Question

Net Present Value Method for a Service Company

Carnival Corporation has recently placed into service some of the largest cruise ships in the world. One of these ships, the Carnival Breeze, can hold up to 3,600 passengers, and it can cost $800 million to build. Assume the following additional information:

There will be 330 cruise days per year operated at a full capacity of 3,600 passengers.

The variable expenses per passenger are estimated to be $110 per cruise day.

The revenue per passenger is expected to be $250 per cruise day.

The fixed expenses for running the ship, other than depreciation, are estimated to be $20,000,000 per year.

The ship has a service life of 10 years, with a residual value of $200,000,000 at the end of 10 years.

Present Value of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 0.890 0.826 0.797 0.756 0.694 3 0.840 0.751 0.712 0.658 0.579 4 0.792 0.683 0.636 0.572 0.482 5 0.747 0.621 0.567 0.497 0.402 6 0.705 0.564 0.507 0.432 0.335 7 0.665 0.513 0.452 0.376 0.279 8 0.627 0.467 0.404 0.327 0.233 9 0.592 0.424 0.361 0.284 0.194 10 0.558 0.386 0.322 0.247 0.162

Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.352 2.991 6 4.917 4.355 4.111 3.784 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192

a. Determine the annual net cash flow from operating the cruise ship.

Revenues	$
Variable expenses
Fixed expenses
Annual net cash flow	$

b. Determine the net present value of this investment, assuming a 12% minimum rate of return. Use the present value tables provided above. If required, round to the nearest dollar.

Present value of annual net cash flows	$
Present value of residual value
Total present value	$
Amount to be invested
Net present value	$

Feedback

a. Subtract the variable expenses and fixed expenses (except depreciation) from the revenues (number of passengers x rate x number of days).

b. Add the present value of the annual net cash flows (annual net cash flows multiplied by the present value of an annuity factor for 10 periods at 12%) and the present value of the residual value. Subtract the amount to be invested.

Answer 1

Solution:

Part a --- Annual Net Cash Flow from operating the cruise ship

	$$
Revenues (3600 Passengers x $250 x 330 days)	$297,000,000
(-) Variable Expenses (330*3600*110)	$130,680,000
(-) Fixed Expenses other then Depreciation (Since depreciation is a non cash item)	$20,000,000
Annual Net Cash Flow	$146,320,000

Part b – Net Present Value

	$$
Present Value of Annual Net Cash Flows ($146,320,000 * PVIFA (12%, 10) i.e. 5.65)	$826,708,000
(+) Present Value of residual value ($200,000,000*PVIF (12%, 10) i.e. 0.322)	$64,400,000
Total Present Value	$891,108,000
(-) Amount to be Invested	$800,000,000
Net Present Value	$91,108,000

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