©2006 Dr. Howard Godfrey – Extra File for Chapter 11

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Chapter 11- BExtra PowerPoint Slides

This file contains explanations of compound interest computations and a selection of short capital budgeting problems.

Your Investment $6,000 You invest $6,000.

Useful Life 4 years

Annual cash inflow $2,000 You receive $8,000.

Is that a good deal?

Capital Budgeting Example - 1

Cash flow = Revenue less Cash Expenses

©2006 Dr. Howard Godfrey – Extra File for Chapter 11

Analysis PV of $1 Present Year Year Year

10% Value 0 1 2

Discount 0.909091 1,818.18 $2,000

cash flows 0.826446 1,652.89 $2,000

Capital Budgeting Example -2

Analysis PV of $1 Present Year Year Year Year Year10% Value 0 1 2 3 4

Discount 0.9090909 1,818.18 $2,000

cash flows 0.8264463 1,652.89 $2,000 0.7513148 1,502.63 $2,000 0.6830135 1,366.03 $2,000

P.V of inflows 6,339.73Initial outlay 1.000000 -6,000.00 -6,000Net P.V. $339.73

Capital Budgeting Example -3

©2006 Dr. Howard Godfrey – Extra File for Chapter 11

Analysis PV of $1 Present Year Year Year Year Year10% Value 0 1 2 3 4

Annuity tableAnnual Savings 3.1698654 6,339.73 $2,000 $2,000 $2,000 $2,000 Initial O utlay -6,000.00 -6,000Net Present Value

$339.73

Capital Budgeting Example -3

©2006 Dr. Howard Godfrey – Extra File for Chapter 11

Analysis PV of $1 Present Year Year Year Year Year10% Value 0 1 2 3 4

Discount 0.9090909 1,818.18 $2,000

cash flows 0.8264463 1,652.89 $2,000 0.7513148 1,502.63 $2,000 0.6830135 1,366.03 $2,000

Present value of inflows

6,339.73Initial outlay 1.000000 -6,000.00 -6,000Net P.V. $339.73

Annuity tableAnnual Savings 3.1698654 6,339.73 $2,000 $2,000 $2,000 $2,000 Initial O utlay -6,000.00 -6,000Net Present Value

$339.73

Capital Budgeting Example -3

Interest- Annual Compounding-1We use 10% interest to make computations simpleOn the first day of 2001, we invest 100.00$

Interest earned in one year-10% 10.00$ Account Balance at the end of 2001 110.00$

Interest earned in one year-10% 11.00$ Account Balance at the end of 2002 121.00$

Interest earned in one year-10% 12.10$ Account Balance at the end of 2003 133.10$

We have invested $100 for 3 years.First year suggests annual earnings will be: $10Compounding of interest increases that amount$100.00 is the Present Value of $133.10$133.10 is the Future Value of $100.00

Interest- Semiannual Compounding-2We earn 10% interest, compounded semiannually.On the first day of 2001, we invest 100.00$

Interest earned in six months (5%) 5.00$ 105.00$

Interest earned in six months (5%) 5.25$ Balance at end of 2001 110.25$

Interest earned in six months (5%) 5.51$ 115.76$

Interest earned in six months (5%) 5.79$ Balance at end of 2002 121.55$

Interest earned in six months (5%) 6.08$ 127.63$

Interest earned in six months (5%) 6.38$ Balance at end of 2003 134.01$

Interest- Semiannual Compounding-3Compare the balances on the

previous slides on:December 31, 2001December 31, 2002December 31, 2003Why are they different?

Review of Interest Computations-4

Compute the Future Value of an InvestmentInvest $40,000 & earn 10%. Balance Balance Balance BalanceWhat is balance in 3 yrs? Start of Start of Start of End of

Yr. 1 Yr. 2 Yr. 3 Yr. 3Investment (Jan 1, Yr1) 40,000$

110%Balance-End of yr 1. (Start of yr. 2.)

110%Balance-End of yr 2. (Start of yr. 3.)

