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Finance for Non-Financial Managers Fifth Edition

Finance for Non-Financial Managers Fifth Edition. Slides prepared by Pierre G. Bergeron University of Ottawa. Time Value of Money. Chapter Objectives. Differentiate between time value of money versus inflation and risk.

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Finance for Non-Financial Managers Fifth Edition

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  1. Finance for Non-Financial ManagersFifth Edition Slides prepared by Pierre G. Bergeron University of Ottawa

  2. Time Value of Money Chapter Objectives • Differentiate between time value of money versus inflation and risk. 2. Explain financial tools that can be used to solve time-value-of-money problems. 3. Differentiate between future values of single sums and future values of annuities. 4. Make the distinction between present values of single sums and present values of annuities 5. Solve capital investment decisions using time-value-of-money decision-making tools. Chapter Reference Chapter 10: Time Value of Money

  3. $1,000 $1,100 $1,000 $1,100 Why Money Has a Time Value Money has a time value because of the existence of interest A dollar earned today will be worth more tomorrow This is called compounding. A dollar earned tomorrow is worth less today This is called discounting.

  4. IRR 10 years @ 30% IRR 10 years @ 20% Table D (4.1925) $ 1,192.60 Table D (3.0915) $ 1,617.33 An Example – 10 years @ 10% Compounding $5,000 Single sum Table A (2.594) $ 12,970 $813.72 Annuity $ 12,970 0 Table C (15.937) Discounting -$5,000 Single sum Table D (6.1446) +$5,000 0 PV $813.72 Annuity NPV

  5. + 149,388 - 612 + 57,275 57.275 12% 7.4694 170,272 8.5136 IRR is 11.9% 20,272 Compounding versus Discounting Insurance companies Years 1 20 Yearly premiums (cash inflows) $1,000 Money is worth 10% ($1,000 x___________) $_______ Death benefit (cash outflow) $ - 50,000 Net cash flow of NFV $________ 7,275 _____________companies Years 1 20 A company invests $150,000 (cash outflow) to modernize a plant. As a result, the company saves $20,000 (cash inflows) each year. -$ 150,000 cash outflow present value of the savings if money is worth 10% +$______ $20,000 X __________ +$______ net cash flow or net present value (NPV) Industrial

  6. 1. Time Value of Money and Inflation Inflation is included in the forecast (ex. revenue, costs, etc.). Once the cash flow has been determined, then this amount is discounted. Years Projected income statement Sales revenue (with inflation) Cost of sales (with inflation) Gross profit Administrative expenses (with inflation) Income before taxes Income taxes Net income Add back amortization Cash flow (with inflation) 1 $100 80 20 10 10 5 5 2 $ 7 2 $110 85 25 12 13 6 7 2 $ 9 3 $120 90 30 14 16 8 8 2 $ 10

  7. 1. Time value of Money and Risk Things to consider 1. Time value of money 2. Inflation 3. Risk Types of projects: High risk, medium risk, low risk, compulsory LR/C ____ ____ ____ ____ • Modernization • Expansion • New facility • New equipment/machinery/vehicle • New product • Anti-pollution equipment • Research and development LR MR LR HR ____ ____ ____ C HR/C

  8. $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 Investment Decisions in Capital Budgeting TIME CASH Cash Inflows (receipts) Cash Outflows (disbursements) 6-49 win of $100,000 Two options Option 1 Option 2 $100,000 today $12,000 $12,000 $12,000 $12,000 $12,000 $12,000 $12,000 $12,000 $12,000 $12,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $16,000 $16,000 $16,000 $16,000 $16,000 $16,000 $16,000 $16,000 $16,000 $16,000

  9. 2. Tools For Solving Time-Value-of-Money Problems • Algebraic Notations • Interest Tables • Financial Calculators and Spreadsheets • Time Lines

