CLA 1 Paper – Financial Management CLA 1 Comprehensive Learning Assessment – CLO 1, CLO 2, CLO 3, CLO 4, CLO 5

CLA 1 Paper – Financial Management CLA 1 Comprehensive Learning Assessment – CLO 1, CLO 2, CLO 3, CLO 4, CLO 5

Please note this CLA 1 assignment consists of two separate parts. The first part gives the cash flows for two mutually exclusive projects and is not related to the second part. The second part is a capital budgeting scenario.

Part 1

Please calculate the payback period, IRR, MIRR, NPV, and PI for the following two mutually exclusive projects. The required rate of return is 15% and the target payback is 4 years. Explain which project is preferable under each of the four capital budgeting methods mentioned above:

Table 1

Cash flows for two mutually exclusive projects

(Please find Table 1 in the attachment)

Part 2

Please study the following capital budgeting project and then provide explanations for the questions outlined below:

You have been hired as a consultant for Pristine Urban-Tech Zither, Inc. (PUTZ), manufacturers of fine zithers. The market for zithers is growing quickly. The company bought some land three years ago for $2.1 million in anticipation of using it as a toxic waste dump site but has recently hired another company to handle all toxic materials. Based on a recent appraisal, the company believes it could sell the land for $2.3 million on an after-tax basis. In four years, the land could be sold for $2.4 million after taxes. The company also hired a marketing firm to analyze the zither market, at a cost of $125,000. An excerpt of the marketing report is as follows:

The zither industry will have a rapid expansion in the next four years. With the brand name recognition that PUTZ brings to bear, we feel that the company will be able to sell 3,600, 4,300, 5,200, and 3,900 units each year for the next four years, respectively. Again, capitalizing on the name recognition of PUTZ, we feel that a premium price of $750 can be charged for each zither. Because zithers appear to be a fad, we feel at the end of the four-year period, sales should be discontinued. PUTZ believes that fixed costs for the project will be $415,000 per year, and variable costs are 15 percent of sales. The equipment necessary for production will cost $3.5 million and will be depreciated according to a three-year MACRS schedule. At the end of the project, the equipment can be scrapped for $350,000. Net working capital of $125,000 will be required immediately. PUTZ has a 38% tax rate, and the required rate of return on the project is 13%.

Now please provide detailed explanation for the following:

Explain how you determine the initial cash flows
Discuss the notion of sunk costs and identify the sunk cost in this project
Verify how you determine the annual operating cash flows
Explain how you determine the terminal cash flows at the end of the project’s life
Calculate the NPV and IRR of the project and decide if the project is acceptable
If the company that is implementing this project is a publicly traded company, explain and justify how this project will impact the market price of the company’s stock

Provide your explanations and definitions in detail and be precise. Comment on your findings. Provide references for content when necessary. Provide your work in detail and explain in your own words. Support your statements with peer-reviewed in-text citation(s) and reference(s). All PA and CLA submissions require at least six (6) peer-reviewed references which should include the source of the data.

Note:

1. Paper needs to be formatted in APA 7th edition

2. Provide your explanations and definitions in detail and be precise.

3. Provide work in detail and explain in your words.

4. Provide references for content when necessary. Support your statement with peer-reviewed in-text citations and references.

5. Need to have at least 6 peer-reviewed articles as the references (Recommend to find the articles from ProQuest), which should include the source of the data. Data and table also needs to have in-text citations.

6. Need to include textbooks as references.

7. Please find the textbook and class PPTs in the attachment section.

8. Comment on your finding.

7. Textbook Information:

Bowerman, B., Drougas, A. M., Duckworth, A. G., Hummel, R. M. Moniger, K. B., & Schur, P. J. (2019). Business statistics and analytics in practice (9th ed.). McGraw-Hill

ISBN 9781260187496

8. Please find the Course Learning Outcome list of this course in the attachment CHAPTER 6
DISCOUNTED CASH FLOW VALUATION (CALCULATOR)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.1
This version relies primarily on the financial calculator with a brief presentation of formulas. The calculator discussed is the TI-BA-II+. The slides are easy to modify for whatever calculator you prefer.

