Final paper

workhelp

MSL660Hall7part1.pdf

Home >Human Resource Management homework help >Final paper

Financial Analysis MBA/MSL 643 Hall #7 Part 1 Time Value of Money

Biblical Foundation

Live right and you will eat from the life-giving tree. And if you act wisely, others will follow.

PROVERBS 11:30

•Does “being” proceed “doing?”

•Can anything great be achieved alone? Why or why not?

Key Concepts

• Be able to compute: ▫ The future value of an investment made today

▫ The present value of cash to be received at some future date

▫ The return on an investment

▫ The number of periods that equates a present value and a future value given an interest rate

▫ The future value of multiple cash flows

▫ The present value of multiple cash flows

• Be able to solve time value of money problems using: ▫ Formulas

▫ A financial calculator

▫ A spreadsheet

• Understand how interest rates are quoted

Key Concepts continued

• Be able to compute the future value of multiple cash flows

• Be able to compute the present value of multiple cash flows

• Understand how interest rates are quoted

Basic Definitions

• Present Value (PV)

▫ The current value of future cash flows discounted at the appropriate discount rate

▫ Value at t=0 on a time line

• Future Value (FV)

▫ The amount an investment is worth after one or more periods.

▫ “Later” money on a time line

Basic Definitions continued

• Interest rate (r) ▫ Discount rate

▫ Cost of capital

▫ Opportunity cost of capital

▫ Required return

▫ Terminology depends on usage

Time Line of Cash Flows

• Tick marks at ends of periods

• Time 0 is today;

• Time 1 is the end of Period 1

CF0 CF1 CF2

0 1 2 3 r%

CF3

+CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF

Future Value General Formula

FV = PV(1 + r)t

FV = future value PV = present value r = period interest rate, expressed

as a decimal t = number of periods

• Future value interest factor = (1 + r)t

Note: “yx” key on your calculator

Example: Future Value

Suppose you invest $100 for one year at 10% per year.

What is the future value in one year?

▫ Interest = 100(.10) = 10

▫ Value in one year

= Principal + interest

= 100 + 10 = 110

▫ Future Value (FV)

= 100(1 + .10) = 110

Suppose you leave the money in for another

year. How much will you have two years

from now?

FV = 100(1.10)(1.10)

= 100(1.10)2 = 121.00

Effects of Compounding

• Simple interest ▫ Interest earned only on the original principal

• Compound interest ▫ Interest earned on principal and on interest received ▫ “Interest on interest” – interest earned on

reinvestment of previous interest payments

• Consider the previous example

▫ FV w/simple interest

= 100 + 10 + 10 = 120

▫ FV w/compound interest

=100(1.10)2 = 121.00

▫ The extra 1.00 comes from the interest of .10(10) =

1.00 earned on the first interest payment

Texas Instruments BA – II Plus

• FV = future value • PV= present value • I/Y*= period interest rate (r) • N = number of periods • PMT = payment (but will equal 0 in

our examples of lump sums)

One of these MUST

be negative

N I/Y PV PMT FV

*I/Y= period interest rate (r)

Interest is entered as a percent, not a decimal

 5% interest = “5”, not “.05”

Example: FV of Lump Sum

• Formula Solution: FV=PV(1+r)t

=100(1.10)5

=100(1.6105)

=161.05

• Suppose you invest the $100 from the previous example for 5 years. How much would you have?

Calculator Keystrokes: 5, N; 10, I/Y; -100, PV; 0, PMT; CPT

FV = 161.05 Excel Solution: =FV(Rate, Nper, Pmt, PV)

=FV(.10, 5, 0,-100) = 161.05

NOTE: Rate = decimal

Present Value

• The current value of future cash flows discounted at the appropriate discount rate

• Value at t=0 on a time line

• Answers the questions:

▫ How much do I have to invest today to have some amount in the future?

▫ What is the current value of an amount to be received in the future?

