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# Calculating IRR by interpolation

Hoboken Ferry is elevating two different ferries. The Weehawken and the Hoboken. The economic data is as follows.

Weehawken Hoboken
Initial Investment \$6 million \$8 million
Yearly Revenue \$4 million \$6 million
Annual Maintenance Cost \$2 million \$3 million
Service Life 10 10

a) Calculate the IRR for Weehawken.
Please use interpolation. (Hint: Use i = 30% to 40% for interpolation)

b) Calculate the IRR for Hoboken.

#### Solution Preview

Please refer attached file for better clarity of formulas and table.

Solution:

Net Cash flow in Year 0=initial investment=(\$6,000,000)
Net cash flow in year 1-10=Revenue-Maintenance=2000000
Let us calculate PV of cash flows at various rates (30%, 31%, 32%, ....40%)

Year End Net Cash flow PV @ 30% PV @ 31% PV @ 32% PV @ 40%
n Cn Cn/(1+30%)^n Cn/(1+31%)^n Cn/(1+32%)^n Cn/(1+40%)^n
0 -6,000,000 -6,000,000 -6,000,000 -6,000,000 -6,000,000
1 2,000,000 1,538,462 1,526,718 1,515,152 1,428,571
2 2,000,000 1,183,432 1,165,433 1,147,842 1,020,408
3 2,000,000 910,332 889,644 869,577 728,863
4 2,000,000 700,256 679,117 658,771 520,616
5 2,000,000 538,658 518,410 499,069 371,869
6 2,000,000 414,352 395,733 378,082 265,621
7 2,000,000 318,733 302,086 286,426 189,729
8 2,000,000 245,179 230,600 216,989 135,521
9 2,000,000 ...

#### Solution Summary

Solution describes the steps to calculate IRR by interpolation.

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