Question

A firm is considering an investment of $480,000 in new equipment to replace old equipment with a book value of $95,000 and a market value of $63,000. If the firm replaces the old equipment with new equipment, it expects to save $120,000 in operating costs the first year. The amount of savings will grow at a rate of 8 percent per year for each of the following five years. Both pieces of equipment belong to asset class 8, which has a CCA rate of 20 percent. The salvage values of both the old equipment and the new equipment at the end of six years are $11,000 and $78,000, respectively. There are other assets in the asset class when the project terminates. In addition, replacement of the old equipment with the new equipment requires an immediate increase in net working capital of $50,000. The firm’s marginal tax rate is 35 percent and cost of capital is 11 percent.

a) What is the initial after-tax cash flow?

b) What is the present value of the incremental CCA tax savings?

c) What is the present value of the incremental after-tax operating cash flows?

d) What is the present value of the incremental ending after-tax cash flow?

e) What is the NPV of the replacement project?

Answer 1

SOLUTION:-

a). Initial after tax cash flow is calculated as follows:-

     Initial investment in equipment $(480000)    cash outflow

       Initial investment in working capital $(50000)      cash outflow

Cash received from the disposal of old machine (i) $75800 cash inflow

  Initial after tax cash flow $(454200) cash outflow

note i:- calculation of Cash received from the disposal of old machine:-

cash recieved from the sale $63000

add tax gain on the loss on sale    =( book value-sale value) * tax rate

= ($95000-$63000)* 35%

=$12800

Cash received from the disposal of old machine = $75800

b). present value of the incremental CCA tax savings

CCA Calculation

• First Year  $240000 (half of $480000) x 20% = $48000 expense claim. This leaves a value of $432000 next year.
• Second Year $432000 x 20% = $86400 CAA. This leaves a value of $345600 next year.
• Third Year $345600 x 20% = $69120 CAA. This leaves a value of $276480 next year.
• Forth Year $276480 x 20% = $55296 CAA . This leaves a value of $221184 next year.
• Fifth Year $221181 x 20% = $44237 CAA . This leaves a value of $176944 next year.
• Sixth Year $176944 x 20% = $35389 CAA.   This leaves a book value of $141555

	year 1	year 2	year 3	year 4	year 5	year 6
CCA (1)	$48000	$86400	$69120	$55296	$44237	$35389
CCA tax savings (1* .35)	$16800	$30240	$24192	$19354	$15483	$12386
PV of $1 Factor for 11%	0.901	0.812	0.731	0.659	0.593	0.535
Discounted Cash Flow	$15136.8	$24555	$17684	$12754	$9181	$6627

present value of the incremental CCA tax savings= sum of Discounted Cash Flow of each year

=$85937.8

c).present value of the incremental after-tax operating cash flows

	year 1	year 2	year 3	year 4	year 5	year 6
before tax operating cash flows (B)	$120000	$129600	$139968	$151165	$163259	$176319
less Tax (T)	42000	45360	48988.8	52907.9	57140.54	61712
after tax operating cash flows (B-T)	78000	84240	90979.2	98257.54	106118.1	114607
PV of $1 Factor for 11%	0.901	0.812	0.731	0.659	0.593	0.535
Discounted Cash Flow	70278	68402.88	66505.8	64751.72	62928.06	61315.06

Calculations made for above table:-

  before tax operating cash flow of year 1= cash flow of year 0 * 108%

present value of the after-tax operating cash flows= sum of Discounted Cash Flow of each year

=$394182

D).present value of the incremental ending after-tax cash flow

Calcutations:-

after tax operating cash flows of year 6 $114607

add CCA tax savings of year 6 $12386

add working capital relase $50000

add After-Tax Cash Flow from Sale of New Machine (i) $65159

less After-Tax Cash Flow Not Received from Sale of Old Machine $(7150)

total $235002

multiplied by PV of $1 Factor for 11%   0.535

present value of the incremental ending after-tax cash flow = $125726

note i

  After-Tax Cash Flow from Sale of New Machine= before-Tax Cash Flow from Sale of New Machine - tax rate

= $100244- 35%

= $65159

before-Tax Cash Flow from Sale of New Machine= cash recieved from sale + tax gain on loss on sale

= $78000+  ($141555-$78000)*.35

= $78000+ $22244

=$100244