Questions 6-9 6. You are considering investing in a retirement fund that require

Question

Questions 6-9

6. You are considering investing in a retirement fund that requires you to deposit $5,000 per year, and you want to know how much the fund will be worth when you retire. What financial technique should you use to calculate this value? (a) Future value of a single payment (b) Future value of an annuity (c) Present value of an annuity (d) Present value of a perpetuity 7. Consider buying a building in Manhattan as a rental property. The cost of the building is $150MM and the annual rent is $12MM forever, commencing next year. Should you buy if r- 8.5%? 8. You want to computerize sales division of your firm. Two dealers make competing offers to you for the same equipment. Dealer A: Pay $85K today, and Dealer B: Pay $12Kper year for 10 years starting one year from now. If the interest rate is 7%, which offer is better? 9. You won a lottery worth $295.7MM. Instead of receiving at once, you decided to receive the prize in 25 annual installments of $11.828 mllion each. Assuming that the first payment oc- curred at the end of one year, what was the present value of the prize? The interest rate at the time was 4.0%.

Explanation / Answer

6) Future value of an Annuity

7)

Present value of rent = 12,000,000 / 0.085

Present value of rent = 141,176,470.6

NPV = 141,176,470.6 - 150,000,000

NPV = -8,823,529.412

Since it has a negative NPV, you should not buy

8)

Present value of annuity = 12,000 * [ 1 - 1 / ( 1 + 0.07)10]] / 0.07

Present value of annuity = 12,000 * 7.023582

Present value of annuity = 84,282.97849

Pay 85K today is better

9)

Present value of prize = 11,828,000 * [ 1 - 1 / ( 1 + 0.04)25]] / 0.04

Present value of prize = 11,828,000 * 15.62208

Present value of prize = 184,777,961.6

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