Question

OpenSeas, Inc. is evaluating the purchase of a new cruise ship. The ship would cost $505 ?million, but would operate for 20 years. OpenSeas expects annual cash flows from operating the ship to be $70.1 million? (at the end of each? year) and its cost of capital is 11.9%

a. Prepare an NPV profile of the purchase using discount rates of 2.0%?, 11.5% and 17.0%. b. Identify the IRR on a graph. c. Is the purchase attractive based on these? estimates?

d. How far off could? OpenSeas' cost of capital estimate be before your purchase decision would? change? ?(NOTE: Subtract the discount rate from the actual IRR. Use Excel to compute the actual? IRR.)

Answer 1

Part A)

NPV can be calculated with the use of following formula:

NPV = Initial Investment + Annual Cash Flow Year 1/(1+Discount Rate)^1 + Annual Cash Flow Year 2/(1+Discount Rate)^2 + Annual Cash Flow Year 3/(1+Discount Rate)^3 + Annual Cash Flow Year 4/(1+Discount Rate)^4 + Annual Cash Flow Year 5/(1+Discount Rate)^5 + Annual Cash Flow Year 6/(1+Discount Rate)^6 + Annual Cash Flow Year 7/(1+Discount Rate)^7 + Annual Cash Flow Year 8/(1+Discount Rate)^8 + Annual Cash Flow Year 9/(1+Discount Rate)^9 + Annual Cash Flow Year 10/(1+Discount Rate)^10 + Annual Cash Flow Year 11/(1+Discount Rate)^11 + Annual Cash Flow Year 12/(1+Discount Rate)^12 + Annual Cash Flow Year 13/(1+Discount Rate)^13 + Annual Cash Flow Year 14/(1+Discount Rate)^14 + Annual Cash Flow Year 15/(1+Discount Rate)^15 + Annual Cash Flow Year 16/(1+Discount Rate)^16 + Annual Cash Flow Year 17/(1+Discount Rate)^17 + Annual Cash Flow Year 18/(1+Discount Rate)^18 + Annual Cash Flow Year 19/(1+Discount Rate)^19 + Annual Cash Flow Year 20/(1+Discount Rate)^20

Using the values provided in the question in the above formula, we can calculated NPV at different discount rates as below:

NPV (2%) = -505 + 70.1/(1+2%)^1 + 70.1/(1+2%)^2 + 70.1/(1+2%)^3 + 70.1/(1+2%)^4 + 70.1/(1+2%)^5 + 70.1/(1+2%)^6 + 70.1/(1+2%)^7 + 70.1/(1+2%)^8 + 70.1/(1+2%)^9 + 70.1/(1+2%)^10 + 70.1/(1+2%)^11 + 70.1/(1+2%)^12 + 70.1/(1+2%)^13 + 70.1/(1+2%)^14 + 70.1/(1+2%)^15 + 70.1/(1+2%)^16 + 70.1/(1+2%)^17 + 70.1/(1+2%)^18 + 70.1/(1+2%)^19 + 70.1/(1+2%)^20 = $641.24 million

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NPV (11.5%) = -505 + 70.1/(1+11.5%)^1 + 70.1/(1+11.5%)^2 + 70.1/(1+11.5%)^3 + 70.1/(1+11.5%)^4 + 70.1/(1+11.5%)^5 + 70.1/(1+11.5%)^6 + 70.1/(1+11.5%)^7 + 70.1/(1+11.5%)^8 + 70.1/(1+11.5%)^9 + 70.1/(1+11.5%)^10 + 70.1/(1+11.5%)^11 + 70.1/(1+11.5%)^12 + 70.1/(1+11.5%)^13 + 70.1/(1+11.5%)^14 + 70.1/(1+11.5%)^15 + 70.1/(1+11.5%)^16 + 70.1/(1+11.5%)^17 + 70.1/(1+11.5%)^18 + 70.1/(1+11.5%)^19 + 70.1/(1+11.5%)^20 = $35.46 million

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NPV (17%) =  -505 + 70.1/(1+17%)^1 + 70.1/(1+17%)^2 + 70.1/(1+17%)^3 + 70.1/(1+17%)^4 + 70.1/(1+17%)^5 + 70.1/(1+17%)^6 + 70.1/(1+17%)^7 + 70.1/(1+17%)^8 + 70.1/(1+17%)^9 + 70.1/(1+17%)^10 + 70.1/(1+17%)^11 + 70.1/(1+17%)^12 + 70.1/(1+17%)^13 + 70.1/(1+17%)^14 + 70.1/(1+17%)^15 + 70.1/(1+17%)^16 + 70.1/(1+17%)^17 + 70.1/(1+17%)^18 + 70.1/(1+17%)^19 + 70.1/(1+17%)^20 = -$110.49 million

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NPV Profile

Discount Rate	NPV (Millions)
2%	$641.24
11.50%	$35.46
17%	-$110.49

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Part b)

The graph based on the NPV profile prepared above is given as below:

The IRR estimate would be close to 13% as can be seen in the above graph. The NPV line touches X-axis after a discount rate of 11.5% and close to 13%.

Actual IRR is calculated with the use of EXCEL as below:

where IRR = IRR(B2:B22) = 12.58%

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Part c)

To answer this part, we will have to calculate NPV at the cost of capital of 11.9% as below:

NPV at 11.9% = -505 + 70.1/(1+11.9%)^1 + 70.1/(1+11.9%)^2 + 70.1/(1+11.9%)^3 + 70.1/(1+11.9%)^4 + 70.1/(1+11.9%)^5 + 70.1/(1+11.9%)^6 + 70.1/(1+11.9%)^7 + 70.1/(1+11.9%)^8 + 70.1/(1+11.9%)^9 + 70.1/(1+11.9%)^10 + 70.1/(1+11.9%)^11 + 70.1/(1+11.9%)^12 + 70.1/(1+11.9%)^13 + 70.1/(1+11.9%)^14 + 70.1/(1+11.9%)^15 + 70.1/(1+11.9%)^16 + 70.1/(1+11.9%)^17 + 70.1/(1+11.9%)^18 + 70.1/(1+11.9%)^19 + 70.1/(1+11.9%)^20 = $21.91 million

Yes, the purchase is attractive based on these estimates as the NPV is positive at the cost of capital.

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Part d)

The cost of capital estimate can change by .68% (12.58% - 11.9%) before the purchase decision would? change. Therefore, if the cost of capital increases by 1%, the purchase decision would change.