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Part I:
Solve 4 of the following time value of money problems by filling inthe 4 columns to the right of the description.
Be sure to solve 1 problem from each of the following 4 categorieslisted under Problem Types. I have completed the first row as anexample.

Part II:
Discuss how you may use time value of money concepts in yourpersonal life. For example, saving for college tuition orretirement, paying off a car loan or home mortgage. Give specificdetails as to how you would use these formulas for more effectivedecision making. Create 1 description and fill in the table foryour newly created question.

Problem Types:
1 pv = present value of $1
2 fv = future value of $1
3 PVAo = Present Value of an Ordinary Annuity of$1 (payment at end of period)
4 FVAo = Future Value of an Annuity of $1(payment at end of period)

Description Type of Problem Table Formula Answer
1 How much money must your rich unclegive you now to finance four years of college, assuming an annualcost of $48,000 and an interest rate of 6% (applied to theprincipal until disbursed)? Present Value of anordinary Annuity PVAo PV = 48,000(3.465) $166,325.07
2 How much interest would you earn ifyou deposited $300 at 6 percent for 27 months?
3 If you deposit $2,000 in a 5-yearcertificate of deposit at 5.2%, how much will it be worth in fiveyears?
4 How much interest would you pay toborrow $670 for eight months at 12 percent?
5 You wish to borrow $18,000 to buy anew auto-mobile. Rate is 8.6% over five years with monthlypayments. Find the monthly payment.
6 What is the future value of $800 at8 percent after six years?
7 How much would you have in savingsif you kept $200 on deposit for eight years at 8% compoundedsemiannually?
8 You choose to invest $50/month in a401(k) that invests in an international stock mutual fund. Assumingan annual rate of return of 9%, how much will this fund worth ifretiring in forty years?
9 What is the future value of anannual deposit of $230 earning 6 percent for 15years?
10 If you invest $600/Year in a 401(k)that invests in an international stock mutual fund. Assuming anannual rate of return of 9%, how much will this fund worth ifretiring in forty years?
11 What amount would you have in aretirement account if you made annual deposits of $375 for 25 yearsearning 12 percent, compounded annually?
12 What is the present value of $2,200earning 15 percent for eight years?
13 How much money must you set asideat age 20 to accumulate retirement funds of $100,000 at age 65,assuming a rate of interest of 7%?
14 To have $6,000 for a child’seducation in 10 years, what amount should a parent deposit in asavings account that earns 12 percent, compoundedquarterly?
15 If you deposit $2,000 in a 5-yearcertificate of deposit at 5.2% with quarterly compounding, how muchwill it be worth in five years?
16 What is the present value of awithdrawal of $200 at the end of each year for 14 years with aninterest rate of 7 percent?
17 How much would you have to depositnow to be able to withdraw $650 at the end of each year for 20years from an account that earns 11 percent?
18 What would be the annual paymentamount for a $20,000, 10-year loan at 7 percent?

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Bunny Greenfelder
Bunny GreenfelderLv2
28 Sep 2019

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Related questions

1. An increase in the discount rate:

A) will increase the present value of future cash flows.

B) will have no effect on net present value.

C) will reduce the present value of future cash flows.

D) is one method of compensating for reduced risk.

2. Suddeth Corporation has entered into a 6 year lease for a building it will use as a warehouse. The annual payment under the lease will be $2,468. The first payment will be at the end of the current year and all subsequent payments will be made at year-ends. If the discount rate is 5%, the present value of the lease payments is closest to (Ignore income taxes.):

See separate handout to determine the appropriate discount factor(s) using table.

A) $12,528

B) $14,103

C) $14,808

D) $11,050

3. At an interest rate of 14%, approximately how much would you need to invest today if you wanted to have $2,000,000 in 10 years? (Ignore income taxes.)

See separate handout to determine the appropriate discount factor(s) using table.

A) $383,436

B) $540,000

C) $740,741

D) $1,043,200

4. A company wants to have $20,000 at the end of a ten-year period by investing a single sum now. How much needs to be invested in order to have the desired sum in ten years, if the money can be invested at 12%? (Ignore income taxes.)