Determine the future and present value of investments with multiple cash flows

Explain how loan payments are calculated and how to find the interest rate on a loan

Describe how loans are amortized or paid off

Show how interest rates are quoted (and misquoted)
Key Concepts and Skills
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Future and Present Values of Multiple Cash Flows

Valuing Level Cash Flows: Annuities and Perpetuities

Comparing Rates: The Effect of Compounding

Loan Types and Loan Amortization
Chapter Outline
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest.
You currently have $7,000 in the account.
How much will you have in three years?
How much will you have in four years?
Multiple Cash Flows – FV (Example 6.1)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.1 (A)
5.4

Find the value at year 3 of each cash flow and add them together.
Today’s (year 0) CF: 3 N; 8 I/Y; -7,000 PV; CPT FV = 8817.98
Year 1 CF: 2 N; 8 I/Y; -4,000 PV; CPT FV = 4,665.60
Year 2 CF: 1 N; 8 I/Y; -4,000 PV; CPT FV = 4,320
Year 3 CF: value = 4,000
Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.58

Value at year 4: 1 N; 8 I/Y; -21,803.58 PV; CPT FV = 23,547.87
Multiple Cash Flows – FV (Example 6.1, CTD.)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.5
Section 6.1 (A)

The students can read the example in the book. It is also provided here.

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in three years? In four years?

Point out that there are several ways that this can be worked. The book works this example by rolling the value forward each year. The presentation will show the second way to work the problem, finding the future value at the end for each cash flow and then adding. Point out that you can find the value of a set of cash flows at any point in time, all you have to do is get the value of each cash flow at that point in time and then add them together.

I entered the PV as negative for two reasons. (1) It is a cash outflow since it is an investment. (2) The FV is computed as positive, and the students can then just store each calculation and then add from the memory registers, instead of writing down all of the numbers and taking the risk of keying something back into the calculator incorrectly.

Formula:
Today (year 0): FV = 7000(1.08)3 = 8,817.98
Year 1: FV = 4,000(1.08)2 = 4,665.60
Year 2: FV = 4,000(1.08) = 4,320
Year 3: value = 4,000
Total value in 3 years = 8817.98 + 4665.60 + 4320 + 4000 = 21,803.58
Value at year 4 = 21,803.58(1.08) = 23,547.87

Suppose you invest $500 in a mutual fund today and $600 in one year.
If the fund pays 9% annually, how much will you have in two years?

Year 0 CF: 2 N; -500 PV; 9 I/Y; CPT FV = 594.05

Year 1 CF: 1 N; -600 PV; 9 I/Y; CPT FV = 654.00

Total FV = 594.05 + 654.00 = 1,248.05
Multiple Cash Flows – FV Example 2
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.6
Section 6.1 (A)

Formula: FV = 500(1.09)2 + 600(1.09) = 1,248.05

How much will you have in 5 years if you make no further deposits?

First way:
Year 0 CF: 5 N; -500 PV; 9 I/Y; CPT FV = 769.31
Year 1 CF: 4 N; -600 PV; 9 I/Y; CPT FV = 846.95
Total FV = 769.31 + 846.95 = 1,616.26

Second way – use value at year 2:
3 N; -1,248.05 PV; 9 I/Y; CPT FV = 1,616.26
Multiple Cash Flows – FV Example 2 (ctd.)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.7
Section 6.1 (A)

Formula:
First way: FV = 500(1.09)5 + 600(1.09)4 = 1,616.26
Second way: FV = 1248.05(1.09)3 = 1,616.26

Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years.
How much will be in the account in five years if the interest rate is 8%?

Year 1 CF: 4 N; -100 PV; 8 I/Y; CPT FV = 136.05

Year 3 CF: 2 N; -300 PV; 8 I/Y; CPT FV = 349.92

Total FV = 136.05 + 349.92 = 485.97
Multiple Cash Flows – FV Example 3
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.8
Section 6.1 (A)

Formula:
FV = 100(1.08)4 + 300(1.08)2 = 136.05 + 349.92 = 485.97

Find the PV of each cash flow and add them

Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178.57

Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318.88

Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427.07

Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = -508.41

Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93
Multiple Cash Flows – pv (Example 6.3)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.9
Section 6.1 (B)

The students can read the example in the book.

