Question

ABC Company sold the rights to use one of their patented processes that will result in them receiving cash payments of $10,000 at the end of every six months for each of the next five years and a lump sum payment of $20,000 at the end of the sixth year. Calculate the total present value of these payments assuming the interest rate is 10% compounded semi-annually.

Answer 1

$77,217

$11,289

Step-by-step explanation:

Fist we will calculate the present value of $10,000 payment

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity. The value of the annuity is also determined by the present value of annuity payment.

Formula for Present value of annuity is as follow

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

Where

P = Annual payment = $10,000

r = rate of return = 10% / 2 = 5%

n = number of period = 5 years x 2 semiannual payments per year = 10 payments

PV of annuity = $10,000 x [ ( 1- ( 1+ 0.05 )^-10 ) / 0.05 ]

PV of Annuity = $77,217

Now we will use the discounting method to calculate the present value of lump sum payment of $20,000

Present value = Future value x Present value factor

PV = FV x ( 1 + r )^-n

PV = $20,000 x ( 1 + 0.1 )^-6

PV = $11,289