See separate handout to determine the appropriate discount factor(s) using table.5

A) $3,254.68

B) $3,539.82

C) $6,440

D) $7,720

5. Amster Corporation has not yet decided on the required rate of return to use in its capital budgeting. This lack of information will prevent Amster from calculating a project's:

Payback

Net Present Value

Internal Rate of Return

A)

No

No

No

B)

Yes

Yes

Yes

C)

No

Yes

Yes

D)

No

Yes

No

THIS IS THE handout to determine the appropriate discount factor(s) using table.5

Time Value of Money Factor for the Present Value of a Sum

PV =FV * TVM Factor

Present Value of a Sum = FV * 1/ (1 + i) n

2%

3%

4%

5%

6%

8%

10%

12%

1

0.9804

0.9709

0.9615

0.9524

0.9434

0.9259

0.9091

0.8929

2

0.9612

0.9426

0.9246

0.9070

0.8900

0.8573

0.8264

0.7972

3

0.9423

0.9151

0.8890

0.8638

0.8396

0.7938

0.7513

0.7118

4

0.9238

0.8885

0.8548

0.8227

0.7921

0.7350

0.6830

0.6355

5

0.9057

0.8626

0.8219

0.7835

0.7473

0.6806

0.6209

0.5674

6

0.8880

0.8375

0.7903

0.7462

0.7050

0.6302

0.5645

0.5066

7

0.8706

0.8131

0.7599

0.7107

0.6651

0.5835

0.5132

0.4523

8

0.8535

0.7894

0.7307

0.6768

0.6274

0.5403

0.4665

0.4039

9

0.8368

0.7664

0.7026

0.6446

0.5919

0.5002

0.4241

0.3606

10

0.8203

0.7441

0.6756

0.6139

0.5584

0.4632

0.3855

0.3220

20

0.6730

0.5537

0.4564

0.3769

0.3118

0.2145

0.1486

0.1037

25

0.6095

0.4776

0.3751

0.2953

0.2330

0.1460

0.0923

0.0588

Time Value of Money Factor for the Present Value of an Annuity

PV = Annuity * TVM Factor

Present Value of an Annuity = X*((1-(1/(1+i)^n))/i)

2%

3%

4%

5%

6%

8%

10%

12%

1

0.9804

0.9709

0.9615

0.9524

0.9434

0.9259

0.9091

0.8929

2

1.9416

1.9135

1.8861

1.8594

1.8334

1.7833

1.7355

1.6901

3

2.8839

2.8286

2.7751

2.7232

2.6730

2.5771

2.4869

2.4018

4

3.8077

3.7171

3.6299

3.5460

3.4651

3.3121

3.1699

3.0373

5

4.7135

4.5797

4.4518

4.3295

4.2124

3.9927

3.7908

3.6048

6

5.6014

5.4172

5.2421

5.0757

4.9173

4.6229

4.3553

4.1114

7

6.4720

6.2303

6.0021

5.7864

5.5824

5.2064

4.8684

4.5638

8

7.3255

7.0197

6.7327

6.4632

6.2098

5.7466

5.3349

4.9676

9

8.1622

7.7861

7.4353

7.1078

6.8017

6.2469

5.7590

5.3282

10

8.9826

8.5302

8.1109

7.7217

7.3601

6.7101

6.1446

5.6502

20

16.3514

14.8775

13.5903

12.4622

11.4699

9.8181

8.5136

7.4694

25

19.5235

17.4131

15.6221

14.0939

12.7834

10.6748

9.0770

7.8431

Please provide the value for each component N= , I=, PV=, FV=,etc so I can learn how to do it in the calculator. thank you

Annuity payment for expected Future Value
6. You wish to retire with $5 Million in 38 years. Youestimate you will earn 8% annually on your

investments. How much must you invest each year in order toreach your goal?a) Ordinary (1st payment made at the end of theyear)b) Due (1st payment made today)

7. You would like to withdraw $80,000 per year duringretirement. You expect to live 20 yearsafter you retire at age 65.How much do you need to have saved by the time you retire if youcan

earn 4% on your funds?


