# Present value of a annual annuity

1. The present value of a ten year $100 annual annuity discounted at 12% is:

a. $32.19

b. $89.28

c. $565.02

d. $310.58

2. The present value of a single sum of $100 to be received in 10 years and discounted at a annual 12% rate on a semi-annual basis is:

a. $32.19

b. $31.18

c. $100

d. $310.58

3. The best way to compare two sums to be received at different times in the future is to compute:

a. The present value of each sum.

b. The future value of each sum

c. Compare each sum directly without regard to compound interest

d. None of these

4. Which factor would you use when computing the present value of a series of rent payments, assuming the rent is paid at the beginning of each period as in a standard lease:

a. PVIFA(periods, rate)

b. FVIFA(periods, rate)

c. PVIFA(periods, rate) x (1+rate)

d. PVIF(periods, rate)

5. A certain stock paid a dividend of $2.00 yesterday and has a history of growth in dividends of 15% annually. What dividend will the stock pay in 10 years?

a. $8.09

b. $20.31

c. $0.49

d. $20.00

6. What is the current value of a bond with a coupon rate of 5%, 10 years to maturity, $1000 par value and YTM of 6%?

a. $1000.00

b. $1060.20

c. $926.40

d. $999.95

7. If a bond with a par value of $1000 is selling for $1075 on the bond market:

a. The YTM is equal to the coupon rate.

b. The YTM is less than the coupon rate.

c. The YTM is greater than the coupon rate.

d. None of the above.

8. If a stock has a constant growth rate of 6% per year and paid a dividend of $5.00 yesterday, what is the value of the stock if the discount rate is 10%?

a. $125.00 per share

b. $132.60 per share

c. $4.80 per share

d. $5.09 per share

9. When considering a project, the theoretically best discount rate to use is:

a. The firms weighted average cost of capital.

b. An adjustment to the weighted average cost of capital based on the risk profile of the project in relation to the risk of the firm generally.

c. Both a and b

d. Neither a nor b

10. You have won the lottery and are offered a cash payout of $5MM or twenty annual payments of $500K. To determine which is better to take, you should:

a. Compare the cash received.

b. Take the $5MM and party on.

c. Compute the present value of the $500K per year and compare to the $5MM cash payment.

d. Compute the future value of the $5MM payment and compare to the sum of the $500K payments.

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#### Solution Preview

1. The present value of a ten year $100 annual annuity discounted at 12% is:

a. $32.19

b. $89.28

c. $565.02

d. $310.58

P=A*((1/r)-((1/(r*((1+r)^n)))

P=present value, A= Annuity= 100 r= rate of interest= 12% n=10

c. $565.02

2. The present value of a single sum of $100 to be received in 10 years and discounted at a annual 12% rate on a semi-annual basis is:

a. $32.19

b. $31.18

c. $100

d. $310.58

P=present value, F= Future value r= rate of interest n=duration

P=F/(1+r)^n

Here r will be divided by half and duration will be multiplied by 2 as there is compounding semiannually

=100/(1+6%)^20

=$31.18 =b is the answer

3. The best way to compare two sums to be received at different times in the future is to compute:

a. The present value of each sum.

b. The future value of each sum

c. Compare each sum directly without regard ...

#### Solution Summary

Response provides the steps to calculate the present value of a annual annuity

Calculate PV, FV and annual amounts of annuity payments

If I borrow 60,000 from the bank at 10% interest over the seven-year life of the loan, what equal annual payments must be made to discharge the loan plus pay the bank its required rate of interest. Annual payments_____. How much of this first payment will be applied to interest? to principal? Also how much of my second payment will be applied to interest? Principal?

Also I have purchased an annuity to begin payment at the end of 2011 (that is the date of the first payment). Assume it is now the beginning of the year 2009. The annuity is for 8,000 per year and is designed to last 10 years. - If the interest rate for this problem calculation is 13 percent, what is the most I should have paid for the annuity. (round PV Factor to 3 decimal places)

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