Finance for NonFinancial Managers Fifth Edition

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
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
An Example 10 years _at_ 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
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
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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
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
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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
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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 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 9.27
6 10.575 12.056 13.744 15.668 17.861 20.362 23.212
26.462
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 1
6.672 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 7
9.497 95.396
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 4.32
8 4.717 5.142 5.604 6.109 6.659 7.258 7.911 8.623
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
1.110 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
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 6.8
66 7.690 8.613 9.646 10.804 12.100 13.552 15.179 1
7.000
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 35.2
36 40.874
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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 1
3.021 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 1
3.580 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 1
4.164 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 4
2.753 48.884 55.750 63.440 72.052 81.699 92.503 10
4.603 118.155 133.334
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 5
0.980 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 6
0.925 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 7
2.939 87.068 103.740 123.413 146.628 174.021 206.3
45 244.487 289.494 342.603
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 8
7.442 105.931 128.117 154.740 186.688 225.026 271.
031 326.237 392.404 471.981
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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
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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 .1
5018 .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
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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 9.4
424 9.5802 9.7066 9.8226
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 8.1
757 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 7.6
446 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 7.1
695 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 6.7
429 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 6.3
587 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 6.0
113 6.0442 6.0726 6.0971
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 8.7
715 8.8832 8.9847 9.0770
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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

• Investment
• Annual savings
• Total savings
• Present value of savings
• (_________ X _______)
• Net present value

- 25,000
- 25,000
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.
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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 projects 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
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How to Use the Interest Tables