You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year and $800 at the end of the fourth year. You can earn 12 percent on very similar investments. What is the most you should pay for this one?

Point out that the question could also be phrased as “How much is this investment worth?”

Remember the sign convention. The negative numbers imply that we would have to pay 1,432.93 today to receive the cash flows in the future.

Formula:
Year 1 CF: 200 / (1.12)1 = 178.57
Year 2 CF: 400 / (1.12)2 = 318.88
Year 3 CF: 600 / (1.12)3 = 427.07
Year 4 CF: 800 / (1.12)4 = 508.41

Example 6.3 Timeline

0
1
2
3
4
200
400
600
800

178.57
318.88
427.07
508.41

1,432.93
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.1 (B)

5.10

You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows.

Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas.

Click on the Excel icon for an example.
Multiple Cash Flows Using a Spreadsheet

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.11
Section 6.1 (B)

Click on the tabs at the bottom of the worksheet to move from a future value example to a present value example.

Lecture Tip: The present value of a series of cash flows depends heavily on the choice of discount rate. You can easily illustrate this dependence in the spreadsheet on Slide 6.10 by changing the cell that contains the discount rate. A separate worksheet on the slide provides a graph of the relationship between PV and the discount rate.

You are considering an investment that will pay you $1,000 in one year, $2,000 in two years, and $3,000 in three years.
If you want to earn 10% on your money, how much would you be willing to pay?

N = 1; I/Y = 10; FV = 1,000; CPT PV = -909.09
N = 2; I/Y = 10; FV = 2,000; CPT PV = -1,652.89
N = 3; I/Y = 10; FV = 3,000; CPT PV = -2,253.94
PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.93
Multiple Cash Flows – PV Another Example
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.12
Section 6.1 (B)

Formula:
PV = 1000 / (1.1)1 = 909.09
PV = 2000 / (1.1)2 = 1,652.89
PV = 3000 / (1.1)3 = 2,253.94

PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92

Another way to use the financial calculator for uneven cash flows is to use the cash flow keys.

Press CF and enter the cash flows beginning with year 0.
You have to press the “Enter” key for each cash flow.
Use the down arrow key to move to the next cash flow.
The “F” is the number of times a given cash flow occurs in consecutive periods.
Use the NPV key to compute the present value by entering the interest rate for I, pressing the down arrow, and then computing the answer.
Clear the cash flow worksheet by pressing CF and then 2nd CLR Work.
Multiple Uneven Cash Flows – Using the Calculator
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.13
Section 6.1 (B)

The next example will be worked using the cash flow keys.

Note that with the BA-II Plus, the students can double check the numbers they have entered by pressing the up and down arrows. It is similar to entering the cash flows into spreadsheet cells.

Other calculators also have cash flow keys. You enter the information by putting in the cash flow and then pressing CF. You have to always start with the year 0 cash flow, even if it is zero.

Remind the students that the cash flows have to occur at even intervals, so if you skip a year, you still have to enter a 0 cash flow for that year.

Your broker calls you and tells you that he has this great investment opportunity.
If you invest $100 today, you will receive $40 in one year and $75 in two years.
If you require a 15% return on investments of this risk, should you take the investment?

Use the CF keys to compute the value of the investment.
CF; CF0 = 0; C01 = 40; F01 = 1; C02 = 75; F02 = 1
NPV; I = 15; CPT NPV = 91.49
No – the broker is charging more than you would be willing to pay.

Decisions, Decisions
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.14
Section 6.1 (B)

You can also use this as an introduction to NPV by having the students put –100 in for CF0. When they compute the NPV, they will get –8.51. You can then discuss the NPV rule and point out that a negative NPV means that you do not earn your required return. You should also remind them that the sign convention on the regular TVM keys is NOT the same as getting a negative NPV.

You are offered the opportunity to put some money away for retirement.
You will receive five annual payments of $25,000 each beginning in 40 years.
How much would you be willing to invest today if you desire an interest rate of 12%?

