# PV Problems 2

For items 1-6 and number 8, you may wish to use this PV Table.

1. Toni is looking at an investment that requires a payment of \$3,152 now, in order to get a \$10,000 lump sum payment at the end of 15 years. What is the Internal Rate of Return (IRR) for this investment. Remember that the IRR is the interest rate that makes the NPV equal to zero.

2. Lena has been offered the possibility of investing \$42,410 now. The investment will earn 10% per year and at the end will pay Lena \$100,000. How many years will it take?

3. Nora purchased an investment for \$12,462. From this investment, she will receive \$1,000 annually for the next 20 years. What rate of interest will Nancy's investment be earning?

4. Betty invests \$7536.08 now for a \$1,000 annuity. She will earn 8% on this annuity. How many payments will she receive?

5. Diana invested \$5,286 in an investment that will pay \$3,000 the first year, \$2,000 the second year, and \$1,000 the third year. What is the Internal Rate of Return (IRR) on this project. Note: you will need to use the PV of \$1 on this one.

6. Charlie wins the lottery prize of \$10,000. Charlie can wait three years to get it, or the state will pay him the present value of \$10,000 today, discounted at 8%. How much will Charlie receive if he takes his winnings today?

7. Payback Period Calculation: Tacoma Manufacturing Company is considering three projects, each of which costs \$21,000. The cash flows for the three projects are as follows:

 YEAR P1 P2 P3 1 7,000 9,500 13,000 2 9,000 9,500 10,000 3 15,000 9,500 11,000

To calculate the Payback Period, figure out how long each project will take to recover the investment. For example, project P1 will not recover the \$21,000 investment in the first year, but after the second year, it gets close with an accumulated amount of 7,000+9,000=\$16,000. In the third year, P1 finally recoups the investment. In fact, assuming that the cash flows are uniform, it will take 1/3 of year 3 (5000/15000) to accumulate the remaining \$5,000 necessary to recover \$21,000.

Note that the Payback Period does not involve the time value of money, which is a weakness. An additional weakness is that the answer is in years, not dollars. In terms of comparing P1, P2, and P3, you could rank the investments as to how short the Payback Period will be.

8. Can you calculate an approximate Internal Rate of Return for the investments in Question 7?