week 8 (module 7) - liability analysis Flashcards
what is the concept of timevalue of money?
a dollar today is worth more than a dollar tomorrow (somewhere in the future)
if we invest the dollar now, we would have the dollar and interest on the dollar
what generalizations do risk and interest factors yield?
- the right to receive an amnt now (pv) is worth more than the right to receive the same amnt later (fv)
- the longer we wait to receive an amnt, the less attractive it is
- the greater the interest rate, the greater the amnt we will receive in the future
- the more risk associated with a cash flow, the higher the interest rate.
if you have 90.91 today, adn can invest it at 10% for one year, our investment will grow to be:
100 dollars
90.91 is the pv of 100 dollars in a year
how to calculate the pv of a single payment
pv of a single payment = future amnt * 1/(1+i)^n
how do you use the pv tables?
- determine # of interest compounding periods (3 years comp. semiann = 6 periods)
- extreme left hand column indicates # of periods
- important to distinguish between years and comp. periods
- table is for comp. periods (years * # of comp. periods per year) - determine interest rate per comp. period
- int rates are usually quoted on per year basis
- rate per compounding period is annual rate / # of comp. periods per year (ex. 10% ann rate would be 10% per period is comp. annually and 5% per period is semiann) - locate pv factor, which is at the intersection of row of appropriate number of compounding periods and the column of the appropriate int rate per compounding period
- multiply factor by $ that will be paid/received in future
compute the pv of 100 to be received 1 year from today discounted at 10% sem ann
of periods (one y, semi ann) = 2
rate per period (10%/2) = 5%
multiplier = 0.90703
pv = 100 * 0.90703 = 90.70
compute the pv of 100 to be received 2 years from today, discounted at 10% compounded semiannually
of periods (2 y, semi ann) = 4
rate per period (10%/2) = 5%
multiplier = 0.82270
pv = 100 * 0.82270 = 82.27
how many cash flows does a bond have?
interest payments + principal payment
what is an annuity
when future cash flows involve the same amnt being paid/received every period
ex. semi ann int payments on bonds, quarterly dividend receipts, monthly insurance premiums
if payment/receipt is equally spaced over time and each cash flow is the same $ amnt, we have an annuity
if 100 is to be received at the end of each of the next 3 years as an annuity, what is the pv of this annuity? (5% ann rate)
y1: 100 * 0.95238 = 95.24
y2: 100 * 0.90703 = 90.70
y3: 100 * 0.86384 = 86.38
total = 272.32
use pv of single amount table of the same percentage but for different years going down with accordance with the period
use pv of annuity table - easier
what is a bond certificate?
purchasers of bonds receive it
specifies:
- issuing comp name
- face value (maturity vlaue, par value, principal)
- maturity date (date when issuing comp is obligated to pay back debt)
- coupon rate (stated interest rate), rental fee on borrowed money
- interest payment dates (dates that interest payments are due, gen 2x a year)
- bond date
what does a bond agreement specify?
series of interest payments (cash outflow)
single payment of face vlaue at maturity
what rate do we use to determine a bond’s market vlaue (its price)?
market rate on the date of the sale
how is the selling price of a bond determined?
- use table of pv of single payments to compute pv of future principal payment at prevailing market rate
- use pv of annuity table to compute pv of future series of interest payments (annuity) at prevailing market rate
- add pv from steps 1 and 2
at what price are bonds sold at?
market price, the amount invetsors are willing to pay -> market price is bond’s pv