  10. 3. Effect of Compounding Problem: If you invest $1,000 in the bank bearing a 10% compound interest, what is the future value of the investment at the end of three years? Beginning Interest Amount Beginning Ending Year amount rate of interest amount amount 1 $1,000 .10 $100 $1,000 $1,100 2 $1,100 .10 $110 $1,100 $1,210 3 $1,210 .10 $121 $1,210 $1,331 F = P (1 + i)n F = $1,000 (1.10)3 F = $1,000 X 1.331 F = $1,331 F = Future amount P = Principal or initial amount i = Interest rate n = Number of years

  11. Future Value of a Single Sum – Table A Compounding Discounting Single sum A B Annuity C D N 9% 10% 11% 12% 14% 16% 18% 20% 1.180 1.392 1.643 1.939 2.288 2.700 3.185 3.759 4.435 5.234 6.176 7.288 8.599 10.147 11.974 14.129 16.672 19.673 23.214 27.393 32.324 38.142 45.008 53.109 62.669 1.200 1.440 1.728 2.074 2.488 2.986 3.583 4.300 5.160 6.192 7.430 8.916 10.699 12.839 15.407 18.488 22.186 26.623 31.948 38.338 46.005 55.206 66.247 79.497 95.396 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1.140 1.300 1.482 1.689 1.925 2.195 2.502 2.853 3.252 3.707 4.226 4.818 5.492 6.261 7.138 8.137 9.276 10.575 12.056 13.744 15.668 17.861 20.362 23.212 26.462 1.160 1.346 1.561 1.811 2.100 2.436 2.826 3.278 3.803 4.411 5.117 5.936 6.886 7.988 9.266 10.748 12.468 14.463 16.777 19.461 22.575 26.186 30.376 35.236 40.874 1.120 1.254 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 3.479 3.896 4.363 4.887 5.474 5.130 6.866 7.690 8.613 9.646 10.804 12.100 13.552 15.179 17.000 1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594 2.853 3.138 3.452 3.798 4.177 4.595 5.054 5.560 6.116 6.728 7.400 8.140 8.954 9.850 10.835 1.090 1.188 1.295 1.412 1.539 1.677 1.828 1.993 2.172 2.367 2.580 2.813 3.066 3.342 3.642 3.970 4.328 4.717 5.142 5.604 6.109 6.659 7.258 7.911 8.623 1.110 1.232 1.368 1.518 1.685 1.870 2.076 2.305 2.558 2.839 3.152 3.498 3.883 4.310 4.785 5.311 5.895 6.544 7.263 8.062 8.949 9.934 11.026 12.239 13.586

  12. Future Value of an Annuity An annuity is defined as a series of payments of fixed amount for a specified number of years. Examples of annuities are mortgages, RRSPs, whole-life insurance premiums. Problem: If you were to receive $1,000 at the end of each year, for the next five years, what would be the value of the receipts if the interest rate is compounded annually at 10%? Amount Interest Future Year received factors Interest value 1 $1,000 1.464 $464 $1,464 2 $1,000 1.331 $331 $1,331 3 $1,000 1.210 $210 $1,210 4 $1,000 1.100 $100 $1,100 5 $1,000 1.000 ---- $1,000 $5,000 $1,105 $6,105 W = R (1 + i)n - 1 i W = $1,000 X 6.105 F = $6,105 W = Value of annuity R = Sum of receipts i = Interest rate n = Number of years

