Fin 40153 intermediate financial management
This presentation is the property of its rightful owner.
Sponsored Links
1 / 27

FIN 40153: Intermediate Financial Management PowerPoint PPT Presentation


  • 60 Views
  • Uploaded on
  • Presentation posted in: General

FIN 40153: Intermediate Financial Management. INTRODUCTION TO VALUATION (TIME VALUE OF MONEY) (BASED ON RWJ CHAPTER 4). Money has “time value”. Why? Because interest rates (and expected returns) are positive. Implies that: A dollar today is worth more than a dollar tomorrow.

Download Presentation

FIN 40153: Intermediate Financial Management

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Fin 40153 intermediate financial management

FIN 40153: Intermediate Financial Management

  • INTRODUCTION TO VALUATION

  • (TIME VALUE OF MONEY)

  • (BASED ON RWJ CHAPTER 4)


Money has time value

Money has “time value”

  • Why?

    • Because interest rates (and expected returns) are positive.

  • Implies that:

    • A dollar today is worth more than a dollar tomorrow.

    • Cash flows at different points in time cannot be added together.


Basic tools for valuation future and present values discounting

Basic Tools for Valuation: Future and Present Values (Discounting)

Terminology:

  • r is the interest rate or as is also referred to as the discount rate

  • PV will be the value today or the present value of a future payment

  • FVn will be the future value of money invested today n years from now

  • If you invest PV today then n years from now it will be worth

    FVn = PV(1+r)n

    This same basic formula can be used to determine the current amount that is equivalent to (i.e. can grow to) a stated future amount, since

    PV = FVn/(1+r)n


Example

Example

You need $20 million five years from now to fund a capital investment. If r = 6%, what amount can be set aside now to fund the investment?

PV = 20.0/(1.06)5 = 20.0/1.33823 = $14.945 million.

What if you can’t really earn r = 6%?


Example1

Example

  • My Uncle Pete wants me to loan him $15,000 today so he can buy some frozen fruit for his new smoothie stand. He says that he is willing to get the full $15,000 back to me in exactly three years, and is willing to give me $3,500 in three years on top of that for interest. What is the annual rate of interest that I am receiving on my loan to Pete under his proposal?

  • 18,500 = 15,000(1+r)3 = 18,500

  • (18,500/15,000) = (1+r)3

  • r = (18,500/15,000)1/3 -1 = 0.0724 = 7.24%

  • On HP10BII: Amber C All

  • 15,000PV

  • 18,500FV

  • 3N

  • 0PMT

  • Push the I/YR key to get 7.24%

  • Note: Must be sure that P/YR is set = 1 !!!


Present value of a series of future cash flows

Present Value Of A Series of Future Cash Flows

  • The present value of a stream of cash flows can be found using the following general valuation formula:

  • In words: (1) discount each cash flow back to the present using the appropriate discount rate, and (2) sum the present values. The latter step is OK, because each future cash flow has been restated as its equivalent amount at a common point in time.


Valuing streams of structured future cash flows

C

C

C

0

1

2

3

Valuing Streams of Structured Future Cash Flows

  • Perpetuity A stream of equal payments, made at equal time intervals, forever.

  • The present value of a perpetuity that pays the amount C at the end of each period, when the discount rate is r, is:

  • Note that this gives the value as of time 0, one period before the first payment arrives.


Example2

Example

  • You wish to endow a Permanent Chair in finance at TCU. The chair needs $150,000/yr forever (in perpetuity).

    • The trustees of TCU can invest your money at 6%/yr through guaranteed investment contracts with the NeverBankrupt Insurance Co.

  • How much money do you need (what is the PV of the perpetuity) ?

  • PV = C / r = 150,000 / 0.06 = $2,500,000


Fin 40153 intermediate financial management

C1

C1(1+g)

C1(1+g)2

0

1

2

3

Valuing Streams of Cash Flows

  • Growing Perpetuity

  • A growing perpetuity is a stream of periodic payments that grow at a constant rate and continue forever.

  • The present value of a perpetuity that pays the amount C1 next period, growing at the rate g indefinitely when the discount rate is r is


Fin 40153 intermediate financial management

Examples

Suppose that the Finance professor to be hired for the Chair wants 5% raises per year guaranteed:

Growing perpetuity: $150,000 received at time t = 1, growing at 5% per period forever and discounted at 6% per period

CC(1 + g) C(1 + g) 2

0123

PV = C/(r –g ) = $150,000/(0.06 – 0.05) = $15,000,000


Sidebar valuation by earnings or cash flow multiples

Sidebar: Valuation by Earnings or Cash Flow “Multiples”

  • Analysts and investors sometimes take a shortcut approach to valuation:

    • multiply earnings or cash flow for the current year by an appropriate “multiple”.

    • The best known of these is the “price/earnings ratio”.

