Question

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 1.9 percent per quarter and a total of 25 quarterly payments will be made.
Required:
If you require an EAR of 12 percent, how much are you being offered for your company?

Answer 1

Answer:

[ 250000 / ( 0.97 ) ] * [ 1 - ( (1 +1.9) / (1+ 2.87 ) ^25 ]  + $800000 is the amount being offered

Explanation:

Amount offered today = $800000

First payment (p) = $250000

EAR = 12 percent

payments increase by 1.9 percent per quarter

Total amount of payments = 25 quarterly payments = 6.25 years

note : there are 4 quarters in a year

How much is been offered for the company

APR = (1+ EAR)^(1/n)*n

        = ( 1 +12%)^(1/4)*4 = 11.49%

( interest rate per annum ) = 11.49%

number of compounding interest per annum = 4

interest rate per period (r) = 2.87%

number of periods(n) = 25

growth rate(g) = 1.9%

first we have to calculate the PV of Cash-flows of the 1st payment ( $250000)

pv = [ p / (r-g) ] * [ 1 - [(1 +g ) / (1 + r)]^n ]

    = [ 250000 / ( 0.97 ) ] * [ 1 - ( (1 +1.9) / (1+ 2.87 ) ^25 ]