110%Future value of payment -3 periods-10% interest

Review of Interest Computations-4-ACompute the Future Value of an InvestmentInvest $40,000 & earn 10%. Balance Balance Balance BalanceWhat is balance in 3 yrs? Start of Start of Start of End of

Yr. 1 Yr. 2 Yr. 3 Yr. 3Investment (Jan 1, Yr1) 40,000$

110%

Balance-End of yr 1. (Start of yr. 2.) 44,000$ 110%

Balance-End of yr 2. (Start of yr. 3.) 48,400$ 110%

Future value of payment -3 periods-10% interest 53,240$

Review of Interest Computations-5What is Future Value factor for 10%, 3 periods?Accumulated amount after 3 years 53,240$ Divide by Current investment 40,000$ Factor ($1.00 grows to $1.331) 1.331 (Find in compound interest tables.)Use Excel to compute factor ExcelWhat is value of 1.1 to third power? =1.1^3Answer 1.331

Review of Interest Computations-6

Use future value factor to compute present value.We need to accumulate $60,000 in 3 years at 10%.How much do we need to invest today?Amount needed in 3 years 60,000$ Divide by Factor for future value -3 yrs at 10% 1.331 Required investment today 45,078.89 Compare PV factor for 3 yrs at 10% with factor: $1.331

Review of Interest Computations-7Compute Present Value of a Future PaymentWe need $60,000 3 years from today. We will earn 10% interest

1/1/01 1/1/02 1/1/03 12/31/03

Future Value 60,000$ Divide by 110% to discount for one year 1.10 Present value at start of year 3 54,545$ Divide by 110% to discount for one year 1.10 Present value at start of year 2 49,587$ Divide by 110% to discount for one yr 1.10 Present value at start of year 1 45,078.89$

Review of Interest Computations-8

Compute PV using factor from tableAmount needed in savings account in 3 years 60,000$ Present value factor from Interest Table 0.751 Answer using factor from PV table 45,060.00$ (Note some rounding error)Use Excel to compute factor ExcelValue of 1 divided by 1.1 to the 3rd power? =1/1.1^3

0.7513148

Review of Interest Computations-9Compute Future Value of an AnnuityDeposit $10,000 each year. Earn interest of 10% per year.Deposit made at end of period 12/31/01 2002 2003Deposit (12-31-01) 10,000$ Interest in 2001 - NoneBalance-1/1/02 - Also at 12-31-01 10,000$ 10,000$ Interest in 2002 at 10% 1,000$ Subtotal 11,000$ Deposit at 12-31-02 10,000$ Balance-1/1/03 - Also at 12-31-02 21,000$ 21,000$ Interest 2003 at 10% 2,100$ Subtotal 23,100$ Deposit on 12-31-03 10,000$ Balance on 12-31-03 33,100$

Review of Interest Computations-10

Factor for F. Val. of Annuity for 3 periods at 10%Future Value 33,100$ Payment 10,000$ Factor (FV / Amount of each payment) 3.31 Factor must be greater than 3,

if the interest rate equals or exceeds zero.Check this in Compound Interest Tables

Review of Interest Computations-11Compute Present Value of an AnnuityWe have land for sale. Buyer “A” offers to pay $60,000 for our land,

payable $20,000 per year for 3 years (payment at end of each year).

Our rate of interest on alternative investments is 10%.

Buyer “B” will make an offer with immediate payment.

How much "immediate payment" is equivalent to the annuity? OR, What is P.V. of the series of payments of $20,000 each?

Review of Interest Computations-12Present Value of Annuity 1/1/2001 12/31/2001 12/31/2002 12/31/2003Payment on 12-31-03 20,000$ Discount for one year 1.10 P.V. at 12-31-02 18,181.82$ Payment on 12-31-02 20,000.00$ Total at 12-31-02 38,181.82$ Discount for one year 1.10 P.V. at 12-31-01 34,710.74$ Payment on 12-31-01 20,000.00$ Total at 12/31/01 54,710.74$ Discount for one year 1.10 P.V. of the annuity at 1-1-02 49,737.04$

Review of Interest Computations-13

Computing P.V. of Annuity using Table or ExcelAnnual payment for 3 years 20,000$ P.V. factor - 10% - See Interest Table 2.487 P. V. based on compound interest table 49,740$ Excel Net Present Value Function NPV=NPV(0.1,20000,20000,20000) $49,737.04Excel Present Value Function (PV)=PV(0.1,3,-20000,,0) $49,737.04

Review of Interest Computations-14In preceding example, we could have been considering a wide variety of ventures, such as the proposed lease of a machine for $20,000 per year for 3 years, after which the machine would belong to us.

We would rather pay $20,000 per year for 3 years than to pay $60,000 today for the asset.At what price would we choose to pay cash, rather than choosing the lease alternative, assuming our cost of capital is 10%?

Interest Problem-CooperCooper plans to invest $2,000 at the end of each of the next ten years. Cooper will earn interest at an annual rate of 6% compounded annually. The future amount of an ordinary annuity of $1 for ten periods at 6% is 13.181. The present value of $1 for ten periods at 6% is 0.558. The present value of an ordinary annuity of $1 for ten periods at 6% is 7.360.