  • Valuation by multiple in the case of infinite-lived, constant growth, cash flows:


Multiples appropriate for valuing infinite lived cash flows with constant growth

Multiples Appropriate for Valuing Infinite-Lived Cash Flows with Constant Growth

Larger multiples are justified by higher cash flow growth,

or by lower interest (discount) rates


Fin 40153 intermediate financial management

2

3

1

0

100

100

100

Annuities

  • An annuity is a series of equal payments made at fixed intervals for a specified number of periods

    • e.g., $100 at the end of each of the next three years

  • If payments occur at the end of each period it is an Ordinary Annuity.

  • If payments occur at the beginning of each period it is an Annuity Due.

Ordinary Annuity


Valuing annuities

Valuing Annuities

  • The present value of a T period annuity paying a periodic cash flow of C when the discount rate is r is:

  • The textbook uses the shorthand notation ATr% to denote the factor in brackets.

  • If we have an annuity due instead, the net effect is that every payment occurs one period sooner, so the value of each payment is higher by the factor (1+r).

  • To obtain the PV with beginning-of-period payments, simply multiply the answer obtained based on end-of-period payments by the factor (1+r).


Annuity example a five year annuity paying 2000 per year with r 5

Annuity Example: A five year annuity paying $2000 per year, with r = 5%.

  • Valuing the payments individually we get:

  • Using the annuity formula we get:

  • Do on HP: PMT=2000, N=5, I/YR=5, FV=0, push PV and get 8658.95 (note it displays as a negative number)


Fin 40153 intermediate financial management

  • Alternatively, suppose you were given $8,658.95 today instead of the annuity

  • Notice that you can replicate the annuity cash flows by investing the present value to earn 5%.

  • This demonstrates that present value calculations provide a literal equality, in that the future cash flows can be converted into the present value and vice versa, if (and only if) the selected discount rate is representative of actual capital market conditions.


Fin 40153 intermediate financial management

C1

C1(1+g)

C1(1+g)T-2

C1(1+g)T-1

0

1

2

T-1

T

Growing Annuities. A stream of regular payments that grows at a constant rate, g.

  • The present value of a T period growing annuity that pays C1 next period, with subsequent payments growing at rate g, when the discount rate is r is:

or


Example growing annuity

Example (growing annuity)

  • A new venture is expected to generate $1 million in free cash flow during its first year. Subsequent cash flows will grow by 4% per year due to market growth and cost savings. Cash flows will continue for 20 years. The appropriate discount rate is 14%.


Annuities with deferred starts

Annuities with Deferred Starts

  • The standard formulas for level and growing annuities assume that the first payment occurs one period from now.

  • If the first payment is deferred until later than one period from now, the standard formulas can still be used, but:

    The answer denotes the value as of one period before the first payment, not the value now.


Fin 40153 intermediate financial management

A Valuation Problem

What is the value of a 10-year annuity that pays $300 a year at the end of each year, if the first payment is deferred until 6 years from now, and if the discount rate is 10%?

0123456789101112131415

300 300 300 • • • • • • 300

The value of the annuity payments as of five years from now is:

Now discount this equivalent payment back 5 years to time zero:


Application of time value analysis planning for retirement

Application of Time Value Analysis: Planning for Retirement.

  • You have determined that you will require $2.5 million when you retire 25 years from now. Assuming an interest rate of r = 7%, how much should you have already saved? set aside each year from now until retirement?

  • Determine the present equivalent of the targeted 2.5 million.

  • PV = 2,500,000/(1.07)25

  • PV = 2,500,000/5.42743 = $460,623.

  • Hmmm, you don’t have that much saved??

  • Determine the annuity payment that has an equivalent present value:


Retirement planning example continued

Retirement Planning Example, Continued.

  • You expect your earnings to grow by 4% per year. Your retirement goal is unchanged but, instead of making equal payments, you wish to make payments that grow along with your earnings. How large should the first payment be? How large should the 25th payment be?


A college planning example

A college planning example

  • You have determined that you will need $60,000 per year for four years to send your daughter to college. The first of the four payments will be made 18 years from now and the last will be made 21 years from now. You wish to fund this obligation by making equal annual deposits over the 21 years. You expect to earn r = 8% per year.

    Time Line:

60

60

60

60

0

1

2

3

17

18

19

20

21

22


College planning cont

College planning, cont.

  • Step 1: Determine the time 17 value of the obligation:

  • Step 2: Determine the equivalent time zero amount:


College planning example continued

College planning example, continued.

  • Step 3: Determine the 21-year annuity that is equivalent to the stipulated present amount.


Verification of answer obtained in college planning example

Verification of Answer Obtained in College-Planning Example


Time value summary

Time Value Summary

  • Discounted cash flow, or present value, analysis is the foundation for valuing assets or comparing opportunities.

  • To use DCF you need to know three things

    • Forecasted cash flows

    • Timing of cash flows

    • Discount rate (reflects current capital market conditions and risk).

  • If there are no simple cash flow patterns, then each cash flow must be valued individually, and the present values summed. You can look for annuities or growing annuities to allow short cuts.

  • Different streams of cash flows can be meaningfully compared (or equated) after they are each converted to their equivalent present values.


  • Login