Question

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $125,080, including freight and installation. Henrie’s has estimated that the new machine would increase the company’s cash inflows, net of expenses, by $40,000 per year. The machine would have a five-year useful life and no salvage value.

Required: 1. Compute the machine’s internal rate of return. (Round your 'IRR' answer to nearest whole percentage.)

2. Compute the machine’s net present value. Use a discount rate of 18%.

3. Suppose that the new machine would increase the company’s annual cash inflows, net of expenses, by only $34,700 per year. Under these conditions, compute the internal rate of return. (Round your 'IRR' answer to nearest whole percentage.)

Answer 1

1) IRR is the rate at which NPV = 0

Total cash outflow= PV of cash inflows

we will use discount factors at random rates for calculating PV of cash inflows

Suppose the rate is 10%

PVAF(10%,5 years)

Years	Cash flows	PV factor	PV
0	($125,080)	1	($125,080) [125,080*1]
1-5	$40,000	3.7908 [1/1.10]^1+[1/1.10]^2+[1/1.10]^3+[1/1.10]^4+[1/1.10]^5	$151,631.50 [40,000*3.7908]

NPV =PV of cash inflows-Cash outflow

$151631-$125,080

=$26,551

Suppose the rate is 15%

Years	Cash flows	PV factor	PV
0	($125,080)	1	($125,080) [125,080*1]
1-5	$40,000	3.3522 [1/1.15]^1+[1/1.15]^2+[1/1.15]^3+[1/1.15]^4+[1/1.15]^5	134,086 [40,000*3,3522]

NPV = $134,086-125,080

=$9006

=

=0.10+0.07569

=18% [ROUND OFF TO NEAREST DOLLAR]

at 18% NPV WOULD BE ZERO

2] NPV AT 18%

Years	Cash flows	PV factor	PV
0	($125,080)	1	($125,080) [125,080*1]
1-5	$40,000	3.127 [1/1.18]^1+[1/1.18]^2+[1/1.18]^3+[1/1.18]^4+[1/1.18]^5	125,080

NPV = 125,080-125,080

=$0

3]

Suppose the rate is 10%

PVAF(10%,5 years)

Years	Cash flows	PV factor	PV
0	($125,080)	1	($125,080) [125,080*1]
1-5	$34,700	3.791 [1/1.10]^1+[1/1.10]^2+[1/1.10]^3+[1/1.10]^4+[1/1.10]^5	$131,548

NPV =PV of cash inflows-Cash outflow

$131,548-$125,080

=$6,468

Suppose the rate is 15%

Years	Cash flows	PV factor	PV
0	($125,080)	1	($125,080) [125,080*1]
1-5	$34,700	3.3522 [1/1.15]^1+[1/1.15]^2+[1/1.15]^3+[1/1.15]^4+[1/1.15]^5	$116,321

NPV = $116,321-125,080

=-$8,759

=

=0.10+0.02

=12% [ROUND OFF TO NEAREST DOLLAR]

at 12% NPV WOULD BE ZERO

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