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 \$350,000 in three months. The
payments will increase at 1.9 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.)
Value of offer $ 8,406,073.00
Explanation
The payments are a growing annuity, so we use the equation for the present value of a growing
annuity. The payment growth rate is 1.9 percent and the EAR is 12 percent. Since the payments are
quarterly, we need the APR, which is:
EAR = (1 - APR/m)$^m$-1
12 = (1 - APR/4)$^4$-1
APR = .1149, or 11.49%
And the quarterly interest rate is:
Quarterly rate = 11.49%/4
Quarterly rate = 2.87%
So, the present value of the payments is:
PV = C\frac{1}{(r-g)} - \frac{1}{(r-g)}\times\frac{(1+g)}{(1+r)}^n
PV = \$350,000\left(\frac{1}{(.0287-.019)} - \frac{1}{(.0287-.019)} \times \frac{(1.019)}{(1-.0287)}^{25}\right)
PV = \$7,606,073.43
When we add the payment made today, we get:
Value of offer = \$7,606,073.43 + 800,000
Value of offer = \$8,406,073.43
