Annuities
Mortgage payment
Annual income from an investment payout
Future Value of annual payments
Calculation of periodic payments
Perpetuities & Annuities
Example - Future Value of annual payments
You plan to save $4,000 every year for 20 years and then
Bond Pricing
Q: How did the calculation change, given semi-annual coupons versus annual coupon
payments?
Bond Yields
Current Yield - Coupon payments for next year divided by bond price.
Yield To Maturity - Interest rate for which the present value of the
Perpetuities & Annuities
Example - Perpetuity
In order to create an endowment, which pays $100,000 per year (at the end of each
year), forever, how much money must be set aside today in the rate of interest is 10%?
continued
If the first perpetuity paymen
Time Value of Money
The PV formula has many applications. Given any variables in the equation, you can
solve for the remaining variable.
Present Values with Compounding
PV of Multiple Cash Flows
Example
Your auto dealer gives you the choice to pay $15,500
Proctor and Gamble Sacrificing Quality
Lower price or higher quality?
Its a decision that consumers have had to make since the day of their very first
transactions, and what virtually every purchase boils down to in the end - the nitty gritty of the
buyin
Bonds
Bonds - Terminology
Bond Legal Agreement that obligates the issuer to make specified payments to the bondholder.
Coupon - The interest payments made to the bondholder (usually due every six months).
Face Value (Par Value or Principal Value) - Paymen
Compound Interest
Example - Compound Interest - Interest earned at a rate of 6% for five years on the previous
years balance.
Interest Earned Per Year =Prior Year Balance x .06
Example - Compound Interest
Interest earned at a rate of 6% for five years on
Future Values and Compound Interest
Future Values and Compound Interest
Present Values
Multiple Cash Flows
Level Cash Flows Perpetuities and Annuities
Inflation & Time Value
Effective Annual Interest Rate
Future Values
Future Value - Amount to which an in
Promotion Evaluations
Promotion with retailers and advertising is vital to P&Gs success as a quality and brand
based company. Consumers need to be convinced that the extra money they are spending on a
P&G product is worth it. So worth it in fact, that the
Bond Yields
Rate of Return In general terms = Earnings per period per dollar invested.
Bond Valuation Spreadsheet
Bond Yield Spreadsheet
Credit risk = risk of default on obligation
Default premium = higher interest rate applied to loans with higher credit
Compounded Interest
If you will be making equal deposits into a retirement account for 10 years (with each payment at
the end of the year), how much must you deposit each year if the account earns 4% compounded
annually and you wish to have $500,000 after
Introduction to Finance and Excel
EXAMPLE
RENT
UTILITIES
PAY
Supplies
MISC.
$1,000.00
$250.00
$1,360.00
$1,750.00
$156.00
$4,516.00
Sales $6,000.00
Pre-tax $1,484.00
Taxes $593.60
Profit $890.40
Line 38:
$11,100.00
What if we change Jim's hours?
What loca
Present Value
Payment of $50,000 arrives in time 1 and $100,000 in time 10.
(a)
The present value = 50,000/(1.04) + 100,000/(1.0410) = $115,633.34
(b)
The value in time period 30 = 50,000 x (1.0429) + 100,000 x (1.0420) = $375,044.89
Alternatively, you ca
Various Cash Flow Balance Sheets
Year:
A. Fixed assets
Investments in fixed assets
0
1
2
3
4
CF, invest. in fixed assets
-5,000,000
0
0
0
0
B. Working capital
Working capital
Change in working capital
CF, invest. in wk capital
600,000
600,000
-600,000
700
Alternative Methods to Compounding Interest
Alternative method 1:
Step 1: Find FV in time 10 of 500,000 in time 30 using EAR = 4.074%: $224,963.57
Step 2: Solve for the payment that equals FV of 224,963.57 using =PMT() and EAR
($18,673.09)
You belong to a
Company Announcements Affecting Stock Prices
An example of a company with an announcement that caused the stock price to increase by more
than 1% is FMT shown below. The news was that the company had successfully arranged for an
increased line of credit.
Project Payback
This project pays back in year 6, so it pays back after the payback cutoff of 5 years and we reject
the project.
Under NPV we accept if the NPV is positive. So we accept under NPV
here.
Under IRR, we accept if the IRR is greater than the r