1. Time Value of Money & BONDS

2. Interest is The cost associated with the use of money
Is an important cost to debtor
Is an Important revenue to the creditor
Since “Time is Money” : Important to any business decision

3. Present Value:
Amount that must be invested today at a given rate to produce a given future value

4. Present Value is based on 3 Variables:
Future Amount
$ amount to be received
Number of periods = N
Length of time until the amount is received
Interest rate = i
Market / yield / discount rate of interest

5. Present Value can be calculated
Manually (using mathematical formulas)
Factor Tables (included in textbook)
Using Financial calculator
Using Excel (PV function)

6. PV Cash Flow Principles: Amounts to be paid/received
LUMP SUM : a single sum at a point in time
Receipt of face amount of the note
ORDINARY ANNUITY: Equal end of the period payments at equal intervals of time
Periodic interest payments made at the end of the period
ANNUITY DUE: Beginning of the period payments at equal intervals of time
Periodic interest payments made at the beginning of the period

7. Time Value of $ Calculations Using Tables in KIMMEL Textbook
APPENDIX C
Present Value of a Lump Sum = Present Value of $1:
TABLE 3 (page c8)
PV of a Series of payments made at the end of the period =
PV of an Ordinary Annuity of $1:
Table 4 (page c10)

8. PV Example #1 Assume you win the lottery. Your choice:
$30,000 per year for the next 15 years (total of $450,000) OR
$1,000,000 in 15 years.
Current interest rate is 9%
Which is a better deal?
Compare using Present Value…

9. Choice B is worth more in TODAY’S DOLLARS
Choice A: PV of an Ordinary Annuity
$30,000 * (n=15, I = 9%)
$241,821
Choice B: PV of a Lump Sum
$274,540
$1,000,000 * (n=15, I = 9%)
Choice B is worth more in TODAY’S DOLLARS

10. PV Example #2
Assume your rich Aunt Edith leaves you some inheritance. You have the option of receiving:
$24,000 over the next 12 years ($2,000/yr) OR
You can have all her government bonds which mature in 10 years at a value of $30,000.
Assume you invest the $ you accumulate in a 10% Money Market account.
Which option is more attractive? (In other words, which is worth more in today’s dollars? )
Compare using Present Value…

11. Choice A is worth more in TODAY’S DOLLARS
Choice A: PV of an Ordinary Annuity
$2,000 * (n=12, i = 10%)
$13,627
Choice B: PV of a Lump Sum
$11,566
$30,000 * (n=10, I = 10%)
Choice A is worth more in TODAY’S DOLLARS

12. Using Present Value to Value a Bond
Present value is relevant to the study of bonds because the value of a bond is based on the present value of two components of future cash flow:
A series of fixed interest payments. (ordinary annuity)
A single payment at maturity. (lump sum payment)
The amount of interest a bond pays is fixed over its life.

13. PV & BONDS
BONDS are recorded at the PV of the Cash expected to be collected
May involve TWO types of future cash flows:
Payment of the face value of the note at maturity (a LUMP SUM payment) &
Periodic Interest Payments (an ordinary the stated interest rate)

14. This interest rate is called the Effective Interest Rate OR
The value of the Bond at any point in time
should be = to the PV of those cash flows
computed at an interest Rate = the rate
of return desired by the lender.
This interest rate is called the
Effective Interest Rate OR
Discount Rate of Interest OR
Yield Rate of Interest OR
Market Rate of Interest

15. IF the Stated Rate of Interest = Market rate
Bond will sell (be recorded) at FACE value
Investors
willing to
pay MORE:
Will earn
MORE!
IF the Stated Rate of Interest > Market rate
Bond will sell (be recorded) at a Premium
Investors
willing to
pay LESS:
Will earn
LESS!
IF the Stated Rate of Interest < Market rate
Bond will sell (be recorded) at a Discount

16. Selling Price of Bond Stated Rate(12%) = Market Rate (10%) Issued at a PREMIUM
Face amount of the Bond: $10,000,000
Stated Interest Rate: 12%
Semi-annual Payments: $10,000,000 * 12% / 2 = $600,000
10 year Bond
Present Value at 5%(Market rate of 10% / 2=5%) :
Lump sum : $10,000,000 * (n=20, i=5%) = $3,768,900
Interest Payments: $600,000 * (n=20, i=5%) = $7,477,326
PV of Bond Face Value ) $11,246,226
1/1/ Cash ,246,226
Bonds Payable ,000,000
Premium on B/P 1,246,226

17. BOND PRICING STEP 1 – Compute the PV of the principal to be repaid
use MARKET rate
PRINCIPAL x PV of $1
(n=number of periods, i=market rate)
STEP 2 – Compute the PV of interest to be paid
(use BOTH rates)
PRINCIPAL x STATED Interest = Interest Payment
Interest Payment x PV of an ANNUITY
(n=number of periods, i =market rate)
STEP 3 – ADD PV of Principal plus PV of Interest Payments
TOTAL = SELLING PRICE OF THE BONDS

18. Selling Price of Bond Stated Rate(12%) = Market Rate (14%) Issued at a DISCOUNT
Face amount of the Bond: $10,000,000
Stated Interest Rate: 12%
Semi-annual Payments: $10,000,000 * 12% / 2 = $600,000
10 year Bond
Present Value at 7%(Market rate of 14% / 2=7%) :
Lump sum : $10,000,000 * .258 (n=20, i=7%) = $2,580,000
Interest Payments: $600,000 * (n=20, i=7%) = $ 6,356,400
PV of Bond Face Value ) $8,936,400
1/1/ Cash ,936,400
Discount on B/P 1,063,600
Bonds Payable ,000,000

19. Selling Price of Bond Stated Rate(10%) = Market Rate (10%)
Face amount of the Bond: $10,000,000
Stated Interest Rate: 10%
Annual Interest Payments: $10,000,000 * 10% = $1,000,000
10 year Bond
Present Value at 10%(Market rate) :
Lump sum : $10,000,000 * (n=10, i=10%) = $3,855,400
Interest Payments: $1,000,000* (n=10, i=10%) = $6,144,570
ROUND $9.999,970
PV of Bond Face Value ) $10,000,000
1/1/ Cash ,000,000
Bonds Payable ,000,000
12/31/04 Bond Interest expense ,000,000
Cash ,000,000

20. Selling Price of Bond Question 4A: No stated interest Market Rate (10%)
Face amount of the Bond: $10,000,000
Present Value at Market rate of 10% :
Lump sum : $10,000,000 * (n=10, i=10%) = $3,855,400
Investors would be willing to PAY: $3,855,400 for a $10,000,000 Bond with no interest payments