powerpoint presentations for finance for non-financial managers: seventh edition
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Copyright © 2014 Nelson Education Ltd. 10–1
PowerPoint Presentations for
Finance for Non-Financial Managers:
Seventh Edition
Prepared by
Pierre BergeronUniversity of Ottawa
Copyright © 2014 Nelson Education Ltd. 10–2
CHAPTER 10
Time-Value-of-Money Concept
Copyright © 2014 Nelson Education Ltd. 10–3
1. Define time value of money, inflation, and risk.
2. Explain the financial tools used to solve time-value-of-money problems.
3. Differentiate between future values of single sums and future values of annuities.
4. Distinguish between present values of single sums and present values of annuities.
5. Make capital investment decisions by using time-value-of-money tools.
Learning Objectives
Copyright © 2014 Nelson Education Ltd. 10–4
Why Money Has a Time Value
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.
Money has a time value because of the
existence of interest
$1,000 $1,100
$1,000 $1,100
LO 1
Copyright © 2014 Nelson Education Ltd. 10–5
An Example—10 years @ 10%
$5,000
Single sum
Compounding
IRR
$ 12,970Table A (2.594)
Table C (15.937)
Discounting
-$5,000 Single sum
+$5,000
0
Table D (6.1446)PV
NPV
$813.72
Annuity
$813.72
Annuity
$ 12,970
0
10 years @ 20% IRR
Table D (4.1925)
$ 1,192.60
10 years @ 30%
Table D (3.0915)
$ 1,617.33
LO 1
Copyright © 2014 Nelson Education Ltd. 10–6
Compounding versus Discounting
companies
Years 1 20
Yearly premiums (cash inflows) $1,000
Money is worth 10% ($1,000 ×___________) $_______
Death benefit (cash outflow) $ - 50,000
Net cash flow of NFV $________
_____________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%
+$______ $20,000 × __________
+$______ net cash flow or net present value (NPV)
Insurance
57.275 + 57,275
7,275
Industrial
8.5136170,272
20,272
12%
7.4694+ 149,388
- 612IRR is 11.9%
LO 1
Copyright © 2014 Nelson Education Ltd. 10–7
Time Value of Money and Inflation
Years
Projected statement of incomeRevenue (with inflation)
Cost of sales (with inflation)
Gross profitExpenses (with inflation)
Profit before taxes
Income tax expense
Profit for the year
Add back depreciationCash 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
Inflation is included in the forecast (e.g., revenue, costs, etc.). Once the cash flow has been determined, then this amount is discounted.
LO 1
Copyright © 2014 Nelson Education Ltd. 10–8
Factors to consider
1. Time value of money2. Inflation3. Risk
Modernization Expansion New facility New equipment/machinery/vehicle New product Anti-pollution equipment Research and development
Types of projects:High risk, medium risk, low risk, compulsory
________________
____________
LR/C
LR
LR
MR
HR
CHR/C
Time Value of Money and Risk LO 1
Copyright © 2014 Nelson Education Ltd. 10–9
Investment Decisions in Capital Budgeting
TIME
Lotto 649 win of $100,000
Two options
Option 1
Option 2
Cash Outflows (disbursements)
Cash Inflows (receipts)
CASH
$10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000 $10,000
$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
$100,000 today
LO 1
Copyright © 2014 Nelson Education Ltd. 10–10
Tools for Solving TMV of Money Problems
• Algebraic Notations
• Interest Tables
• Financial Calculators and Spreadsheets
• Time Lines
LO 2
Copyright © 2014 Nelson Education Ltd. 10–11
Effect of Compounding
F = Future amount
P = Principal or initial amount
i = Interest rate
n = Number of years
F = P (1 + i)n
F = $1,000 (1.10)3
F = $1,000 X 1.331
F = $1,331
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?
