + (450/1+0.05)^3 + (450/1+0.05)^4 + (150/1+0.05)^5 = 0 + 262.50 + 472.50 + 472.50 + 472.50 + 157.50 = $1,837.50 b) Stream A PV= (0/1+1^0 + (150/1+0)^1 + (450/1+0)^2 + (450/1+0)^3 + (450/1+0)^4 + (250/1+0)^5 = 0 + 150 + 450 + 450 + 450 + 250 = $1,750 Stream B PV= (0/1+0)^0 + (250/1+0)^1 + (450/1+0)^2 + (450/1+0)^3 + (450/1+0)^4 + (150/1+0)^5 = 0 + 250 + 450 + 450 + 450 + 150 = $1,750 5-23 FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS FV= P*(1+i) ^ t a) 12% compounded annually for 5 years N= 5, I = 12, PV= -500 FV= $881.17 b) 12% compounded semiannually for 5 years.

TEXTBOOK PROBLEMS 8 N=5, I= 6, PV= -500 FV= $895.42 c) 12% compounded quarterly for 5 years N= 20, I= 3, PV= -500 FV= $903.06 d) 12% compounded monthly for 5 years. N=60, I= 3, PV= -500 FV= $908.35 e) 12% compounded daily for 5 years N= 1825, I= 0.032877, PV= -500 FV= $910.07 f) The frequency of interest is increasing as compounding interest durations lengthen. 5-24 PRESENT VALUE FOR VARIOUS DISCOUNTING PERIODS PV= FV/(1 + r) ^ n a) 12% nominal rate, semiannual compounding, discounted back 5 years N= 10, I= 6, FV= 500 PV= $279.20 b) 12% nominal rate, quarterly compounding, discounted back 5 years N= 20, I= 3, FV= 500 PV= $443.72 c) 12% nominal rate, monthly compounding, discounted back 1 year N= 12, I= 1, FV= 500

TEXTBOOK PROBLEMS 9 PV= $443.72 d) The frequency of compounding with discounting causes a decrease over time. 5-25 FUTURE VALUE OF AN ANNUITY FV= P * ((1 + i) ^ n-1)/i a) FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually PMT= 400, I= 6, N= 10 FV= $5,272.32 b) FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly PMT= 400, I=3, N=20 FV= $5,374.07 c) Part B grew in size as the annuity matured. Because it happens every three months, there is greater compounding. 5-27 EFFECTIVE VERSUS NOMINAL INTEREST RATES a) Bank A EAR/EFF = (1+i/n) ^n-1 = (1+0.02/1) ^1-1 =1% Bank B EAR/EFF = (1+i/n) ^n-1 = (1+0.0175/365) ^365-1 = 1.0176% Bank B would be the best choice because its EAR/EFF is higher than Bank A.

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TEXTBOOK PROBLEMS 10 b) Because of the frequency with which interest compounds, there is a distinction between annual and daily compounding interest. The bank would be picked based on the frequency of compounding interest over the course of a year. 11-17 CAPITAL BUDGETING CRITERIA A) What is each project’s NPV? NPV A= $762.49 B= $356.23 B) What is project’s IRR? IRR A= 18.0967% B= 23.9727% C) What is each project’s MIRR? MIRR A= 15.10% B= 17.03% D) Project A would be selected because all the values are higher than project B. If the WACC increased to 18%, project B would be selected.

TEXTBOOK PROBLEMS 11 E) F) The crossover rate would be 14% G) A= 28.1349% B= 30.1439% 11-23 CAPITAL BUDGETING CRITERIA A) Project A NPV= 7.7399% IRR= 19.1940 MIRR= 16.50% Project B NPV= 6.5549% IRR= 22.5156% MIRR= 15.57% B) I believe that both projects should be chosen because the NPV is more than zero. C) I believe that Project A should be chosen because of its higher NPV.

TEXTBOOK PROBLEMS 12 D) E) If the WACC was 15%, I would choose Project B because its NPV would then be higher than Project A. F) Where the NPV for both projects cross each other is the cross rate. G) Yes. Because both projects are evaluated in the same way, there may be a conflict between them.

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