Question

A company is considering purchasing a backhoe that will cost $110,000. It will last 6 years with a salvage value of $20,000 and will reduce maintenance and operating costs by $30,000 per year. The after-tax MARR of the company is 9% and the tax rate is 55%.

a) What is the exact after-tax IRR (%) for this investment?!

b) What is the approximate after-tax IRR (%)?1

Answer 1

Internal Rate of Return (IRR) for an investment is the rate at which the Net Present Value (NPV) of the investment is ZERO.

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows.

IRR is calculated manually by selecting two arbitrary rates at which the NPV of the investment is higher than and lower than zero respectively. Select an arbitrary discount rate to calculate NPV at such a rate by discounting cash flows by that rate and label the rate as r1 and NPV as NPV1. As we know that NPV is inversely related to the Discounting rate i.e. if we keep on increasing the discounting rate then the respective NPV will keep on decreasing. If NPV1 is positive then select a rate higher than r1 where NPV is negative, similarly, if NPV1 is negative then select a rate lower than r1 where NPV is positive.and label the rate as r2 and respective NPV as NPV2. Then IRR is calculated by substituting the respective values in the following formula:

Where r1 is the rate at which NPV is positive and r2 is the rate at which NPV is negative and so on.

In the given question,

The Cost of purchasing backhoe = $110,000

Life of backhoe = 6Years

Salvage value of backhoe = $20,000

Hence,

Depreciation p.a.= (Cost of Machine - Salvage Value) / Life of Machine

Depreciation p.a.= ($110,000-$20,000) / 6

= $15,000

The reduction in maintenance and operating cost of $30,000 p.a. is considered to be as incremental cash inflow.

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Incremental Cash Inflow		$30,000	$30,000	$30,000	$30,000	$30,000	$30,000
Less: Depreciation		($15,000)	($15,000)	($15,000)	($15,000)	($15,000)	($15,000)
Income Before Tax		$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
Less: Tax @ 55%		($8,250)	($8,250)	($8,250)	($8,250)	($8,250)	($8,250)
Net Income		$6,750	$6,750	$6,750	$6,750	$6,750	$6,750
Add: Depreciation		$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
Net Operating Cash Flows		$21,750	$21,750	$21,750	$21,750	$21,750	$21,750
Add: Terminal Cash Flow							$20,000
Initial Investment Outlay	($110,000)
Net Cash Flows	($110,000)	$21,750	$21,750	$21,750	$21,750	$21,750	$41,750

Let's Calculate NPV at r1=8% and r2=9%

Period	CashFlow	PV Factor @ 8%	PV @ 8%($)	PV Factor @ 9%	PV @ 9%($)
0	-110000	1	-110000	1	-110000
1	21750	0.925926	20138.89	0.917431	19954.13
2	21750	0.857339	18647.12	0.84168	18306.54
3	21750	0.793832	17265.85	0.772183	16794.99
4	21750	0.73503	15986.9	0.708425	15408.25
5	21750	0.680583	14802.68	0.649931	14136.01
6	41750	0.63017	26309.58	0.596267	24894.16
NPV			3151.025		-505.924

IRR= 8%+(3151.025*(9-8))/(3151.025-(-505.924))

IRR= 8.8616%