2
3.
An investment offers the following year-end cash flows: 1
st
year: $20,000; 2
nd
year:
$30,000; and 3
rd
year: $15,000.
Using a 15% discount rate, convert this series of
irregular cash flows to an equivalent (in present value terms) 3-year annuity.
SOLUTION:
First we need to discount the three payments to figure out their present value:
PV = 17,391+22,684+9,863=49,938.36
Solving for PMT in:
PVA(PMT, 3 years,15%) = 49,938.36,
yields
PMT = 21,871.85.
4.
You have just won the Publisher’s Sweepstakes and you can either have a lump sum
payment of $1,000,000 immediately or annuity of $100,000 per year for the rest of
your life with the first payment in one year.
If you expect to live 20 years and the
discount rate is 10%, which alternative should you choose (ignoring taxes)?
SOLUTION:
PVA ($100,000, 20 years, 10%) = 851,356.37
Take the lump payment.
5.
If the interest rate in problem #5 is 7%, does this change your answer?
SOLUTION:
PVA ($100,000, 20 years, 7%) = 1,059,401.42
Take the annuity.
6.
What is the present value of $1,000,000 received 10 years from now at a discount rate
of 300% per year?
SOLUTION:
PV=$1,000,000/(1+3.0)
10
= ¢95.37
7.
It is 1/1/2001 and you will receive $100,000 per year for the next 25 years.
The
payments are made on June 30
th
of each year.
If the annual discount rate is 10% and
the 6 month rate is (1+.10)
1/2
, then what is the value of this annuity today?