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 $700,000 today and annuity payments for the balance. The first payment will be for $180,000 in three months. The payments will increase at 2.3 percent per quarter and a total of 30 quarterly payments will be made. If you require an EAR of 10 percent, how much are you being offered for your company

Answer 1

To calculate the total offer for the company, compute the present value of the increasing annuity payments and add the $700,000 initial payment, considering an effective annual rate of 10%.

Step-by-step explanation:

The calculation of how much the company is being offered requires determining the present value of an annuity with increasing payments. The potential buyer has offered $700,000 upfront and a series of 30 quarterly payments, starting at $180,000 and increasing by 2.3% each quarter. These payments need to be discounted back to their present value using the effective annual rate (EAR) of 10%. You must calculate the present value of each payment and sum these up to determine the total present value of the annuity, to which you would then add the initial $700,000 payment to find the total amount being offered for the company.

Answer 2

$5,890,521.80

Step-by-step explanation:

initial payment: 700000

quarter 1: 180000

quarter 2: 184140

quarter 3: 188375

quarter 4: 192708

quarter 5: 197140

quarter 6: 201674

quarter 7: 206313

quarter 8: 211058

quarter 9: 215912

quarter 10: 220878

quarter 11: 225959

quarter 12: 231156

quarter 13: 236472

quarter 14: 241911

quarter 15: 247475

quarter 16: 253167

quarter 17: 258990

quarter 18: 264947

quarter 19: 271040

quarter 20: 277274

quarter 21: 283652

quarter 22: 290176

quarter 23: 296850

quarter 24: 303677

quarter 25: 310662

quarter 26: 317807

quarter 27: 325116

quarter 28: 332594

quarter 29: 340244

quarter 30: 348069

now we must determine the quarterly interest rate:

1.10 = (1 + i)⁴

⁴ √1.10 = ⁴ √(1 + i)⁴

1.024113689 = 1 + i

i = 0.024113689 = 2.4113689% ≈ 2.4114%

Now we need to determine the present value of this annuity and our discount rate is 2.4114%. I will use an excel spreadsheet to determine the present value of the 30 quarterly payments and then add the initial payment.

$5,190,521.80 + $700,000 = $5,890,521.80