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# Funding your Retirement Financial Question

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Problem 1:

Funding your retirement you plan to retire in exactly 20 years. Your goal is to
create a fund that will allow you to receive \$20,000 at the end of each year for
the 30 years between retirement and death (a psychic told you would die exactly
30 years after you retire). You know that you will be able to earn 11% per year
during the 30-year retirement period.

a. How large a fund will you need when you retire in 20 years to provide the
30-year, \$20,000 retirement annuity?

b. How much will you need today as a single amount to provide the fund calculated
in part a if you earn only 9% per year during the 20 years preceding
retirement?

c. What effect would an increase in the rate you can earn both during and prior
to retirement have on the values found in parts a and b? Explain.

Problem 2:
Funding budget shortfalls As part of your personal budgeting process, you
have determined that in each of the next 5 years you will have budget shortfalls.
In other words, you will need the amounts shown in the following table at the
end of the given year to balance your budget?that is, to make inflows equal
outflows. You expect to be able to earn 8% on your investments during the
next 5 years and wish to fund the budget shortfalls over the next 5 years with
a single amount.

End of year Budget shortfall
1 \$ 5000
2 4000
3 6000
4 10,000
5 3,000

a. How large must the single deposit today into an account paying 8% annual
interest be to provide for full coverage of the anticipated budget shortfalls?

b. What effect would an increase in your earnings rate have on the amount
calculated in part a? Explain.

Problem 3:
Loan amortization schedule Joan Messineo borrowed \$15,000 at a 14%
annual rate of interest to be repaid over 3 years. The loan is amortized into
three equal, annual, end-of-year payments.

a. Calculate the annual, end-of-year loan payment.

b. Prepare a loan amortization schedule showing the interest and principal
breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage
of time.

Problem 4:
Monthly loan payments Tim Smith is shopping for a used car. He has found
one priced at \$4,500. The dealer has told Tim that if he can come up with a
down payment of \$500, the dealer will finance the balance of the price at a 12%
annual rate over 2 years (24 months).

a. Assuming that Tim accepts the dealer's offer, what will his monthly (end-ofmonth)
payment amount be?

b. Use a financial calculator or Equation 4.15a (found in footnote 9) to help
you figure out what Tim's monthly payment would be if the dealer were
willing to finance the balance of the car price at a 9% annual rate.

Problem 5:
Basic bond valuation Complex Systems has an outstanding issue of \$1,000-
par-value bonds with a 12% coupon interest rate. The issue pays interest
annually and has 16 years remaining to its maturity date.

a. If bonds of similar risk are currently earning a 10% rate of return, how
much should the Complex Systems bond sell for today?

b. Describe the two possible reasons why similar-risk bonds are currently
earning a return below the coupon interest rate on the Complex Systems
bond.

c. If the required return were at 12% instead of 10%, what would the current
value of Complex Systems' bond be? Contrast this finding with your findings
in part a and discuss.

Problem 6:
Common stock valuation?Zero growth Scotto Manufacturing is a mature
firm in the machine tool component industry. The firm's most recent common
stock dividend was \$2.40 per share. Because of its maturity as well as its stable
sales and earnings, the firm's management feels that dividends will remain at the
current level for the foreseeable future.

a. If the required return is 12%, what will be the value of Scotto's common stock?

b. If the firm's risk as perceived by market participants suddenly increases,
causing the required return to rise to 20%, what will be the common stock
value?

c. Judging on the basis of your findings in parts a and b, what impact does risk
have on value? Explain.

#### Solution Preview

Problem 1:

Funding your retirement You plan to retire in exactly 20 years. Your goal is to
create a fund that will allow you to receive \$20,000 at the end of each year for
the 30 years between retirement and death (a psychic told you would die exactly
30 years after you retire). You know that you will be able to earn 11% per year
during the 30-year retirement period.

a. How large a fund will you need when you retire in 20 years to provide the
30-year, \$20,000 retirement annuity?

You can use present value of annuity formula by using the following equation.

PVA = W x 1 - 1 where PVA is the present value
(1 + R)N W is the amount received each quarter
R R is the interest rate
N is the period

PVA = 20,000 x 1 - 1
(1 + 0.11)30
0.11

PVA = 173,875.85

b. How much will you need today as a single amount to provide the fund calculated
in part a if you earn only 9% per year during the 20 years preceding
retirement?

PV = FV/(1 + R)N
PV = 173,875.85/(1 + 0.09)20
PV = 31,024.82

c. What effect would an increase in the rate you can earn both during and prior
to retirement have on the values found in parts a and b? Explain.

An increase in the rate you can earn both during and prior to retirement will result in lower values for both a and b because the higher the rate the lower the present value.

Problem 2:
Funding budget shortfalls As part of your personal budgeting process, you
have determined that in each of the next 5 years you will have budget shortfalls.
In other words, you will need the amounts shown in the following table at the
end of the given year to balance your budget-that is, to make inflows equal
outflows. You expect to be able to earn 8% on your investments during the
next 5 years and wish to fund the budget shortfalls over the next 5 ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer how large a fund will you need when you retire in 20 years to provide the 30-year, \$20,000 retirement annuity. 6 questions total; attached as Word and Excel.

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