Question

You have successfully started and operated a company for the past 10 years. You have decided that it is time to sell your company and spend time on the beaches of Hawaii. A potential buyer is interested in your company, but he does not have the necessary capital to pay you a lump sum. Instead, he has offered $800,000 today and annuity payments for the balance. The first payment will be for $250,000 in three months. The payments will increase at 1.6 percent per quarter and a total of 20 quarterly payments will be made. If you require an EAR of 11 percent, how much are you being offered for your company? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

$5,225,417

Step-by-step explanation:

first payment 800000

1 quarter 250000

2 quarters 254000

3 quarters 258064

4 quarters 262193

5 quarters 266388

6 quarters 270650

7 quarters 274981

8 quarters 279380

9 quarters 283851

10 quarters 288392

11 quarters 293006

12 quarters 297694

13 quarters 302458

14 quarters 307297

15 quarters 312214

16 quarters 317209

17 quarters 322284

18 quarters 327441

19 quarters 332680

20 quarters 338003

11% = (1 + i/4)⁴

i = 0.106

quarterly interest = 2.65%

Now we need to determine the present value of this annuity and our discount rate is 2.65%. I will use an excel spreadsheet to determine the present value of the 20 quarterly payments and then add the initial payment.

$4,425,417 + $800,000 = $5,225,417