The investment at end of ten years would be:a. $14,720 b. $21,200 c. $26,362 d. $27,478

Interest Problem-Cooper

Cooper - Compound InterestInterest rate 6%Period to invest 10 YearsAmount to invest 2,000 Per yrFV of annuity of $1 at 6% 13.181 10 YrsFuture amount 26,362$

Boone-Interest ComputationsBoone has incurred an investment of $18,492 and will received $4,000 per year for the next six years. Ignoring tax effects, the internal rate of return (rounded to the nearest percent) is: (Use interest tables.)a. 6% b. 8% c. 10% d. 12% e. 16%

Table 2. Present Value of annuity of $1F. V. $1 $1 $1 $1

Period 5% 6% 7% 8%1 0.95238 0.94340 0.93458 0.92593 2 1.85941 1.83339 1.80802 1.78326 3 2.72325 2.67301 2.62432 2.57710 4 3.54595 3.46511 3.38721 3.31213 5 4.32948 4.21236 4.10020 3.99271 6 5.07569 4.91732 4.76654 4.62288

Present Value of $1Table 1. Present Value of $1 to be received after n number of periods.

F. V. $1 $1 $1Period 1% 2% 10%

1 0.99010 0.98039 0.90909 2 0.98030 0.96117 0.82645 3 0.97059 0.94232 0.75131 4 0.96098 0.92385 0.68301 5 0.95147 0.90573 0.62092 6 0.94205 0.88797 0.56447 7 0.93272 0.87056 0.51316 8 0.92348 0.85349 0.46651 9 0.91434 0.83676 0.42410

10 0.90529 0.82035 0.38554

P. V. of Annuity of $1 for n PeriodsTable 2. Present Value of $1 to be received at at the end of each period for n periods.

F. V. $1 $1 $1Period 1% 2% 10%

1 0.99010 0.98039 0.90909 2 1.97040 1.94156 1.73554 3 2.94099 2.88388 2.48685 4 3.90197 3.80773 3.16987 5 4.85343 4.71346 3.79079 6 5.79548 5.60143 4.35526 7 6.72819 6.47199 4.86842 8 7.65168 7.32548 5.33493 9 8.56602 8.16224 5.75902

10 9.47130 8.98259 6.14457

Future Value of $1Table 3. Future Value of $1 (after n periods) to be invested today.

F. V. $1 $1 $1 $1Period 1% 2% 5% 10%

1 1.01000 1.02000 1.05000 1.10000 2 1.02010 1.04040 1.10250 1.21000 3 1.03030 1.06121 1.15763 1.33100 4 1.04060 1.08243 1.21551 1.46410 5 1.05101 1.10408 1.27628 1.61051 6 1.06152 1.12616 1.34010 1.77156 7 1.07214 1.14869 1.40710 1.94872 8 1.08286 1.17166 1.47746 2.14359 9 1.09369 1.19509 1.55133 2.35795

10 1.10462 1.21899 1.62889 2.59374

Future Value of Annuity of $1Table 4. Future Value (after n periods) of $1 to be received or paid at the end of each period for n periods.

F. V. $1 $1 $1 $1Period 1% 2% 5% 10%

1 1.00000 1.00000 1.00000 1.00000 2 2.01000 2.02000 2.05000 2.10000 3 3.03010 3.06040 3.15250 3.31000 4 4.06040 4.12161 4.31013 4.64100 5 5.10101 5.20404 5.52563 6.10510 6 6.15202 6.30812 6.80191 7.71561 7 7.21354 7.43428 8.14201 9.48717 8 8.28567 8.58297 9.54911 11.43589 9 9.36853 9.75463 11.02656 13.57948

10 10.46221 10.94972 12.57789 15.93742

NPV Example• Original investment (cash outflow):

$6,075• Useful life: four years• Annual income generated

from investment (cash inflow): $2,000

• Minimum desired rate of return: 10%

PV PresentYears Amount Factor Value

0 ($6,075) 1 ($6,075)1 2,000 0.9091 1,8182 2,000 0.8264 1,6533 2,000 0.7513 1,5034 2,000 0.683 1,366

$265 Net present value

Net PV Example

NPV ExamplePV Present

Years Amount Factor Value 0 ($6,075) 1 ($6,075)

1-4 2,000 3.17 6,340Net present value $265

NPV QuestionA proposed project has an expected economic

life of eight years. In the calculation of the net present value of the proposed project, salvage value would be

a. Excluded from the calculation of the net present value.

b. Included as a cash inflow at the estimated salvage value.

c. Included as a cash inflow at the future amount of the estimated salvage value.

d. Included as a cash inflow at the present value of the estimated salvage value.