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
Y
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 Matur
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 in
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
Examp
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 b
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 mont
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 Inte
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
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 = h
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%
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) +
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
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 224,9
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
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