Use cash flow keys:
CF; CF0 = 0; C01 = 0; F01 = 39; C02 = 25,000; F02 = 5; NPV; I = 12; CPT NPV = 1,084.71
Saving For Retirement
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.1 (B)

5.15

Saving For Retirement Timeline

0 1 2 … 39 40 41 42 43 44
0 0 0 … 0 25K 25K 25K 25K 25K
Notice that the year 0 cash flow = 0 (CF0 = 0)
The cash flows in years 1 – 39 are 0 (C01 = 0; F01 = 39)
The cash flows in years 40 – 44 are 25,000 (C02 = 25,000; F02 = 5)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.1 (B)

5.16

Suppose you are looking at the following possible cash flows:
Year 1 CF = $100;
Years 2 and 3 CFs = $200;
Years 4 and 5 CFs = $300.
The required discount rate is 7%.

What is the value of the cash flows at year 5?
What is the value of the cash flows today?
What is the value of the cash flows at year 3?
Quick Quiz – Part I
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.17
Section 6.1

The easiest way to work this problem is to use the uneven cash flow keys and find the present value first and then compute the others based on that.

CF0 = 0; C01 = 100; F01 = 1; C02 = 200; F02 = 2; C03 = 300; F03 = 2; I = 7; CPT NPV = 874.17

Value in year 5: PV = 874.17; N = 5; I/Y = 7; CPT FV = 1,226.07
Value in year 3: PV = 874.17; N = 3; I/Y = 7; CPT FV = 1,070.90

Using formulas and one CF at a time:
Year 1 CF: FV5 = 100(1.07)4 = 131.08; PV0 = 100 / 1.07 = 93.46; FV3 = 100(1.07)2 = 114.49
Year 2 CF: FV5 = 200(1.07)3 = 245.01; PV0 = 200 / (1.07)2 = 174.69; FV3 = 200(1.07) = 214
Year 3 CF: FV5 = 200(1.07)2 = 228.98; PV0 = 200 / (1.07)3 = 163.26; FV3 = 200
Year 4 CF: FV5 = 300(1.07) = 321; PV0 = 300 / (1.07)4 = 228.87; PV3 = 300 / 1.07 = 280.37
Year 5 CF: FV5 = 300; PV0 = 300 / (1.07)5 = 213.90; PV3 = 300 / (1.07)2 = 262.03

Value at year 5 = 131.08 + 245.01 + 228.98 + 321 + 300 = 1,226.07
Present value today = 93.46 + 174.69 + 163.26 + 228.87 + 213.90 = 874.18 (difference due to rounding)
Value at year 3 = 114.49 + 214 + 200 + 280.37 + 262.03 = 1,070.89 (difference due to rounding)

Annuity – finite series of equal payments that occur at regular intervals
If the first payment occurs at the end of the period, it is called an ordinary annuity.
If the first payment occurs at the beginning of the period, it is called an annuity due.

Perpetuity – infinite series of equal payments
Annuities and Perpetuities Defined
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.2
5.18

Perpetuity: PV = C / r

Annuities:
Annuities and Perpetuities – Basic Formulas

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.19
Section 6.2

Lecture Tip: The annuity factor approach is a short-cut approach in the process of calculating the present value of multiple cash flows and it is only applicable to a finite series of level cash flows. Financial calculators have reduced the need for annuity factors, but it may still be useful from a conceptual standpoint to show that the PVIFA is just the sum of the PVIFs across the same time period.

You can use the PMT key on the calculator for the equal payment.

The sign convention still holds.

Ordinary annuity versus annuity due
You can switch your calculator between the two types by using the 2nd BGN 2nd Set on the TI BA-II Plus.
If you see “BGN” or “Begin” in the display of your calculator, you have it set for an annuity due.
Most problems are ordinary annuities.
Annuities and the Calculator
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.20
Section 6.2

Other calculators also have a key that allows you to switch between Beg/End.

After carefully going over your budget, you have determined you can afford to pay $632 per month toward a new sports car.
You call up your local bank and find out that the going rate is 1 percent per month for 48 months.
How much can you borrow?

