Question

A company is evaluating the purchase of Machine A. The new machine would cost $120,000 and would be depreciated for tax purposes using the straight-line method over an estimated ten-year life to its expected salvage value of $20,000. The new machine would require an addition of $30,000 to working capital. In each year of Machine A’s life, the company would reduce its pre-tax costs by $40,000. The company has a 12% cost of capital and is in the 35% marginal tax bracket.

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

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

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

This problem follows Problem #2. It is now five years later. The company did buy Machine A, but just this week Machine B came on the market; Machine B could be purchased to replace Machine A. If acquired, Machine B would cost $80,000 and would be depreciated for tax purposes using the straight-line method over an estimated five-year life to its expected salvage value of$20,000. Machine B would also require $30,000 of working capital but would save an additional $20,000 per year in pre-tax operating costs. Machine A’s salvage value remains $20,000, but it could be sold to-day for $40,000.

1. Identify the incremental cash flows from converting to Machine B
2. Calculate this investment’s net present value (NPV).
3. Calculate this investment’s internal rate of return (IRR).
4. Should the company convert to Machine B? Why or why not?

Answer 1

Investment in Machine A
a.Incremental Cash flows
Initial Investment	-120000	Yr.0
Initial NWC	-30000	Yr.0
NWC recovered	30000	Yr.10
Annual depn. Tax shields(120000-20000)/10*35%	3500	Yrs .1-10
After-tax salvage value(20000*(1-35%))	13000	Yr 10
Annual after-tax reduction in costs(40000*(1-35%)	26000	Yrs .1-10

b.NPV of the Investment--M/c   A
Initial Investment	-120000
Initial NWC	-30000
PV of NWC recovered(30000/1.12^10)	9659.20
PV of depn. Tax shields(120000-20000)/10*35%*5.65022	19775.77
PV of after-tax salvage value(20000*(1-35%)/1.12^10)	4185.65
PV of after-tax reduction in costs(40000*(1-35%)*5.65022)	146905.72
NPV of M/c A Purchase	30526.34

c.IRR of the investment

At IRR,NPV =0, so

0=-120000-30000+(30000/(1+r)^10)+(3500*(1-(1+r)^-10)/r)+(13000/(1+r)^10)+(40000*(1-35%)*(1-(1+r)^-10)/r)

solving the above, for r, we get the IRR as

16.38%

P/A,i=12%, n=10%= 5.65022

Investment in Machine B
A.Incremental Cash flows
Initial Investment	-80000	Yr.5
After-tax Sale value of M/c A (Ref. wkgs.)	50500	Yr.5
Incl.NWC reqd.(30000-30000)	0	Yr.5
Incl. NWC recovered(30000-30000)	0	Yr.10
Incl.Annual depn. Tax shields((80000-20000)/5*35%)-3500 for M/c A	700	Yrs .5-10
Incl.After-tax salvage value--Ignored as M/c A's lost compensated		Yr.10
Incl. Annual after-tax reduction in costs(60000-40000)*(1-35%))	13000	Yrs .5-10

Workings for After-tax Sale value of M/c A
Book Value of M/c A	70000
Sale value at end yr. 5	40000
Loss on sale(70000-40000)	30000
Tax CF saved on loss(30000*35%)	10500
ATCF on sale(40000+10500)	50500

Incremental Cash flow workings	M/c A current CFS		M/c B		Incremental CFs
Initial Investment		Yr.5	-80000	Yr.5	-80000
Initial NWC	-30000	Yr.5	-30000	Yr.5	0
ATCF on sale of M/c A (ref.wkgs.)	0		50500	Yr.5	50500
NWC recovered	30000	Yr.10	30000	Yr.10	0
Annual depn. Tax shields(120000-20000)/10*35% &(80000-20000)/10*35%	3500	Yrs .5-10	4200	Yrs .5-10	700
After-tax salvage value of M/c s A(lost) & B	13000	Yr 10	13000	Yr.10	0
Annual after-tax reduction in costs(40000*(1-35%) & 60000*(1-35%)	26000	Yrs.5-10	39000	Yrs .5-10	13000

B. NPV of the Incremental CFs=

Discounting the incremental CFS ,at 12%

-80000+50500+(700*3.60478)+(13000*3.60478)=

19885.49

C. IRR of the Incremental CFS:

0= -80000+50500+(700*(1-(1+r)^-5)/r)+(13000*(1-(1+r)^-5)/r)

36.72%

D. YES . The company should convert to Machine B

as the NPV of the incremental cash flows is POSITIVE, which will add value to the company.

  P/A,i=12%, n=5%= 3.60478