week 8

Question 1

what is the concept of timevalue of money?

Answer 1

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

Question 2

what generalizations do risk and interest factors yield?

Answer 2

1. the right to receive an amnt now (pv) is worth more than the right to receive the same amnt later (fv)
2. the longer we wait to receive an amnt, the less attractive it is
3. the greater the interest rate, the greater the amnt we will receive in the future
4. the more risk associated with a cash flow, the higher the interest rate.

Question 3

if you have 90.91 today, adn can invest it at 10% for one year, our investment will grow to be:

Answer 3

100 dollars

90.91 is the pv of 100 dollars in a year

Answer 4

pv of a single payment = future amnt * 1/(1+i)^n

Question 5

how do you use the pv tables?

Answer 5

1. 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)
2. 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)
3. 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

Question 6

compute the pv of 100 to be received 1 year from today discounted at 10% sem ann

Answer 6

of periods (one y, semi ann) = 2
rate per period (10%/2) = 5%
multiplier = 0.90703
pv = 100 * 0.90703 = 90.70

Question 7

compute the pv of 100 to be received 2 years from today, discounted at 10% compounded semiannually

Answer 7

of periods (2 y, semi ann) = 4
rate per period (10%/2) = 5%
multiplier = 0.82270
pv = 100 * 0.82270 = 82.27

Question 7

how many cash flows does a bond have?

Answer 7

interest payments + principal payment

Question 8

what is an annuity

Answer 8

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

Question 9

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)

Answer 9

y1: 100 * 0.95238 = 95.24
y2: 100 * 0.90703 = 90.70
y3: 100 * 0.86384 = 86.38
total = 272.32