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# Calculating PV/FV of annuities, bond price and YTM

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Problem: If you invest \$8000 per period for the following number of periods, how much would you have?
a.7 years at 9 percent
b.40 years at 11 percent

Problem: The western sweeptakes has just informed you that you have won \$1 million. The amount is to be paid at the rate of \$50000 a year for the next 20 years. With a discount rate of 12%, what is the present value of your winnings.

Problem: Dr Oats, a nutrition professor, invests \$8000 in a piece of land that is expected to increase in value by 14% per year for the next five years. She will then take the proceeds and provide herself with a 10-year annuity. Assuming a 14 percent interest rate for the annuity, how much will this annuity be?

Problem: Essex Biochemical Company has a \$1000 par value bond that pays 10 percent annual interest. The company yield to maturity on such bonds in the market is 7 percent. Compute the price of the bonds for these maturity dates:
a.30 years
b.15 years
c.1 year

Problem: Bonds issued by Coleman Manufacturing Company have a par value of \$1,000, which, of course, is also the amount of principal to be paid at maturity. The bonds are currently selling for \$850. They have 10 years remaining to maturity. The annual interest payment is 8 percent (\$80). Compute the approximate yield to maturity.

Problem: Laser optics will pay a common stock dividend of \$1.60 at the end of year (D1). The required rate of return on common stock (Ke) is 13%. The firm has a constant growth rate(g) of 7 percent. Compute the current price of the stock(Po).

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#### Solution Preview

Please refer attached files for better clarity of formulas and tables.

Solution:

Problem: If you invest \$8000 per period for the following number of periods, how much would you have?
a.7 years at 9 percent
b.40 years at 11 percent

Future Value of a lump sum amount (PV) can be found by
FV=PV*(1+i)^n
a)i=interest rate=9%
n=number of periods=7
PV=\$8000
FV=8000*(1+0.09)^7=\$14624.31
b)i=interest rate=11%
n=number of periods=40
PV=\$8000
FV=8000*(1+0.40)^7=\$84330.80

Now, I am soving this problem assuming that payment of \$8000 is made per year.
a)
C=periodic payment=\$8000
n=number of periods=7
i=interest rate=9%
Future value of annuity=C*((1+i)^n-1)/i
=8000*((1+9%)^7-1)/9%
=\$73603.48
b.40 years at 11 percent
C=periodic payment=\$8000
n=number of periods=40
i=interest rate=11%
Future value of annuity=C*((1+i)^n-1)/i
=8000*((1+11%)^40-1)/11%
=\$4,654,608.53

Problem: The western sweeptakes has just informed you that you have won \$1 million. The amount is ...

#### Solution Summary

There are 6 problems. Solutions to first three problems explain the steps and formulas to calculate present and future values of annuities. Solutions to remaining problems explain the methodology to find price of bond, yield of bond and price of constant growth dividend paying stock.

\$2.19