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# Time Value of Money

1. You want to put some money away for your child's college education. College will cost \$65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest?

2. In order to help you through college, your parents just deposited \$25,000 into a bank account paying 8% interest. Starting next year, you plan to withdraw equal amounts for the account at the end of each of the next four years. What is the most you can withdraw annually?

3. What is the market value of a bond that will pay a total of forty semiannual coupons of \$50 each over the remainder of its life? Assume the bond has a \$1,000 face value and an 8% yield to maturity (YTM).

4. What would you pay for a bond that pays an annual coupon of \$35, has a face value of \$1,000, matures in 7 years, and has a yield to maturity (YTM) of 8%?

5. What would you pay for a share of ABC Corporation stock today if the next dividend will be \$2 per share, your required return on equity investments is 12%, and the stock is expected to be worth \$110 one year from now?

#### Solution Preview

Note:
Note: the abbreviations have the following meanings

PVIF= Present Value Interest Factor
FVIF= Future Value Interest Factor
Ordinary Annuity
PVIFA= Present Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIF( n, r%)= =1/(1+r%)^n

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%

1.  You want to put some money away for your child's college education. College will cost \$65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest?

We have to find the Present Value of a Future Value

n= 18
r= 8.00%
PVIF (18 periods, 8.% rate ) = 0.250249

Future value= \$65,000
Therefore, present value= \$16,266.19 =65000x0.250249