Question

(Organizing cash flows, NPV, IRR) A company is evaluating the purchase of Machine X to improve product quality. The new machine would cost $1,000,000 and would be depreciated for tax purposes using the straight-line method over an estimated seven-year life to its expected salvage value of $125,000. The new machine would require an addition of $100,000 to working capital. In each year of Machine X’s life, the company would increase its pretax receipts by $400,000. The company has an 11% cost of capital and is in the 35% marginal tax bracket.

a. Identify the incremental cash flows from investing in Machine X.

b. Calculate the investment’s net present value (NPV).

c. Calculate the investment’s internal rate of return (IRR).

d. Should the company purchase Machine X? Why or why not?

Answer 1

Answer - a

Statement showing cash flows

Amount ($)

Particulars	Working	Year 1 to 7
Increase in receipts	Given	400,000
Depreciation	($1,000,000 - $125,000) / 7	-125,000
Profit before tax		275,000
Tax	35% of Profit before tax	-96,250
Profit after tax		178,750
Depreciation	Add back	125,000
Cash Flow		303,750

Answer - b

Net present value can be calculated using above calculated cash flows and using given discount rate of 11% which is the cost of capital of the company.

Statement showing Net Present Value

Amount ($)

Year	Particulars	Notes / Working	Amount (A)	Discount Factor @ 11% (B)	Present Value         (A * B)
0	Machine X cost	Given	-1,000,000	1	-1,000,000
0	Increase in Working Capital	Given	-100,000	1	-100,000
1 to 7	Cash Flow	Calculated above	303,750	4.7122	1 431,330
7	Salvage value of Machine X	Given	125,000	0.4817	60,207
7	Working Capital realization	Given	100,000	0.4817	48,166
	Net Present Value	439,703

Answer - c

For calculating  investment’s internal rate of return (IRR) we must have two NPVs one positive and another negative so as to interpolate the IRR.

Let us take the discount rate of 22% to calculate another NPV

Year	Particulars	Notes / Working	Amount (A)	Discount Factor @ 22% (B)	Present Value         (A * B)
0	Machine X cost	Given	-1,000,000	1	-1,000,000
0	Increase in Working Capital	Given	-100,000	1	-100,000
1 to 7	Cash Flow	Calculated above	303,750	3.4155	1,037,460
7	Salvage value of Machine X	Given	125,000	0.2486	31,074
7	Working Capital realization	Given	100,000	0.2486	24,859
	Net Present Worth	-6,607

Hence, NPV is negative at discount rate of 22%

Now, let us interpolate the IRR using the below mentioned formula:

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] * Difference of rates

Where -

Lower rate is 11%

Difference of rates is 11% (22% - 11%)

Lower rate NPV is $439,703 (calculated in Answer-b above)

Higher rate NPV is -$6,607 (calculated above)

On putting these figures in the above formula, we get -

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] * Difference of rates

IRR = 11 + [$439,703 / ($439,703 + $6,607)] * 11

IRR = 11 + [$439,703 / $446,310] * 11

IRR = 11 + 10.84

IRR = 21.84%

Answer - d

As per the required rate of return of the company of 11%, the company should purchase Machine X, since it generates a positive net present value of $439,703 using the discount rate of 11%. The internal rate of return of the investment also indicates that the investment would generate more return than the cost of capital of the company, hence company should purchase Machine X.