# Time Value of Money and Equivalent Annuity

Please do your own work and do not share your work with others. Please type a numerical solution in the space provided for each problem -- thanks.

1. How much will you have at the end of 16 years if put $8680 per year at the end of each year into a saving account earning 1.8% annually? _________

2. How much do you need to invest today (once) to have $589,000 at the end of 18 years if you can earn 6.5% annually? ____________

3. Assume that you have accumulated $75,000 in student loan debt. You pick a 12-year horizon to pay of the loan. If the loan has a 6.75% annual rate, what will your monthly payments be? _________________

4. You plan to work for the next 37 years and earn 6.5% on your investments during your working years. In retirement, you expect to need $92,000 per year during each of your 25 years of retirement and (during this time) you expect to earn 4.6% on investments. How much do you need to invest at the end of each year (while working) to allow this to happen? _______________

5. A bond can be purchased for $965 today. This bond pays $62 in interest each year in annual year end payments. The bond has a par or maturity value of $1,000 and has 9 years to maturity. What is the expected yield to maturity for this bond? (Two decimal places please - for example 8.25%)_______________

6. A different bond pays 5.2% annual interest once per year, has 9 years to maturity, and a $1,000 par or maturity value. Given the risk level of this bond the market demands a 8.2% interest rate. What is the value of this bond today?_______________

7. Joe Inc.'s preferred stock is expected to pay a $2.27 dividend annually and is expected to do this forever. Joe Inc. is in a high risk business that requires an 8% return. What is the estimated value of Joe Inc.'s preferred stock?_______________

8. Bill Inc. common stock is expected to pay a $1.32 dividend at the end of the year and is in a risk class that requires an 8.5% required return. If this dividend is expected to grow forever at a 4.2% rate, what is the estimated value of Bill Inc.'s common stock? _______________

9. Joe's Technology must choose between two repeatable methods of producing a new product. The initial costs and year-end cash benefits are as follows:

Year 0 1 2 3 4 5

Method M -$1,500,000 600,000 750,000 500,000 200,000

Method N -$2,500,000 1,200,000 900,000 700,000 400,000 300,000

Assume all cash flows occur at year-end and the company's required return is 6.25 percent.

Please compute the net present value ______________ and the equivalent annuity ________________ for Method M

Please compute the net present value ______________ and the equivalent annuity ________________ for Method N

Which production method should be used? _______________

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#### Solution Summary

This solution illustrates how to compute the present value of a lump-sum and an annuity, the future value of a lump-sum, the required payments to have a future value, the net present value and equivalent annual annuity for different projects, and the current value of preferred stock, common stock and bonds.