Graduate School of Business Administration 548 ...



Graduate School of Business Administration 548 - Corporation Finance MBA.PM

Spring 2007 Semester - J. K. Dietrich

Present Value Analysis and Formulas

(1) Any single future cash flow can be discounted or its present value calculated using the general formula (Text, p. 73):

. Example: [pic]

A U.S. Treasury strip (zero-coupon bond) yielding (2/18/03) 3.16% maturing in November 2008 (T=5.665) has a present value of $. 8384 (actual price = 83:17 = .8353). You can use a calculator or Excel to calculate this answer.

(2) Any sequence of future cash flows can be discounted or its present value calculated using the general formula (Text, p. 75):

Example:

A mortgage-backed bond is expected to pay $1220 in year one, $1500 in year two, $1720 in year 3, $1550 in year 4, and $1200 and is priced to yield (2/18/03) 250 basis points over the 5-year Treasury, or 2.90%+2.50% = 5.40% = .054. The present value is $6,155.15

(3) If a cash flow is paid annually (or periodically) forever then the present value of the payments can be calculated using the perpetuity formula (Text, p. 80):

Example:

Duke Energy 6.375%’A’ preferred ($25 par) pays $.3944 dividend per quarter yielding 6.22% or 1.555% = .01555 per quarter.

Graphical representation of perpetuity cash flows:

(4) If you can assume that a beginning (first period) cash flow will grow after the first period at a constant rate g, the present value of the cash flows can be calculated using the growing perpetuity formula (Text, p. 81):

Example:

A building has first-month after tax cash flow (rental income net of operating costs) of $10,500 and are expected to increase at the assumed annual inflation rate of 2%, while real estate is currently being capitalized at 10%, yielding a value of $1.5 million.

Graphical representation of cash flows for a growing perpetuity:

(5) If a cash flow is paid annually (or periodically) for T periods the present value of the payments can be calculated using the annuity formula (Text, p. 84):

Example:

You require $10,000 per year at the end of each year for tuition and have a savings account paying 2.5% = .025 interest. You must have $37,620 in the account one-year before first payment is due.

(6) If you can assume that a beginning (first period) cash flow will grow after the first period at a constant rate g for T periods, the present value of the cash flows can be calculated using the growing annuity formula (Text, p. 88):

Example:

You plan to start saving $2,000 next year expecting an 8% = .08 return and you plan that your annual saving will grow at 2.5% = .025 after the first year.

Graphical representation of annuity and growing annuity:

Graduate School of Business Administration 548 - Corporation Finance MBA.PM

Spring 2007 Semester - J. K. Dietrich

Summary of Present Value Formulas

.

.

GENERAL FORMULAS

.

PERPETUAL CASH FLOWS – FOR QUICK CALCULATIONS

CASH FLOWS OVER LIMITED TIME HORIZON – PRACTICAL

-----------------------

[pic]

Time

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Single Cash Flow

Sequence of Cash Flows

Perpetuity

Growing Perpetuity

Annuity

Growing Annuity

Annuity

[pic]

[pic]

[pic]

Single Cash Flow

[pic]

Sequence of Cash Flows

[pic]

Perpetuity

[pic]

[pic]

Growing Perpetuity

Annuity

Growing Annuity

[pic]

Annuity

Growing Annuity

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download