Question

OpenSeas, Inc., is evaluating the purchase of a new cruise ship. The ship will cost $500 million, and will operate for 20 years. OpenSeas expects annual cash flows from operating the ship to be $70 million and its cost of capital is 12%.

a. Prepare a NPV profile of the purchase. Do from rate 0% to 20% (please show me the formula you use, I have been trying to figure it out and cant)

b. Identify the IRR on the graph or calculate it from the data.

c. Should OpenSeas proceed with the purchase?

d. How far off could OpenSeas' cost of capital estimate be before your purchase decision would change?

Answer 1

a.

Project Life = 20 years

Initial Investment = $ 500 Million

Cost of Capital(i) = 12%

Annual Cash Inflows = 70 Million

Computation of PV of Cash Inflows

PV of Cash Inflows = [$ 70 Million* PVAF(i%, 20yrs)]

Computation of NPV (E = D - A)

NPV = PV of Cash Inflows - PV of Cash Out flows

Rate (i)	PVAF(i%,20yrs)	Intial Cash outflow	Annual Cash Outflow	PV of Cash Inflow	NPV
A	B	C	D	E = D x B	F = E - C
1%	18.04555	$        500,000,000	$        70,000,000	$ 1,263,188,707.64	$    763,188,707.64
2%	16.35143	$        500,000,000	$        70,000,000	$ 1,144,600,334.12	$    644,600,334.12
3%	14.87747	$        500,000,000	$        70,000,000	$ 1,041,423,240.23	$    541,423,240.23
4%	13.59033	$        500,000,000	$        70,000,000	$      951,322,844.15	$    451,322,844.15
5%	12.46221	$        500,000,000	$        70,000,000	$      872,354,723.98	$    372,354,723.98
6%	11.46992	$        500,000,000	$        70,000,000	$      802,894,485.30	$    302,894,485.30
7%	10.59401	$        500,000,000	$        70,000,000	$      741,580,997.19	$    241,580,997.19
8%	9.818147	$        500,000,000	$        70,000,000	$      687,270,318.52	$    187,270,318.52
9%	9.128546	$        500,000,000	$        70,000,000	$      638,998,196.84	$    138,998,196.84
10%	8.513564	$        500,000,000	$        70,000,000	$      595,949,460.38	$      95,949,460.38
11%	7.963328	$        500,000,000	$        70,000,000	$      557,432,968.22	$      57,432,968.22
12%	7.469444	$        500,000,000	$        70,000,000	$      522,861,053.70	$      22,861,053.70
13%	7.024752	$        500,000,000	$        70,000,000	$      491,732,610.46	$      (8,267,389.54)
14%	6.623131	$        500,000,000	$        70,000,000	$      463,619,138.61	$    (36,380,861.39)
15%	6.259331	$        500,000,000	$        70,000,000	$      438,153,203.16	$    (61,846,796.84)
16%	5.928841	$        500,000,000	$        70,000,000	$      415,018,862.97	$    (84,981,137.03)
17%	5.627767	$        500,000,000	$        70,000,000	$      393,943,713.53	$ (106,056,286.47)
18%	5.352746	$        500,000,000	$        70,000,000	$      374,692,254.80	$ (125,307,745.20)
19%	5.100862	$        500,000,000	$        70,000,000	$      357,060,349.50	$ (142,939,650.50)
20%	4.86958	$        500,000,000	$        70,000,000	$      340,870,581.34	$ (159,129,418.66)

(b)

Computation of IRR
At IRR, PV of Cash Inflows = PV of Cash Outflows , i.e., NPV =0
At i = 12%, NPV is positive, and at i = 13%. NPV is negative
Hence, IRR will be inbetween 12% and 13%
The exact rate can be obtained by Interpolation.
IRR = [12+($ 522,861,053.70 - $ 500,000,000)/($ 522,861,053.70 - $ 491,732,610.46)]*(13-12)
IRR =	12.73%

(c) Yes, Openseas should proceed with the project, as the NPV is Positive (i.e., PV of Cash inflows are higher than PV of Cash Outflows) and the Internal Rate of Return is greater than the Cost of Capital.

(d) Tha maximum cost of capital for this project is 12.73% (i.e., IRR of the Project), beyond which the project will have Negative NPV and hence unviable to accept the project.

Computation of PVAF:

PVAF(i%,n periods) =[1- ((1+i)^-n)]/i