Present Value of an Annuity
8. As part of an agreement for investing in a start-upcompany, you will receive $10,000 at the endof each year for thenext 3 years. If the agreed upon interest rate is 15%, what is theamount of

money you are required to invest.

9. Part A) From the sale of your family property, youwill receive $25,000 today and again eachyear for the next 15years. If the discount rate is 7%, compute the present value ofyour future

payments.Part B) Instead of receiving annual payments, you couldreceive $200,000 lump sum. Should youtake the lump sum instead?


Perpetuity
10. You plan to purchase a small service company. Youanticipate receiving annual cash flows of$60,000 per yearindefinitely. (A) If you require an 8% return on your investment,what is themost you should pay for this company? (B) What is theNPV if you can purchase it for $500,000?

Just yesterday I posted a key question as to why the statelottery might hypothetically offer you an upfront lump-sum paymentof $50 million or an ongoing annuity of a $5 million check eachyear for 20 years (totaling $100 million in checks). Remember thatthis was just my simplified hypothetical example. A few peopleattempted the answer to this further above, but here's what'sreally going on...it has to do with Net Present Value (NPV). It'sbecause future-year dollars are worth less, and the further you gointo the future, the less those dollars are worth in terms oftoday's dollars. And that is why, when financial analysts look at adecision involving multi-year cash flows, they will use discountfactors to convert all of the future-year dollars to present value(i.e., this year's dollars) and add them up to yield the NPV of allof the amounts to put a final answer in terms of today's value.Where do these discount factors come from? They're derived from thereciprocal of the famous compound interest formula, but you justneed to go and look at two tables in your textbook in Chapter 12,Appendix 12A, Table A (present value of $1 due in n periods) andTable B (present value of an annuity of $1 per period). Class, Icannot stress to you enough how widely-used this concept is, andthe importance of understanding how these discount factors areapplied to solve for net present value (NPV) and a related metric,internal rate of return (IRR). You will likely need to read, andreread, Chapter 12 and closely walk through some textbook exampleswhere each year's cash flows are multiplied by the appropriatediscount factor to convert all of that money into this year'sdollars (present value). We are surrounded by this financialanalysis methodology when faced with a decision on a lotterypayout, a retirement payout (lump sum versus annuity), and many ofour states and cities right now are dealing with issues relating tothe calculation of NPV in assessing whether they currently haveenough money in the appropriate accounts to meet the futureretirement payment obligations they've made to their publicemployees. This is an economic issue that has been on the brink ofexploding for a long time (don't take my word for it, it's beendiscussed in multiple articles in the NY Times, Wall StreetJournal, The Economist), but I'm not going to add all of that intothis discussion here. Let's learn to walk before we try to run.Would you like to see how the lottery payouts I described would bemultiplied by each year's financial discount factor? Just take alook at my attached Excel workbook, and note that there are threetabs: the first assumed a 0% cost of capital (no financialdiscounting done), the second assumed a 5% cost of capital, and thethird sheet inserted a 10% cost of capital. You'll see how thesedifferent interest rates changed the discount factor multipliersand ultimately changed the NPV of each alternative (the value ofthe lump sum or the annuity, all shown in present value). Also,this example just shows money moving one way (i.e., to the state,it's cash out of their pocket...to the lottery winner, it's cashinto their pocket). In many NPV and IRR examples, money will moveboth ways over multiple years...cash flows that are expenses orinvestments are outflows and are shown as negative, while revenuesor other incoming money are inflows and are shown as positive.Please look closely at my attached Excel workbook (all three tabs)and also walk through all of the examples in the chapter showinghow to do NPV and IRR problems. There are also examples in the textof simpler metrics including payback period and accounting rate ofreturn. It's typically very hard stuff for students to master. Now,for those of you who've looked at the chapter examples, maybeyou've figured this out already:

1. What is the key difference between Tables A and B in Chapter12, Appendix 12A, and how and when are each of them used in ananalysis?

2. What do we mean by “Year 0” in a financial analysis? Whatvalue do we use for the discount factor or multiplier for the cashflow in Year 0 of a financial analysis?

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