Question

1. Reel Fast Charters, based in the Bahamas, runs multi-day fishing charters for wealthy anglers. They have been very successful in their first five years in operation and Brian (the owner) is considering adding a second boat. A new 80’ Viking would cost $5,000,000 with another $1,000,000 needed to upgrade the interior to a level that would attract the wealthy clients they desire. The boat would be depreciated straight-line over 15 years, but would be sold at the end of five years, for an estimated $5,000,000. The new boat would generate estimated additional revenue of $2,000,000 per year and would have associated expenses of $625,000. No additional working capital would be necessary. The firm’s tax rate is 30% and the required rate of return is 12%. Calculate the NPV and IRR. Should the new boat be purchased?

Answer 1

SOLUTION:

Profit for each year (cash inflow each year / annuity) = Revenue - Expenses = $2,000,000 - $625,000 = $1,375,000

PV of total cash inflows = (cash inflow each year * PVAF_(12%,5)) + (Salvage value at the end of 5 years * PVF_(12%,5))

= ($1,375,000 * 3.605) + ( $5,000,000 *  0.567) = $4,956,875 + $2,835,000

= $7,791,875

PV of cash outflows = cost of boat + upgradation cost =  $5,000,000 + $1,000,000 = $6,000,000

NPV = PV of cash inflows - PV of cash outflows =  $7,791,875 -  $6,000,000 = $1,791,875

Calculation for IRR

We know at IRR, PV of cash outflows equals PV of total cash inflows or NPV is zero. Since our NPV was positive at rate of return of 12%, we know that our IRR is above 12% for sure. Now we will use trial and error method for finding IRR.

At IRR = 20%

NPV = {(cash inflow each year * PVAF_(20%,5)) + (Salvage value at the end of 5 years * PVF_(20%,5))} - PV of cash outflow

= {($1,375,000 *2.991 ) + ( $5,000,000 *  0.402)} - $6,000,000

= $6,122,625 - $6,000,000

= $122,625

At IRR = 21%

NPV = {(cash inflow each year * PVAF_(21%,5)) + (Salvage value at the end of 5 years * PVF_(21%,5))} - PV of cash outflow

= {($1,375,000 *2.926 ) + ( $5,000,000 *  0.386)} - $6,000,000

= $5,953,250 - $6,000,000

= - $46,750

Since NPV is positive at 20% and negative at 21% IRR lies between 20% and 21%. We will now do interpolation to find the value of IRR.

Interpolation = Lower rate+(NPV at Lower rate / NPV at Lower rate - NPV at Higher rate) X Difference between rate

= 20% + { $122,625 / [$122,625 - (-$46,750)]} * (21%-20%)  

= 20% + 0.724 = 20.724%

Hence, IRR is 20.724%