Question

Degnan Dance Company, Inc., a manufacturer of dance and exercise apparel, is considering replacing an existing piece of equipment with a more sophisticated machine.The following information is given.

Exsting machine/ proposed machine
$100,000/ $150,000
Purchased 2 years ago/ Installation $20,000
Depreciation using MACRS over a 5-year recover schedule/ Depreciation - the MACRS
Current market value = $105,000/ 5 year recvery schedule will be used
Five year usable life remaining/ five year usable life expected

Earnings before depreciation and taxes:
Year/ Existing machine/ proposed machine
1/ $160,000/ $170,000
2/$150,000/ $170,000
3/$140,000/$170,000
4/$140,000/$170,000
5$140,000/$170,000

The firm pays 40 percent taxes on ordinary income and capital gains. Degnan’s cost of capital is 8%.

Set up a spreadsheet to compute:
1. The initial investment,
2. The incremental annual cash flows, and
3. The net present value.
4. Should Degnan make the investment in the sophisticated machine? Why?

Answer 1

NPV.METHODThe required rate of return is 10%Incremental cash flows:Proposed machine:Initial cash flows: Purchase price + installation = $170,000Operating cash flows:

Using a 5-yr MACRS schedule, depreciation for the proposed machine for 5 years is:

Yr.1:170000 * 0.2 = 34000

2: 170000 * 0.32 = 54400

3:32640

4:19580

5:19580

OCFs:Yr12345

EBDepr170000170000170000170000 170000

-Depr34000544003264019580 19580

EBIT136000115600137360150420 150420

-taxes54400462405494860168 60168

+Depr34000544003264019580 19580

OCF115600123760115052109832 109832

Terminal cash flow:

Sale of proposed machine (at book value):

Book value = 170000 – 34000 – 54400 – 32640 – 19580 – 19580 = 9800

Existing machine:

Sale of existing machine (included in initial cash flows):

Book value = 100000 – (100000 * 0.2) – (100000 * 0.32) =48000

Cash flow from sale: 105000 – (105000 – 48000) * 0.4 = 82200

Operating cash flows lost:

The existing machine is to be used for 5 more years:

Depreciation:

Yr.1:100000 * 0.192 =19200

2: 100000 * 0.1152 = 11520

3: 100000 * 0.1152 = 11520

4: 100000 * 0.0576 = 5760

5: 0

OCFs:Yr12345

EBDepr160000150000140000140000 140000

-Depr1920011520115205760 0

EBIT140800138480128480 134240140000

-taxes56320553925139253696 56000

+Depr1920011520115205760 0

OCF103680946088860886304 84000

NPV:

(-170000 + 82200)+(115600 – 103680)/1.1

+ (123760 – 94608)/1.1^2 + (115052 – 88608) /1.1^3 +(109832 – 86304)/1.1^4

+ (109832 + 9800 – 84000) /1.1^5= 5191

ACCEPT