• Present Value = the current value of an amount to be received in the future

• Why is it worth less than face value?

▫ Opportunity cost

▫ Risk & Uncertainty

Discount Rate = ƒ (time, risk)

FV = PV(1 + r)t

• Rearrange to solve for PV

PV = FV / (1+r)t

PV = FV(1+r)-t

• “Discounting” = finding the present value of one or more future amounts.

• Finding PVs is discounting, and it’s the reverse of compounding.

What’s the PV of $100 due in 3 Years if r = 10%?

10% 0 1 2 3

PV = ?

100

Formula: PV = FV/(1+r)t = 100/(1.10)3 = $75.13

Calculator: 3, N; 10, I/Y; 0, PMT;100, FV; CPT PV = -75.13

Excel: =PV(.10,3,0,100) = -75.13

The Basic PV and FV Equation for a Lump Sum

PV = FV / (1 + r)t

There are four parts to this equation

▫ PV, FV, r and t

▫ Know any three, solve for the fourth

• Be sure and remember the sign convention

+CF = Cash INFLOW -CF = Cash OUTFLOW

Present Value and Future Value of a Lump Sum

Recap

Future Value of a Series of Multiple Cash Flows

• 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 3 years?

• How much in 4 years?

• Find the value at year 3 of each cash flow and add them together.

▫ Year 0: FV = $7,000(1.08)3 = $ 8,817.98

▫ Year 1: FV = $4,000(1.08)2 = $ 4,665.60

▫ Year 2: FV = $4,000(1.08)1 = $ 4,320.00

▫ Year 3: value = $ 4,000.00

▫ Total value in 3 years = $21,803.58

• Value at year 4 = $21,803.58(1.08)= $23,547.87

If you deposit $100 in one year, $200 in two years and $300 in three years, how much will you have in three years at 7 percent interest?

TIMELINE

200*(1.07) =

Total interest = $628.49-600=28.49

* (1.07)^2 =

4 5

-$300.00

$628.49

-$200.00

100*(1.07)^2 = $114.49

$719.56

$300.00

$214.00

-$100.00

0 1 2 3

Example: FV of a Series of Multiple CFs

with a Timeline

If you deposit $100 in one year, $200 in two years and $300 in three years, how much will you have in three years at 7 percent interest?

Example: FV of a Series of Multiple CFs

Using Excel

Rate 7% Year Nper CF FV Function

1 2 -100 $114.49 =FV(0.07,2,0,-100) 2 1 -200 $214.00 =FV(0.07,1,0,-200) 3 0 -300 $300.00 =FV(0.07,0,0,-300)

Total FV at Year 3 $628.49 Total FV at Year 5 $719.56 =(628.49)*(1.07)^2

Example: FV of a Series of Multiple CFs

• 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%?

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

0 1 2 3 4 5

$100 $300 300*(1.08)2 =

100*(1.08)2 =

$349.92

$136.05

$485.97

PV of a Series of Multiple Cash Flows

You are offered an investment that will pay

 $200 in year 1,

 $400 the next year,

 $600 the following year, and

 $800 at the end of the 4th year.

 You can earn 12% on similar investments.

 What is the most you should pay for this one?

Find the PV of each cash flow and add them:

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

Total PV = $1,432.93

Present Value of a Multiple Series of Cash Flows

Timeline

400200 800600178.57

318.88

427.07

508.41

1,432.93

0 1 2 3 4

= 1/(1.12)2 x

= 1/(1.12)3 x

= 1/(1.12)4 x

Time

(years)

Multiple Uneven Cash Flows

• Repeat for all cash flows, in order.

• To find NPV:

▫ Press NPV button and I appears on the screen

▫ Enter the interest rate (in %), press ENTER and arrow down to display NPV.

▫ Press CPT

• Press the CF button

• CF0 is displayed as 0.00

• Enter the Period 0 cash flow

▫ If an outflow, press +/- to change the sign

• To enter the figure in the cash flow register, press ENTER.

