How much is the following Annuity worth?
1. $5,000 EACH YEAR DISCOUNTED 3 years at 10%?
2. $5,000 EACH YEAR DISCOUNTED 3 years at 7%?
3. $10,000 EACH YEAR DISCOUNTED 2 years at 12%?
4. $10,000 EACH YEAR DISCOUNTED 2 years at 9%?
5. $3,000 EACH YEAR DISCOUNTED 7 years at 12%?
6. $3,000 EACH YEAR DISCOUNTED 7 years at 5%?
7. $4,000 EACH YEAR DISCOUNTED 20 years at 10%?
8. $4,000 EACH YEAR DISCOUNTED 30 years at 12%?
9. $2,000 EACH YEAR DISCOUNTED 20 years at 10%?
10. $2,000 EACH YEAR DISCOUNTED 30 years at 12%?

1. You invest $5,000 in Account A FOR 10 years and earn 10% return. You invest
$3,000 in Account B FOR 10 years at 8%. How much do you have in 10 years in
total?

2. You invest $25,000 for 10 years at 8%. You open a second account and invest
$3,000 each year for 10 years at 10%. How much do you have in total?

3. You are offered $100,000 in 10 years.
a. Using a discount rate of 8% what is it worth today?
b. Using a discount rate of 10% what is it worth today?

4. What is the value of an annuity that will pay you $5,000 each year for 30 years at a discount rate of 6%? What is the value of the annuity if you use a 12% dis-count rate?

1. Your Uncle Scooter wants you to invest in his pie shop. He wants only $15,000
and will pay you back in 8 years. Knowing the wheels fell off his last venture you
demand 14% return. How much does Scooter need to pay you in 8 years?

2. Uncle Scooter says you have a screw loose, but will give you $11,000 in 8 years.
What is the present value of the offer? K = 14

3. You explain the present value to your Uncle Scooter who is perplexed (not un-
common for Scooter). Scooter adds 2 pies a week to the $11,000 deal for 8 years.
The pies are worth $10.50 each and you want the pies. What is the new present
value? K=14

4. Scooter takes on a partner who is a part-time finance instructor, smart, and is
good looking. Because of this you reduce your return requirement from 14% to
10%. Use the needed data from question 3 and determine the present value.

TIME FOR SOME HARD STUFF

1. You have $30,000 in an IRA that will earn 14% into the future. Your 401K has a
$35,000 balance and you add $4,500 per year and it will earn 12%. You have two
Zero coupon bonds with a current return of 8% maturing in 25 years with a face
value of $25,000 for each bond. After maturing, you will invest the balance of the
Zero’s at 5% until you retire. How much money do you have in 30 years?

2. Using the answer from question 1, answer the following question. You want to
retire in 30 years and be retired for 20 years. All investments will earn 10% in
retirement. How much will you be able to withdraw each year in retirement?

3. How much do you need to deposit each year in a retirement plan if you plan
to retire in 30 years, be retired for 25 years and want $125,000 in retirement in-
come? K = 12 before retirement and K = 10 after retirement?

When valuing bonds you need four pieces of information:
1. Bonds Face Value
2. Maturity Date
3. Coupon Rate

4. The interest rate in the current market environment
Valuing a Bond takes 2 steps:
1. Use PVA to discount the interest payments
2. Use PV$ to value the return of principle.

Example:
You have a bond with a face value of $10,000; a coupon rate of 8%; maturity date
is 20 years from today and the current rate environment is 10%.
Solve as follows:
$10,000 .08 (coupon rate) = $800 interest payment per year
Use the interest rate of the current environment in the present value equations.
$10,000 PV$ K = 10 N = 20 (.1486) = $1,486
$800 PVA K = 10 N = 20 (8.5136) = $6,811
Bond Value = $8,297
Valuing Bonds

A bond with a face value of $25,000;
Coupon rate of 10% maturing in 30 years.

What is the value of the bond in a . . .
1a) 5% rate environment =
1b) 8% rate environment =
1c) 12% rate environment =

A bond with a face value of $100,000;
Coupon rate of 7% maturing in 10 years.
What is the value of the bond in a . . .
2a) 6% rate environment =
2b) 9% rate environment =
2c) 10% rate environment