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 $500,000 today and annuity payments for the balance. The first payment will be for $320,000 in three months. The payments will increase at 1.8 percent per quarter and a total of 25 quarterly payments will be made.

 

If you require an EAR of 12 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

You have been offered $500,000 today and rest in 25 quarterly annuities of $320,000 being first payment at the end of 3 months further each payment would increase by 1.8% each quarter.

EAR = 12%

Calculating the Nominal interest rate compounded quarterly using EAR formula:-

where, EAR = 12%

r = Periodic Interest rate

m = no of times compounding in a year = 4

Taking 4-root on both sides,

1.028737 = (1+r/4)

r = 11.4949%

Now, Calculating the Present Value of 25 periodic annuities:-

Where, C= Periodic Payments = $320,000

r = Periodic Interest rate = 11.4949%/4 = 2.873725%

g = growth rate = 1.8%

n= no of periods = 25

Present value = $6,876,185.80

Total amount being offered to you in today terms = $6,876,185.80 + $500,000

= $7,376,185.80