Question

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $105,510, including freight and installation. Henrie’s estimated the new machine would increase the company’s cash inflows, net of expenses, by $30,000 per year. The machine would have a five-year useful life and no salvage value.

Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using table.

Required:

1. What is the machine’s internal rate of return? (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

2. Using a discount rate of 13%, what is the machine’s net present value? Interpret your results.

3. Suppose the new machine would increase the company’s annual cash inflows, net of expenses, by only $25,735 per year. Under these conditions, what is the internal rate of return? (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

Answer 1

NPV= NET PRESENT VALUE

IRR= INTERNAL RATE OF RETURN

(1)&(2)

internal rate of return is the rate of return at which NPV is zero

present value cash inflow = cash outflow

net present value is difference between present value of cash inflows and cash outflow.

years	cash flow	PV factor at 13%	present value
1-5	30000	3.517 [1/1.13]1+[1/1.13]2+[1/1.13]3+[1/1.13]4+[1/1.13]5	$105,510 [30000*3.517]
0	-105510	1	$-105,510
		Net present value	0	[105,510-105,510]

as at 13% NPV is Zero IRR is 13%

NPV at 13% is ZERO

it means that there will be no benefit no Loss from the new machine.

there are no additional cash inflows over and above the intial investment as the money value of $1 in future is lesser than $1 value today due to time value of money(interest).

(3)we will find NPV at two random rates to find IRR

R1 = 10%

years	cash flow	PV factor at 10%	present value
1-5	$25,735	3.791 [1/1.10]1+[1/1.10]2+[1/1.10]3+[1/1.10]4+[1/1.10]5	$97,561
0	$-105,510	1	$-105,510
		Net present value	$7949	[$97,561-$105,510]

r2=8%

years	cash flow	PV factor at 8%	present value
1-5	$25,735	3.993	$102,760 [25735*3.993]
0	$-105,510	1	$-105,510
		Net present value	$-2,750	[$100,760-$105,510]

NPV1=-$7949

npv 2 =-$2750

irr= R1+ [NPV1 *(R2-R1)]/(NPV1-NPV2)

=0.10 + [-7949 * (0.08-0.10)/(-7949-(-2750)

=0.10 + [-158.98/-5199]

=0.10-0.0305

=6.95

=7%

AT 7% net present value WOULD BE ZERO

=0.10+0.031

=13%