Finance Chapter 6
What is the formula to convert from the quoted rate to the EAR
(1+ r/n)^n=(1+j)^n --> j formula
What must you multiply an annuity by to make it an annuity due? Why?
(1+r) where r is the discount rate This is because there is an extra payment at t=0 for annuities due (the payment at the beginning of the month)
If calculating the PV of an annuity, what is the FV of an annuity?
0 - leave blank on calculator
What are the two ways to calculate future values for multiple cash flows
1) compound the accumulated balance forward one year at a time 2) calculate the future value of each cash flow and add them up
Hoffstein corporation is about to pay a dividend of $3/share. Investors anticipate that the annual dividend will rise by 6%/year forever. r=11. What is the price of the stock today?
3 * 1.06 = 3.18 PV = 3 + 3.18/(.11-.06) = $66.6 The formula will only calculate the PV for all dividends beginning a year from now. For true PV must add this year's dividend on to the PV
What is a balloon payment?
A balloon payment mortgage is a mortgage which does not fully amortize over the term of the note, thus leaving a balance due at maturity. The final payment is called a balloon payment because of its large size
What is an annuity?
A level stream of cash flows for a fixed period of time (payments are the same each month)
What is an annuity due?
An annuity paid at the beginning of the period
What is a perpetuity?
An annuity with no forseeable end date
What is the assumed timing of annuity payments?
At the end of the period
What is the underlying timing assumption for growing perpetuities
Cash flows are received and disbursed at discrete regularly spaced intervals
What is the formula to calculate the EAR with continuous compounding
EAR = (e^quoted rate) -1
What is the EAR
Effective annual rate - the interest rate expressed as if it were compounded only once per year
What is the formula for the PV of a growing annuity?
PV = (C/(r-g))[1-((1+g)/(1+r))^t]
What is the formula for a growing perpetuity
PV = cash flow/(r-growth rate)
What is the formula to calculate a perpetuity
PV*r = cash flow
What is the formula to calculate a perpetuity
PV*r = cash flow or PV = Cash flow/r
What do you have to do for an annuity due?
Set your calculator to calculate payments at the beginning of the period
What is an interest only loan?
The borrower pays the interest payments monthly and repays the original loan amount in the future
What does the numerator signify for a growing perpetutity
The cash flow is the cash flow ONE PERIOD FROM NOW. In a question if you are given 'the company is about to pay a dividend of $3 and expect it to grown 6%/year forever' the cash flow will be 3*1.06 = 3.18
What is an amortized loan?
The lender requires the borrower to repay the loan over time. The repayment of the principle remains the same with a smaller and smaller percentage going toward the interest payments as the principle decreases
What is the PV of future cash flows?
The money you would need today to pay out the future cash flows indicated
What is a growing annuity?
a finite number of growing cash flows
what is an example of a perpetuity?
a fixed rate stock
what is an example of an annuity due?
a least payment --> e.g. rent is due at the begining of the month
What is a perpetutity
an annuity with indefinite cash flows
what is an APR
annual percentage rate - the monthly rate or semiannual rate multiplied by the number of periods. It is not the effective annual rate
What is the compounding period for a mortgage by law?
semi annual
What is a pure discount loan?
the borrower repays the loan in one lump sum payment
what is the quoted interest rate?
the interest rate expressed in terms of the interest payment made each month