Question

The Titanic Shipbuilding Company has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of $265,000 at the end of each of the next two years. At the end of the third year the company will receive payment of $625,000. Assume the IRR of this option exceeds the cost of capital.

The company can speed up construction by working an extra shift. In this case, there will be a cash outlay of $575,000 at the end of the first year, followed by a cash payment of $625,000 at the end of the second year. Use the IRR rule to show the (approximate) range of opportunity costs of capital at which the company should work the extra shift. (Enter your answers as a percent rounded to 2 decimal places. Enter the smallest percent first.)

The company should work the extra shift if the cost of capital is between  % and  %

Answer 1

The company should work extra shift if the cost of capital is between 22.46% and 64.64%

Calculations and explanations:

The cash flow scenario for the 2 situations are:

Year	Projected schedule	Accelerated shift
1	-265,000.00	-575,000.00
2	-265,000.00	625,000.00
3	625,000.00

We can use incremental analysis over here:

	c1	c2	c3
Projected schedule	-265,000.00	-265,000.00	625,000.00
Accelerated shift	-575,000.00	625,000.00
Incremental flows	-310,000.00	890,000.00	-625,000.00

We now need to find IRRs of the incremental flows shown above. Let the IRR be x.

Thus -310,000/(1+x) + 890,000/(1+x)^2 - 625,000/(1+x)^3 = 0

Now let 1+x be y

So, -310,000/y + 890,000/y^2 - 625,000/y^3 = 0

or, -310,000y^2 + 890,000y - 625,000 = 0

This is a quadratic equation in which a = -310,000, b = 890,000 and c = -625,000

So, y = [-b+-(b^2 - 4ac)^0.5]/2a

= [-890,000+/(890,000^2 - 4*-310,000*-625,000)^0.5]/2*-310,000

Solving we get y as 1.646398 or 1.224569

Now y = 1+x or x = y-1. So x will be either 0.646398 or 0.224569

The company should work extra shift if the cost of capital is between 22.46% and 64.64%