  13. Future Value of an Annuity – Table C Compounding Discounting Single sum A B Annuity C D N 9% 10% 11% 12% 14% 16% 18% 20% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1.000 2.090 3.278 4.573 5.985 7.523 9.200 11.029 13.021 15.193 17.560 20.141 22.953 26.019 29.361 33.003 36.974 41.301 46.019 51.160 56.765 62.873 69.532 76.790 84.701 1.000 2.100 3.310 4.641 6.105 7.716 9.487 11.436 13.580 15.937 18.531 21.384 24.523 27.975 31.773 35.950 40.545 45.599 51.159 57.275 64.003 71.403 79.543 88.497 98.347 1.000 2.110 3.342 4.710 6.228 7.913 9.783 11.859 14.164 16.722 19.561 22.713 26.212 30.095 34.405 39.190 44.501 50.396 56.940 64.203 72.265 81.214 91.148 102.174 114.413 1.000 2.120 3.374 4.779 6.353 8.115 10.089 12.300 14.776 17.549 20.655 24.133 28.029 32.393 37.280 42.753 48.884 55.750 63.440 72.052 81.699 92.503 104.603 118.155 133.334 1.000 2.140 3.440 4.921 6.610 8.536 10.731 13.233 16.085 19.337 23.045 27.271 32.089 37.581 43.842 50.980 59.118 68.394 78.969 91.025 104.768 120.436 138.297 158.659 181.871 1.000 2.160 3.506 5.066 6.877 8.977 11.414 14.240 17.519 21.322 25.733 30.850 36.786 43.672 51.660 60.925 71.673 84.141 98.603 115.380 134.840 157.415 183.601 213.977 249.214 1.000 2.180 3.572 5.215 7.154 9.442 12.142 15.327 19.086 23.521 28.755 34.931 42.219 50.818 60.965 72.939 87.068 103.740 123.413 146.628 174.021 206.345 244.487 289.494 342.603 1.000 2.200 3.640 5.368 7.442 9.930 12.916 16.499 20.799 25.959 32.150 39.581 48.497 59.196 72.035 87.442 105.931 128.117 154.740 186.688 225.026 271.031 326.237 392.404 471.981

  14. 4. Effect of Discounting Problem: If you were to receive $1,000 in three years from now, what would be the present value of that amount if you were to discount it at 10%? Beginning Discount Present Year amount rate value 3 $1,000 0.75131 $751.31 P = F 1 (1 + i)n P = $1,000 1 (1 + .10)3 F = $1,000 1 1.331 P = $1,000 x .75131 P = $751.31 P = Present value F = Sum to be received i = Interest rate n = Number of years

  15. Present Value of a Single Sum – Table B Compounding Discounting Single sum A B Annuity C D N 9% 10% 11% 12% 13% 14% 15% 16% 0.90090 .81162 .73119 .65873 .59345 .53464 .48166 .43393 .39092 .35218 .31728 .28584 .25751 .23199 .20900 .18829 .16963 .15202 .13768 .12403 .11174 .10067 .09069 .08170 .07361 0.89286 .79719 .71178 .63552 .56743 .50663 .45235 .40388 .36061 .32197 .28748 .25667 .22917 .20462 .18270 .16312 .14564 .13004 .11611 .10367 .09256 .08264 .07379 .06588 .05882 0.88496 .78315 .69305 .61332 .54276 .48032 .42506 .37616 .33288 .29459 .26070 .23071 .20416 .18068 .15989 .14150 .12522 .11081 .09806 .08678 .07680 .06796 .06014 .05322 .O4710 0.87719 .76947 .67497 .59208 .51937 .45559 .39964 .35056 .30751 .26974 .23662 .20756 .18207 .15971 .14010 .12289 .10780 .09456 .08295 .07276 .06383 .05599 .04911 .04308 .03779 0.86957 .75614 .65752 .57175 .49718 .43233 .37594 .32690 .28426 .24718 .21494 .18691 .16253 .14133 .12289 .10686 .09293 .08080 .07026 .06110 .05313 .04620 .04017 .03493 .03038 0.86207 .74316 .64066 .55229 .47611 .41044 .35383 .30503 .26295 .22668 .19542 .16846 .14523 .12520 .10793 .09304 .08021 .06914 .05961 .05139 .04430 .03819 .03292 .02838 .02447 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.91743 .84168 .77218 .70843 .64993 .59627 .54703 .50187 .46043 .42241 .38753 .35553 .32618 .29925 .27454 .25187 .23107 .21199 .19449 .17843 .16370 .15018 .13778 .12640 .11597 0.90909 .82645 .75131 .68301 .62092 .56447 .51316 .46651 .42410 .38554 .35049 .31863 .28966 .26333 .23939 .21763 .19784 .17986 .16351 .14864 .13513 .12285 .11168 .10153 .09230

