PowerPoint Presentations for Finance for Non-Financial Managers: Seventh Edition

Copyright © 2014 Nelson Education Ltd. 10–1

PowerPoint Presentations for

Finance for Non-Financial Managers:

Seventh Edition

Prepared by

Pierre BergeronUniversity of Ottawa


CHAPTER 10

Time-Value-of-Money Concept


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


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


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


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


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


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


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


Tools for Solving TMV of Money Problems

• Algebraic Notations

• Interest Tables

• Financial Calculators and Spreadsheets

• Time Lines

LO 2


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


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


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




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


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




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


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


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



Present Value of an Annuity—Table D

N 9% 10% 11% 12% 13% 14% 15% 16%

LO 4


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:


(_________ 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


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: $________


(________ 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


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


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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