Corporate Finance Ch. 4-5
For a given length of time, the higher the discount rate, the
lower the present value is.
A series of constant cash flows that arrive or are paid at the end of each period is called an
ordinary annuity.
Should we make the new investment?
-If PV of deposits > PV of withdrawals -> it's a good investment! OR...if NPV>0 DO IT!
How to Compare Loan Options
1. Find the respect EAR's 2. Find the monthly payments, larger monthly payments -> quicker the loan will be paid off
Amortized Loans
A loan with scheduled periodic payments of both principal and interest At specified intervals (most commonly monthly), you make your "payment", which is a combination of that period's interest PLUS a repayment of principal This is the most common structure for home mortgages. Application of APV problem with r=APR/#periods
Consol
A type of perpetuity.
Internal Rate of Return (IRR)
the interest rate that makes the net present value of the investment equal to zero (equates present and future value)
Discounted Cash flow valuation DCF
Valuation calculating the present value of a future cash flow to determine its value today.
Net Present Value
"Net" meaning the net or combined effect of all the future pluses and minuses
Calculating Net Future Value (multiple future cash flows)
1. Calculate NPV 2. Use time value to convert to FV ex: Back Pay
Which payment method typically charges the highest interest rates?
Payday Loans. Very high APR and EAR
Stated Interest Rate
The interest rate expressed in terms of the interest payment made each period. Also, quoted interest rate.
The expression 1 + r is sometimes called the
future value interest factor or just future value factor.
Why do these high rates for payday loans exist?
• There are "overhead costs" (store fronts cost money) • There are "fixed costs per loan" (I'm only making $15, I have to pay someone to make the loan, process paperwork, keep track of repayment -- $15 isn't a lot of money to cover "people costs" • I will have significant loan losses (non-repayment of principal) While the interest rates are high, the profits are "normal". Without the high rates, these loans would not be available
What happens to the future value of an annuity if you increase the rate, r? What happens to the present value?
Assuming positive cash flows and a positive interest rate, the present value will fall, and the future value will rise.
What happens to a future value if you increase the rate, r?
The future value rises, assuming a positive rate of return.
Annual Percentage Rate APR (NOM)
The interest rate charged per period multiplied by the number of periods per year. To use for APV, you need to divide APR by relevant period. • In simple terms, the APR is the rate that does NOT reflect compounding, thus EAR > APR (because it reflects compounding)
Effective Annual Rate EAR (EFF)
The interest rate expressed as if it were compounded once per year. "annual discount rate"
Interest rates can be quoted in a variety of ways. For financial decisions, it is important that
any rates being compared be first converted to effective rates.
For a given rate of return, the value at some point in the future of an investment made today can be determined by calculating the
future value of that investment.
Modern Perpetuities: Preferred Stock
"Preferred Stock" is a hybrid security between debt and equity in a capital structure -Generally a fixed "par value" -Generally a fixed dividend payment -Treated as "shareholders' equity" in balance sheet -In bankruptcy or liquidation, has preference behind debt but ahead of common stock
Annuity
A level stream of CONSTANT cash flows for a FIXED period of time.
Perpetuity
An annuity in which the cash flows continue forever. P=C/r
Future Value FV
The amount of money an investment will grow to over some period of time at some given interest rate.
Discount Rate
The rate used to calculate the present value of future cash flows.
Find Remaining Balance on a Mortgage after X payments
•Start as you would with any annuity problem: <PV>: -35,000,000 <N>: 360 <I/Y>: 6.1/12= <CPT><PMT> • <2nd><PV> (this is the 'Amort' or Amortization function) • <2nd><CE/C> (clear work) •1 <ENTER>, followed by down arrow (you are telling the calculator we want to start with payment 1) •60 <ENTER>, followed by down arrow ('end with payment 60') •You will now see BAL= -32,609,016 - this is your remaining balance
With simple interest, the interest is not
reinvested, so interest is earned each period only on the original principle.
