Consider a project that costs $1 million today but yields no returns for several years.Once the project becomes productive,it yields $250,000 annually forever.Suppose two firms are examining this project,a Japanese firm with a cost of capital of 7% and a U.S.firm with a cost of capital of 13%.Approximately how many more years than the U.S.firm would the Japanese firm be willing to wait until the project starts generating cash?

Question

Quizplus · Accepted Answer

To calculate the present value of the perpetuity, we can use the formula: 
PV = annual cash flow / cost of capital
For the Japanese firm: 
PV = $250,000 / 0.07 = $3,571,429. 
So the present value of the project for the Japanese firm is $3,571,429. 
For the U.S.firm: 
PV = $250,000 / 0.13 = $1,923,077. 
So the present value of the project for the U.S.firm is $1,923,077. 
The difference between the present values is: 
$3,571,429 - $1,923,077 = $1,648,352. 
This means that the Japanese firm values the project $1,648,352 more than the U.S. firm. 
To find out how many years the Japanese firm would be willing to wait for the project to start generating cash, we can use the formula for the present value of a lump sum: 
PV = FV / (1 + r)^n
where FV is the future value (in this case, $1 million), r is the cost of capital (0.07 for the Japanese firm), and n is the number of years. We want to solve for n: 
$3,571,429 = $1,000,000 / (1 + 0.07)^n
n = ln($1,000,000 / $3,571,429) / ln(1 + 0.07) = 14.19 years
So the Japanese firm would be willing to wait approximately 14 years longer than the U.S. firm for the project to start generating cash flows. Therefore, the answer is A) 14 years.

Consider a Project That Costs $1 Million Today but Yields