Answer
a) 11%--no, 10%--yes, 9%--yes, 8%--yes
b) 10.67%
Work Step by Step
cost of project = 10 million dollars
payoff time = 4 years
payoff value = 15 million dollars
a)
interest rate = 8%
$10000000*(1+.08)^4$
$10000000*1.08^4$
$10000000*1.36048896$
$13,604,889.60$
Since this value is less than the payoff value, then the company should undertake the project.
Interest rate = 9%
$10000000*(1+.09)^4$
$10000000*1.09^4$
$10000000*1.41158161$
$14,115,816.10$
Since this value is less than the payoff value, then the company should undertake the project.
Interest rate = 10%
$10000000*(1+.10)^4$
$10000000*1.1^4$
$10000000*1.4641$
$14,641,000$
Since this value is less than the payoff value, then the company should undertake the project.
Interest rate = 11%
$10000000*(1+.11)^4$
$10000000*1.11^4$
$10000000*1.51807041$
$15,180,704.10$
Since this value is greater than the payoff value, then the company should not undertake the project.
b)
$1000000*(1+x)^4=15000000$
$1000000*(1+x)^4/10000000=15000000/10000000$
$(1+x)^4=1.5$
$\sqrt{(1+x)^4} = \sqrt 1.5$
$(1+x)^2 = 1.224745$
$\sqrt {(1+x)^2} = \sqrt {1.224745}$
$1+x = 1.10668$
$1+x-1=1.10668-1$
$x = .10668$
At an interest rate of 10.668%, the project is at break-even. It is at this interest rate where the project is between profitability and non-profitability.