Problem:
Year
1
2
3
Beginning amount
$1,000
$1,100
$1,210
Interest rate
.10
.10
.10
Amount of interest
$100
$110
$121
Beginning amount
$1,000
$1,100
$1,210
Ending amount
$1,100
$1,210
$1,331
LO 3
Copyright © 2014 Nelson Education Ltd. 10–12
Compounding Discounting
Single sum A BAnnuity C D
12345678910111213141516171819202122232425
1.0901.1881.2951.4121.5391.6771.8281.9932.1722.3672.5802.8133.0663.3423.6423.9704.3284.7175.1425.6046.1096.6597.2587.9118.623
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 9.85010.835
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 9.93411.02612.23913.586
1.1201.2541.4051.5741.7621.9742.2112.4762.7733.1063.4793.8964.3634.8875.4745.1306.8667.6908.6139.646
10.80412.10013.55215.17917.000
1.1401.3001.4821.6891.9252.1952.5022.8533.2523.7074.2264.8185.4926.2617.1388.1379.276
10.57512.05613.74415.66817.86120.36223.21226.462
1.1601.3461.5611.8112.1002.4362.8263.2783.8034.4115.1175.9366.8867.9889.266
10.74812.46814.46316.77719.46122.57526.18630.37635.23640.874
1.1801.3921.6431.9392.2882.7003.1853.7594.4355.2346.1767.2888.599
10.14711.97414.12916.67219.67323.21427.39332.32438.14245.00853.10962.669
1.2001.4401.7282.0742.4882.9863.5834.3005.1606.1927.4308.916
10.69912.83915.40718.48822.18626.62331.94838.33846.00555.20666.24779.49795.396
Future Value of a Single Sum—Table A
N 9% 10% 11% 12% 14% 16% 18% 20%
LO 3
Copyright © 2014 Nelson Education Ltd. 10–13
Future Value of an AnnuityAn 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 = Value of annuity
R = Sum of receipts
i = Interest rate
n = Number of years
W = R (1 + i)n - 1
i
W = $1,000 X 6.105
F = $6,105
LO 3
Copyright © 2014 Nelson Education Ltd. 10–14
Compounding Discounting
Single sum A BAnnuity C D
123456789
10111213141516171819202122232425
1.0002.0903.2784.5735.9857.5239.200
11.02913.02115.19317.56020.14122.95326.01929.36133.00336.97441.30146.01951.16056.76562.87369.53276.79084.701
1.0002.1003.3104.6416.1057.7169.487
11.43613.58015.93718.53121.38424.52327.97531.77335.95040.54545.59951.15957.27564.00371.40379.54388.49798.347
1.0002.1103.3424.7106.2287.9139.783
11.85914.16416.72219.56122.71326.21230.09534.40539.19044.50150.39656.94064.20372.26581.21491.148
102.174114.413
1.0002.1203.3744.7796.3538.115
10.08912.30014.77617.54920.65524.13328.02932.39337.28042.75348.88455.75063.44072.05281.69992.503
104.603118.155133.334
1.0002.1403.4404.9216.6108.536
10.73113.23316.08519.33723.04527.27132.08937.58143.84250.98059.11868.39478.96991.025
104.768120.436138.297158.659181.871
1.0002.1603.5065.0666.8778.977
11.41414.24017.51921.32225.73330.85036.78643.67251.66060.92571.67384.14198.603
115.380134.840157.415183.601213.977249.214
1.0002.1803.5725.2157.1549.442
12.14215.32719.08623.52128.75534.93142.21950.81860.96572.93987.068
103.740123.413146.628174.021206.345244.487289.494342.603
1.0002.2003.6405.3687.4429.930
12.91616.49920.79925.95932.15039.58148.49759.19672.03587.442
105.931128.117154.740186.688225.026271.031326.237392.404471.981
Future Value of an Annuity—Table C
N 9% 10% 11% 12% 14% 16% 18% 20%
LO 3
Copyright © 2014 Nelson Education Ltd. 10–15
Effect of Discounting
P = Present value
F = Sum to be received
i = Interest rate
n = Number of years
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
Year
3
Beginning amount
$1,000
Discount rate
0.75131
Present value
$751.3
If you were to receive $1,000 three years from now, what would be the present value of that amount if you were to discount it at 10%?
