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# TVM Concepts

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

2.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?

3.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
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 \$ 5,000
2 4,000
3 6,000
4 10,000
5 3,000

1.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?

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

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.

1.Calculate the annual, end-of-year loan payment.
2.Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.
3.Explain why the interest portion of each payment declines with the passage of time.

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).

1.Assuming that Tim accepts the dealer's offer, what will his monthly (end-of-month) payment amount be?
2.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.

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.

1.If bonds of similar risk are currently earning a 10% rate of return, how much should the Complex Systems bond sell for today?
2.Describe the two possible reasons why similar-risk bonds are currently earning a return below the coupon interest rate on the Complex Systems bond.
3.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.

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.
1.If the required return is 12%, what will be the value of Scotto's common stock?
2.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?
3.Judging on the basis of your findings in parts a and b, what impact does risk have on value? Explain.

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#### Solution Preview

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Solution

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.

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

Periodic amount =R=\$20000
Number of periods=n=30
Interest rate=r=11%
Let us find present value of this ordinary annuity
PV= R/r*(1-1/(1+r)^n)=20000/11%*(1-1/(1+11%)^30)= \$173875.85
I should have \$173875.85 when I retire in 20 years.

2.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?

Here FV=\$173875.85 (refer part a)
Interest rate=r=9%
Number of periods=n=20
PV=?
PV=FV/(1+r)^n=173875.85/(1+9%)^20=\$31024.82
Today I should have \$31024.82 .

3.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 interest rate during retirement 30-year period will lead to a lower PV of annuity i.e. amount needed at the end of 20-year will decrease. A single amount needed today will also decrease.
An increase in interest rate during 20-year period will lower the single amount needed today.

Problem 2
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 \$ 5,000
2 4,000
3 ...

#### Solution Summary

There are six problems. Solutions to these problems explain the methodology to calculate present value of future cash flows, loan payments, price of a bond and value of a stock.

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