To determine how much you can borrow, we need to calculate the present value of $632 per month for 48 months at 1 percent per month.
Annuity – Example 6.5
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.2 (A)
5.21

You borrow money TODAY so you need to compute the present value.
48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 ($24,000)

Formula:

Annuity – Example 6.5 (ctd.)

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.22
Section 6.2 (A)

The students can read the example in the book.

After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow?

Note that the difference between the answer here and the one in the book is due to the rounding of the Annuity PV factor in the book.

Suppose you win the Publishers Clearinghouse $10 million sweepstakes.
The money is paid in equal annual end-of-year installments of $333,333.33 over 30 years.
If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?

30 N; 5 I/Y; 333,333.33 PMT;
CPT PV = 5,124,150.29
Annuity – Sweepstakes Example
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.23
Section 6.2 (A)

Formula:
PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29

You are ready to buy a house, and you have $20,000 for a down payment and closing costs.
Closing costs are estimated to be 4% of the loan value.
You have an annual salary of $36,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income.
The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan.
How much money will the bank loan you?
How much can you offer for the house?
Buying a House
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.24
Section 6.2 (A)

It might be good to note that the outstanding balance on the loan at any point in time is simply the present value of the remaining payments.

Bank loan
Monthly income = 36,000 / 12 = 3,000
Maximum payment = .28(3,000) = 840
30×12 = 360 N
.5 I/Y
-840 PMT
CPT PV = 140,105

Total Price
Closing costs = .04(140,105) = 5,604
Down payment = 20,000 – 5,604 = 14,396
Total Price = 140,105 + 14,396 = 154,501
Buying a House (ctd.)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.25
Section 6.2 (A)

You might point out that you would probably not offer 154,501. The more likely scenario would be 154,500 , or less if you assumed negotiations would occur.

Formula
PV = 840[1 – 1/1.005360] / .005 = 140,105

The present value and future value formulas in a spreadsheet include a place for annuity payments.

Click on the Excel icon to see an example.
Annuities on the Spreadsheet – Example

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.2 (A)

5.26

You know the payment amount for a loan, and you want to know how much was borrowed. Do you compute a present value or a future value?

You want to receive 5,000 per month in retirement.
If you can earn 0.75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement?
Quick Quiz – Part II
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.27
Section 6.2 (A)

Calculator
PMT = 5,000; N = 25×12 = 300; I/Y = .75; CPT PV = 595,808

Formula
PV = 5000[1 – 1 / 1.0075300] / .0075 = 595,808

Suppose you want to borrow $20,000 for a new car.
You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month).
If you take a 4-year loan, what is your monthly payment?

4(12) = 48 N; 20,000 PV; .66667 I/Y; CPT PMT = 488.26
Finding the Payment
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.28
Section 6.2 (A)

Formula
20,000 = PMT[1 – 1 / 1.006666748] / .0066667
PMT = 488.26

Another TVM formula that can be found in a spreadsheet is the payment formula.
PMT(rate, nper, pv, fv)
The same sign convention holds as for the PV and FV formulas.

Click on the Excel icon for an example.
Finding the Payment on a Spreadsheet

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.2 (A)

5.29

You ran a little short on your spring break vacation, so you put $1,000 on your credit card.
You can afford only the minimum payment of $20 per month.
The interest rate on the credit card is 1.5 percent per month.
How long will you need to pay off the $1,000?
Finding the Number of Payments – Example 6.6
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.2 (A)

5.30

The sign convention matters!
1.5 I/Y
1,000 PV
-20 PMT
CPT N = 93.111 months = 7.75 years

And this is only if you don’t charge anything more on the card!
Finding the Number of Payments – Example 6.6 (ctd.)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.31
Section 6.2 (A)

You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can only afford to make the minimum payment of $20 per month. The interest rate on the credit card is 1.5 percent per month. How long will you need to pay off the $1,000?

This is an excellent opportunity to talk about credit card debt and the problems that can develop if it is not handled properly. Many students don’t understand how it works, and it is rarely discussed. This is something that students can take away from the class, even if they aren’t finance majors.

