Question

"What is the DISCOUNTED payback period for an investment of $55,000 with an annual investment income of $9,000 starting at the end of the first year (i=5% annual). Enter your answer in YEARS rounded to the nearest tenth of a year."

Answer 1

$Discounted Payback Period = \ln (1\div (1 - (OI\times i \div CF))) \div \ln (1+i)$

Here, Given Data:

OI = Initial Outflow or investment = $55000

i = rate = 5% = 0.05

CF = Cash inflow or income = $9000

Now, put above values in equation of Discounted Payback Period:

$Discounted Payback Period = \ln (1\div (1 - (55000\times 0.05 \div 9000))) \div \ln (1+0.05)$

$Discounted Payback Period = \ln (1\div (1 - 0.306)) \div \ln (1.05)$

$Discounted Payback Period = \ln (1\div 0.694) \div \ln (1.05)$

$Discounted Payback Period = \ln (1.44) \div \ln (1.05)$

$Discounted Payback Period = 0.3646 \div 0.0488$

• So, the DISCOUNTED payback period is 7.5 YEARS.