  16. Present Value of an Annuity Problem: Suppose your company deposits $1,000 in your bank account at the end of each year during the next five years; what is the present value of that gift if the interest rate is 10%? Beginning Interest Present Year amount factors value 1 $1,000 0.9091 $909 2 $1,000 0.8264 $826 3 $1,000 0.7513 $751 4 $1,000 0.6830 $683 5 $1,000 0.6209 $621 $5,000 $3,790 B = R 1- (1 + i)-n i W = $1,000 X 3.7908 F = $3,790.80 B = Present value of annuity R = Fixed annuity i = Interest rate n = Number of years

  17. Present Value of an Annuity – Table D Compounding Discounting Single sum A B Annuity C D N 9% 10% 11% 12% 13% 14% 15% 16% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.9174 1.7591 2.5313 3.2397 3.8896 4.4859 5.0329 5.5348 5.9852 6.4176 6.8052 7.1607 7.4869 7.7861 8.0607 8.3125 8.5436 8.7556 8.9501 9.1285 9.2922 9.4424 9.5802 9.7066 9.8226 0.9091 1.7355 2.4868 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0215 8.2014 8.3649 8.5136 8.6487 8.7715 8.8832 8.9847 9.0770 0.9009 1.7125 2.4437 3.1024 3.6959 4.2305 4.7122 5.1461 5.5370 5.8892 6.2065 6.4924 6.7499 6.9819 7.1909 7.3792 7.5488 7.7016 7.8393 7.9633 8.0751 8.1757 8.2664 8.3481 8.4217 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.5620 7.6446 7.7184 7.7843 7.8431 0.8850 1.6681 2.3612 2.9745 3.5172 3.9976 4.4226 4.7988 5.1317 5.4262 5.6869 5.9176 6.1218 6.3025 6.4624 6.6039 6.7291 6.8399 6.9380 7.0248 7.1016 7.1695 7.2297 7.2829 7.3300 0.8772 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161 5.4527 5.6603 5.8424 6.0021 6.1422 6.2651 6.3729 6.4674 6.5504 6.6231 6.6870 6.7429 6.7921 6.8351 6.8729 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.3125 6.3587 6.3988 6.4338 6.4641 0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 4.6065 4.8332 5.0286 5.1971 5.3423 5.4675 5.5755 5.6685 5.7487 5.8178 5.8775 5.9288 5.9731 6.0113 6.0442 6.0726 6.0971

  18. 2,754 9.0770 1,000 9.0770 9,077 +$______ 15,923 $______ 5. Using Interest Tables in Capital Budgeting • You invest $25,000 in an asset. • It generates $1,000 in savings each year. • The expected life of the asset is 25 years. • Your cost of capital is 10%. How much must you save each year if you want to make 10% on your asset? • Investment • Annual savings: $1,000 • Total savings: $25,000 • Present value of savings • (_________ X $_______) • Net present value -$ 25,000 -$ 25,000 • Investment • Annual savings: • Total savings: • Present value of savings • (_________ X $_______) • Net present value 2,754 +$_______ 68,850 +$_______ +$______ 25,000 0 -$______ When the discount rate makes the inflows (savings) equal to the outflow (investment), it is called the_________. In this case, the IRR is ______ . IRR 10%.

  19. 6.0971 4,100 An Example of a Capital Project But, if you want to make 16% on the $25,000 asset, how much must your asset generate in savings or cash each year? • Investment • Annual savings:$ _______ • Total savings: $________ • Present value of savings • (________ x $________ ) • Net present value Here, the discount rate that makes your savings equal to your investment is__________ . Therefore this is your_______. - $ 25,000 4,100 16 % 102,500 IRR 25,000 0 +$________ +$________ • The hurdle rate is . . . • The cost of capital _____ • Adjusted for the project’s risk _____ • Hurdle rate _____ 10 % 6 % 16 %

  20. The Balance Sheet Assets $25,000 Loan $25,000 Savings $ ________ Payments $ _________ Gives _________% Costs __________% Per year Per year 2,754 4,100 16 10 The company earns ______% or $ _____ each year after paying the loan. 6 1,346

  21. These two tables are used in capital budgeting How to Use the Interest Tables

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