Problem:
LO 4
Copyright © 2014 Nelson Education Ltd. 10–16
Compounding Discounting
Single sum A BAnnuity C D
12345678910111213141516171819202122232425
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
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 .7971
.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 .04710
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
Present Value of a Single Sum—Table B
N 9% 10% 11% 12% 13% 14% 15% 16%
LO 4
Copyright © 2014 Nelson Education Ltd. 10–17
Present Value of an Annuity
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 = Present value of annuity
R = Fixed annuity
i = Interest rate
n = Number of years
B = R 1- (1 + i)-n
i
W = $1,000 X 3.7908
F = $3,790.80
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%?
Problem:
LO 4
Copyright © 2014 Nelson Education Ltd. 10–18
123456789
10111213141516171819202122232425
0.91741.75912.53133.23973.88964.48595.03295.53485.98526.41766.80527.16077.48697.78618.06078.31258.54368.75568.95019.12859.29229.44249.58029.70669.8226
0.90091.71252.44373.10243.69594.23054.71225.14615.53705.88926.20656.49246.74996.98197.19097.37927.54887.70167.83937.96338.07518.17578.26648.34818.4217
0.89291.69012.40183.03733.60484.11144.56384.96765.32825.65025.93776.19446.42356.62826.81096.97407.11967.24977.36587.46947.56207.64467.71847.78437.8431
0.88501.66812.36122.97453.51723.99764.42264.79885.13175.42625.68695.91766.12186.30256.46246.60396.72916.83996.93807.02487.10167.16957.22977.28297.3300
0.87721.64672.32162.91373.43313.88874.28834.63894.94645.21615.45275.66035.84246.00216.14226.26516.37296.46746.55046.62316.68706.74296.79216.83516.8729
0.86961.62572.28322.85503.35223.78454.16044.48734.77165.01885.23375.42065.58315.72455.84745.95426.04726.12806.19826.25936.31256.35876.39886.43386.4641
0.86211.60522.24592.79823.27433.68474.03864.34364.60654.83325.02865.19715.34235.46755.57555.66855.74875.81785.87755.92885.97316.01136.04426.07266.0971
0.90911.73552.48683.16993.79084.35534.86845.33495.75906.14466.49516.81377.10347.36677.60617.82378.02158.20148.36498.51368.64878.77158.88328.98479.0770
Compounding Discounting
Single sum A BAnnuity C D
Present Value of an Annuity—Table D
N 9% 10% 11% 12% 13% 14% 15% 16%
LO 4
Copyright © 2014 Nelson Education Ltd. 10–19
Using Interest Tables in Capital Budgeting1. You invest $25,000 in an asset.
2. It generates $1,000 in savings each year.
3. The expected life of the asset is 25 years.
4. Your cost of capital is 10%.
How much must you save each year if you want to make 10% on your asset?
1. Investment
2. Annual savings: $1,000
3. Total savings: $25,000
4. Present value of savings
(_________ X $_______)
Net present value
1. Investment
2. Annual savings:
3. Total savings:
4. Present value of savings
(_________ X $_______)
Net present value
When the discount rate makes the inflows (savings) equal to the outflow (investment), it is called the_________.
In this case, the IRR is ______ .
-$ 25,000 -$ 25,000
9.0770 1,000 25,000 0-$______
+$_______
9.0770 2,754
2,754
68,850
15,923 9,077+$______
+$_______
+$______$______
IRR
10%.
LO 5
Copyright © 2014 Nelson Education Ltd. 10–20
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?
1. Investment
2. Annual savings: $ _______
3. Total savings: $________
4. 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_______.
The hurdle rate is . . .
1. The cost of capital _____
2. Adjusted for the project’s risk _____
3. Hurdle rate _____
4,100
102,500
6.0971 4,100
- $ 25,000
+$________
+$________
25,000
0
16 %
10 %
6 %
16 %
IRR
LO 5
Copyright © 2014 Nelson Education Ltd. 10–21
The Statement of Financial Position
Assets $25,000 Loan $25,000
Savings $ ________ Payments $ _________
Gives _________% Costs __________%
Per year Per year
The company earns ______% or $ _____
each year after
paying the loan.
4,100 2,754
16 10
6 1,346
LO 5
Copyright © 2014 Nelson Education Ltd. 10–22
How to Use the Interest Tables
To compound To discount
Single sum Table A Table B
Annuity Table C Table D
These two tables are used in
capital budgeting
LO 5
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