Question

Humphrey, Inc. is considering purchasing equipment costing $30,000 with a 6-year useful life. The equipment will provide cost savings of $7,300 and will be depreciated straight-line over its useful life with no salvage value. Humphrey, Inc. requires a 10% rate of return. Present Value of an Annuity of 1 Period 8% 9% 10% 11% 12% 15% 6 4.623 4.486 4.355 4.231 4.111 3.784 What is the approximate internal rate of return for this investment?

Answer 1

ANSWER: 12.284%

CALCULATIONS:

	At 8%	At 15%
Present value of cash inflows
[$7,300 x 4.623 present value annuity factor (8%, 6 years)]	$33,748
[$7,300 x 3.784 present value annuity factor (15%, 6 years(]		$27,623
(Less): Initial cost	($30,000)	($30,000)
Net present value	$3,748	($2,377)

IRR:

IRR =

• r1 = higher discount rate chosen
• r2=lower discount rate chosen
• NPVa= NPV at r1
• NPVb=NPV at r2

= 8% + [$3,748/($3,748- (-$2,377)] (15%-8%)

= 8% + [$3,748/($3,748+$2,377)] (15%-8%)

= 8% + ($3,748/$6,125) (7%)

= 8%+ 0.612 (7)

= 8%+4.284

= 12.284%