Mortgage/Loan "Points"
Points are effectively "prepaid interest", paid at the time you take out a loan A point on a loan is simply one percentage point of the loan amount. So if you take a loan with X points you'd be getting a PV of (Loan - X percent of loan)
Calculate APR to EAR (effective annual rates)
Press 2nd 2 NOM= Type interest rate/APR and hit enter Hit ↓ twice C/Y=times it's compounded per year (365/#periods) Hit ↑ to EFF and hit CPT
Calculating Net Present Value (multiple future cash flows)
Step 1: Always begin by clearing the Cash Flow worksheet. To do so: Press [CF] to turn the CF worksheet on. Press [2nd] CLR Work Quit Step 2: Press [CF]. The display should show: CF0= 0.00000. Step 3: Type the numeric amount of the cash flow for time period 'zero'. Then press [+\-] to change this amount to a cash outflow. The [+\-] key is a toggle key. Press [Enter]. Step 4: Press the down arrow key to display C01. Type in the cash amount for period 1, then press [Enter]. Press the down arrow key to display F01. Press [Enter] to accept the default amount of 1.00000. Step 5: Press the down arrow key to display C02. Type in the cash amount for period 2, then press [Enter]. Press the down arrow key to display F02. Press the down arrow key again to accept F02, and to move to the next field which will display as C03. Step 6: Type in the cash amount for each subsequent period in the same manner. Once all cash flows are inputted, use the up and down arrow keys to scroll through the Cash Flow worksheet to verify your input. Step 7: To compute NPV: Press [NPV] to display i = 0.0000. Enter the required rate of return in decimal format 'as-if' there is a percentage sign following. (e.g., 7.45) Press [Enter]. Press the down arrow key, then press [Cpt] to display the dollar amount of the NPV.
Pure Discount Loans/Zero Coupon Loan
The borrower receives money today and repays a single lump sum at some time in the future. Simple Time Value Problem -Loan Principal is your APV -You are given N and I/Y -You are solving for PMT
Present Value PV
The current value of future cash flows discounted at the appropriate discount rate.
The current worth of a future cash flow can be determined for a given rate of return by calculating
the present value of the cash flow involved.
What happens to a present value if you increase the rate, r?
The present value falls.
As you increase the length of time involved, what happens to the present value of an annuity?
The present value of an annuity will increase at a decreasing rate due to the greater number of payments further and further
Compounding
The process of accumulating interest in an investment over time to earn more interest.
Two reasons for higher discount rates
- Risk of repayment - Currency risk
Negative Interest Rates
In theory, this can't happen • In reality, government regulation causes this - European banks are required to hold government debt to meet regulatory requirements, irrespective of rate - As a result, they hold it, even though the rates are negative at present - Swiss rates have been especially low because the Swiss franc is viewed as a stronger currency than the Euro
Why would a company be willing to accept such a small amount today in exchange for a promise to repay about four times that amount in the future?
It's a reflection of the time value of money.
Annuity Due
An annuity for which the cash flows occur at the beginning of the period. As a convention, annuity payments are always assumed to be made or received at the end of a period (e.g., after discounting the value for that period), unless explicitly stated otherwise
As you increase the length of time involved, what happens to the future value of an annuity?
As you increase the time, there will be more annuity payments. The future value of an annuity will increase at an increasing rate due to both the greater number of payments and the greater compounded interest.
Interest Only Loans
Borrower pays interest each period and repays the entire principal at some point in the future (maturity). If there is just one period then an interest only and a pure discount loan are the same thing. Annual interest expense: X% of Principal = Expense Monthly payment = $Expense/ 12
Discount
Calculate the present value of some future amount.
What is discounting?
Discounting is the process of determining the value today of an amount to be received in the future. The practice of deducting the interest on a loan in advance (Ex: On a $100 loan, the interest is deducted from the total while the remainder is deposited in the account). Future cash flows are discounted at the discount rate; the higher the discount rate, the lower the present value of the future cash flows.
What is compounding?
When funds earn interest on interest. We find the future values with compounding.
Many loans are
annuities. The process of paying off a loan gradually is called amortizing the loan.
Compounding the interest means earning
interest on interest, so we call the result compound interest.
Present values and discount rates are
inversely related. Increasing the discount rate decreases the present value and vise versa.
Bullet Loan
loan typically with no amortization and full amount due at end of loan term