1000 = 20(1 – 1/1.015t) / .015
.75 = 1 – 1 / 1.015t
1 / 1.015t = .25
1 / .25 = 1.015t
t = ln(1/.25) / ln(1.015) = 93.111 months = 7.75 years

Suppose you borrow $2,000 at 5%, and you are going to make annual payments of $734.42.
How long before you pay off the loan?

Sign convention matters!!!
5 I/Y
2,000 PV
-734.42 PMT
CPT N = 3 years
Finding the Number of Payments – Another Example
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

5.32
Section 6.2 (A)

2000 = 734.42(1 – 1/1.05t) / .05
.136161869 = 1 – 1/1.05t
1/1.05t = .863838131
1.157624287 = 1.05t
t = ln(1.157624287) / ln(1.05) = 3 years

Suppose you borrow $10,000 from your parents to buy a car.
You agree to pay $207.58 per month for 60 months.
What is the monthly interest rate?

Sign convention matters!!!
60 N
10,000 PV
-207.58 PMT
CPT I/Y = .75%
Finding the Rate
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

6C-‹#›

Section 6.2 (A)

5.33

Trial and Error Process
Choose an interest rate and compute the PV of the payments based on this rate.
Compare the computed PV with the actual loan amount.
If the computed PV > loan amount, then the interest rate is too low.
If the computed PV < loan amount, then the interest rate is too high. Adjust the rate and repeat the process until the computed PV and the loan amount are equal. Annuity – Finding the Rate Without a Financial Calculator Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› Section 6.2 (A) 5.34 You want to receive $5,000 per month for the next 5 years. How much would you need to deposit today if you can earn 0.75% per month? What monthly rate would you need to earn if you only have $200,000 to deposit? Suppose you have $200,000 to deposit and can earn 0.75% per month. How many months could you receive the $5,000 payment? How much could you receive every month for 5 years? Quick Quiz – Part III Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.35 Section 6.2 (A) Q1: 5(12) = 60 N; .75 I/Y; 5000 PMT; CPT PV = -240,867 PV = 5000(1 – 1 / 1.007560) / .0075 = 240,867 Q2: -200,000 PV; 60 N; 5000 PMT; CPT I/Y = 1.439% Trial and error without calculator Q3: -200,000 PV; .75 I/Y; 5000 PMT; CPT N = 47.73 (47 months plus partial payment in month 48) 200,000 = 5000(1 – 1 / 1.0075t) / .0075 .3 = 1 – 1/1.0075t 1.0075t = 1.428571429 t = ln(1.428571429) / ln(1.0075) = 47.73 months Q4: -200,000 PV; 60 N; .75 I/Y; CPT PMT = 4,151.67 200,000 = C(1 – 1/1.007560) / .0075 C = 4,151.67 Suppose you begin saving for your retirement by depositing $2,000 per year in an IRA. If the interest rate is 7.5%, how much will you have in 40 years? Remember the sign convention! 40 N 7.5 I/Y -2,000 PMT CPT FV = 454,513.04 Future Values for Annuities Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.36 Section 6.2 (B) FV = 2000(1.07540 – 1)/.075 = 454,513.04 Lecture Tip: It should be emphasized that annuity factor tables (and the annuity factors in the formulas) assumes that the first payment occurs one period from the present, with the final payment at the end of the annuity’s life. If the first payment occurs at the beginning of the period, then FV’s have one additional period for compounding and PV’s have one less period to be discounted. Consequently, you can multiply both the future value and the present value by (1 + r) to account for the change in timing. You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is made today. How much will you have at the end of 3 years? 2nd BGN 2nd Set (you should see BGN in the display) 3 N -10,000 PMT 8 I/Y CPT FV = 35,061.12 2nd BGN 2nd Set (be sure to change it back to an ordinary annuity) Annuity Due Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6C-‹#› 5.37 Section 6.2 (C) Note that the procedure for changing the calculator to an annuity due is similar on other calculators. Formula: FV = 10,000[(1.083 – 1) / .08](1.08) = 35,061.12 What if it were an ordinary annuity? FV = 32,464 (so you receive an additional 2,597.12 by starting to save today.) Annuity Due Timeline