Question

The owner of a business expects to make a net profit of $21,000 in the end of each year over the next five years and to be able to sell the business at the end of the fifth year for $120,000. The owner of the business also believes that the appropriate annual discount rate is 7%. Calculate the (present) value of the business.

B) A small company received a $80,000 loan at a 7% annual interest rate and the loan must be repaid in 6 equal end-of-year installments. Calculate the amount of the yearly payment.

Answer 1

a). PV of Business = [CF(i) / (1 + r)ⁱ]

=1

= [$21,000 * {(1 - 1.07^-5) / 0.07}] + [$120,000 / (1 + 0.07)⁵]

= [$21,000 * {0.2870 / 0.07}] + [$120,000 / 1.4026]

= [$21,000 * 4.1002] + $85,558.34

= $86,104.15 + $85,558.34 = $171,662.49

b). Yearly Payment = [Loan Amount * r] / [1 - (1 + r)^-n]

= [$80,000 * 0.07] / [1 - (1 + 0.07)^-6]

= $5,600 / 0.3337 = $16,783.66