• Arrow down to C01. Enter a value, arrow

down to F01 and enter

how many times C01

occurs (default is

1).

Example: Multiple Uneven Cash Flows

CF Function on the Calculator

• 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 CFs at year 5?

• What is the value of the CFs today?

Display You Enter

Press CF C00 0, ENTER, C01 100, ENTER, F01 1, ENTER, C02 200, ENTER, F02 2, ENTER, C03 300, ENTER, F03 2, ENTER,

Press NPV I 7 ENTER,

Press CPT NPV = 1432.93

Example continued

Using Excel

Example: PV and FV of CFS

Using the Timeline

874.12

PV 213.90 $

228.87 $ 163.26 $ 174.69 $

93.46 $

7% Period

CFs

100

200

300

300.00 $ 321.00 $ 228.98 $ 245.01 $ 131.08 $

FV = 1,226.07 $

Annuities and Perpetuities

• 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.

• Perpetuity: PV = PMT / r

• Annuities:

 

  

  

   





   





 



1)r1( PMTFV

)r1(

1 1

PMTPV

Setting Annuity and Time Value Parameters

• The PMT key on the calculator is used for the equal payment

• The sign convention still holds

• Ordinary annuity versus Annuity due

▫ Switch your calculator between the two types (see below)

▫ If you see “BGN” in the display of your calculator, you have it set for an annuity due

▫ Most problems are ordinary annuities (END mode).

• Set END for an ordinary annuity or BGN for an annuity due

▫ Press 2nd and then BGN

▫ This is a toggle switch. The default is END.

▫ To change to BEGIN, press 2nd and ENTER to go back and

forth.

▫ Press 2nd and QUIT to exit.

Important Points to Remember

• Interest rate and time period must match!

▫ Annual periods  annual rate

▫ Monthly periods  monthly rate

• The Sign Convention

▫ Cash inflows are positive

▫ Cash outflows are negative

• 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 .75% per month?

60, N

0.75, I/Y

5000, PMT

0, FV

CPT PV = -

240866.87

=PV(0.0075,60,5000,0)

Excel

Calculator

PV and FV of Multiple CFs Recap

Interest Rates

• Effective Annual Rate (EAR)

▫ The interest rate expressed as if it were compounded once per

year.

▫ Used to compare two alternative investments with different

compounding periods

• Annual Percentage Rate (APR) “Nominal”

▫ The annual rate quoted by law

▫ APR = periodic rate X number of periods per year

▫ Periodic rate = APR / periods per year

APR 1 EAR 



  

 

m = number of compounds per year

Example: Effective Annual Rate (EAR)

• Which savings accounts should you choose: ▫ 5.25% with daily compounding.

▫ 5.30% with semiannual compounding.

• First account:  EAR = (1 + .0525/365)365 – 1 = 5.39%

• Second account:  EAR = (1 + .053/2)2 – 1 = 5.37%

Questions for Reflection & Study

• What is the difference between simple interest and compound interest?

• Suppose you have $500 to invest and you believe that you can earn 8% per year over the next 15 years.

• How much would you have at the end of 15 years using compound interest?

▫ How much would you have using simple interest?

• What is the relationship between present value and future value?

• Suppose you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today?)

• If you could invest the money at 8%, would you have to invest more or less than at 6%? How much?

Questions for Reflection & Study cont.

• What is the relationship between present value and future value?

• Suppose you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today?

• If you could invest the money at 8%, would you have to invest more or less than at 6%? How much?

• 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?

• You want to receive $5,000 per month in retirement. If you can earn .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?

• What is the difference between APR and EAR?

What next?

• Take the Hall Quiz

• Complete your detailed reading

• Answer the discussion questions

• Complete the writing assignments

References

• Financial Statements and some additional information was provided by slides from Essentials of Corporate Finance, 7th edition (2011), by Ross, Westerfield and Jordon.

This concludes Hall 7 Part 1