Present/Annual Worth Review

1. **A **is an investment opportunity that promises a given future
flow of cash (different amounts at different times). If the MARR is given
as 10%, how can you determine the most you would be willing to pay for **A**
at this time?

2. **A **is an investment opportunity that requires an investment
of the amount P now, and promises a given future flow of cash (different
amounts at different times). Given the MARR, how would you determine whether
**A** is an
acceptable investment?

3. **A **is an investment opportunity that requires an investment
of the amount P now, and promises a given future flow of cash (different
amounts at different times). How would you determine the rate of return
associated with **A**?

4. Assuming cash flows roughly comparable in value, which cash flows are more likely to affect an economic decision, those near the present or those far in the future?

5. You will pay $100 at times 0, 2, 4, 6, ... . You will receive $120 at times 1, 3, 5, 7, ... . This sequence of payments goes on forever. Write the formula for the NAW of this cash flow in terms of the interest rate i.

6. If you could get the opportunity described in problem 5 by paying an additional amount P at time 0. How much should be willing to pay? Your MARR is 20%.

7. To borrow $1000 you will make monthly payments at 12% nominal interest per year. You will pay for 24 months. Write the formulas for the quantities below.

a. What is the monthly payment?

b. What is the effective interest rate?

c. What is the payoff value of the loan at the end of one year? (after 12 payments)

8. To borrow $1000 you will make monthly payments at 12% nominal interest per year. You will pay for 24 months. The first payment is $50. Each subsequent payment will increase by an amount x.

a. What is the value of x?

b. What is the payoff value of the loan at the end of one year? (after 12 payments)

9. **B** requires an investment of $1000 and promises an annual (end
of year) return of $100 for five years. What must be the selling price of
**B **after five years to make this an acceptable investment? The MARR
is 10%. Write the formula without evaluating.

10. **A **is an investment opportunity that requires an investment
of the amount P now, and promises a given future flow of cash (different
amounts at different times). The sum of the future cash flows is greater
than P.

a. What is the net present value of **A** when calculated with zero
interest?

b. What is the net present value of **A** when calculated with a very
large interest?

11. C is a positive income that will come to you n years from now.

a. What happens to the present value of C as the interest rate increases? Explain using a formula.

b. What happens to the present value of C as n increases? Explain with a formula.

12. You evaluate the NPV of a cash flow at two different interest rates.

at i = 10%, NPV = -20, and at i = 13%, NPV = +10.

a. Estimate the i at which NPV = 0.

b. Is this an investment or a borrowing situation? Why?

13. A machine costs $1000. The operating cost in the first year is $100 and increases by $100 for every year thereafter. The machine is sold after 10 years with a salvage value of $500. Write the formula for the NAW of costs. The MARR is 10%.

14. A machine costs $1000. The operating cost for the first five years is $100. Starting with year 6 it increases by $100 for every year thereafter. The machine is sold after 10 years with a salvage value of $500. Write the formula for the NAW of costs. The MARR is 10%.

15. Two machines **A** and **B** are alternatives for some function.
Initial investment, operating costs, and salvage values are given. Both
machines have the same lives. Explain how you would select the best when
the MARR is given.

16. Two machines **A** and **B** are alternatives for some function.
Initial investment, operating costs, and salvage values are given. Machine
**A**has a life of 4 years, while machine **B** has a life of 3 years.
Explain how you would select the best when the MARR is given.

17. You borrow $1000 by promising to make ten equal monthly payments of $100. What interest rate are you paying for the loan?

18. You borrow $1000 by promising to pay $20 a month for ten months. At the end of the tenth month you also pay an extra $1000. What nominal and effective interest rates are you paying on the loan?