Question

Signs For Fields Machinery Ltd. is considering the replacement of some technologically obsolete machinery with the purchase of a new machine for $72,000. Although the older machine has no market value, it could be expected to perform the required operation for another 10 years. The older machine has an unamortized capital cost of $27,000. The new machine with the latest in technological advances will perform essentially the same operations as the older machine but will effect cost savings of $17,500 per year in labour and materials. The new machine is also estimated to last 10 years, at which time it could be salvaged for $11,500. To install the new machine will cost $7,000. Signs For Fields has a tax rate of 30 percent, and its cost of capital is 15 percent. For accounting purposes, it uses straight-line amortization, and for tax purposes its CCA is 20 percent.

a. Should Signs for Fields Machinery purchase the new machine?

b. If the old machine has a current salvage value of $9,000, Should Signs For Fields purchase the new machine?

c. Calculate the IRR and PI for part a.

Answer 1

a) In the given question, Net Present Value of the new equipment needs to be calculated, which will help to make the final decision.

Formula to calculate NPV: = -Initial Investment + [(Cash Inflow₁)/(1+R)¹] + [(Cash Inflow₂)/(1+R)²] + [(Cash Inflow₃)/(1+R)³]…..+ [(Cash Inflow_n)/(1+R)ⁿ]

Where,

R is the required rate of return per period;

n is number of years.

NPV of the new machinery:

Initial investment = Cost of Machinery + Installation Cost
=> $72,000 + $7,000 = $79,000

R = 15%

n = 10 Years

Net Cost Savings per Year:

Year	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10
Cost savings in labour and materials	$17,500	$17,500	$17,500	$17,500	$17,500	$17,500	$17,500	$17,500	$17,500	$17,500
Add: Amortization on new machinery - 20% CCA for five years	$14,400	$14,400	$14,400	$14,400	$14,400	$0	$0	$0	$0	$0
Less: Amortization foregone on old machinery - $27,000/10 Years	$2,700	$2,700	$2,700	$2,700	$2,700	$2,700	$2,700	$2,700	$2,700	$2,700
Add: Tax saved on amortization of new machinery	$4,320	$4,320	$4,320	$4,320	$4,320	$0	$0	$0	$0	$0
Less: Tax foregone on amortization of old machinery	$810	$810	$810	$810	$810	$810	$810	$810	$810	$810
Add: Salvage value of new machinery	$0	$0	$0	$0	$0	$0	$0	$0	$0	$11,500
Net Cost Savings	$ 32,710	$ 32,710	$ 32,710	$ 32,710	$ 32,710	$ 13,990	$ 13,990	$ 13,990	$ 13,990	$ 25,490

NPV = -$79,000 + [($32,710)/(1+0.15)] + [($32,710)/(1+0.15)²] + [($32,710)/(1+0.15)³] + [($32,710)/(1+0.15)⁴] + [($32,710)/(1+0.15)⁵] + [($13,990)/(1+0.15)⁶] + [($13,990)/(1+0.15)⁷] + [($13,990)/(1+0.15)⁸] + [($13,990)/(1+0.15)⁹] + [($25,490)/(1+0.15)¹⁰]

=> -$79,000 + ($32,710/1.15) + ($32,710/1.3225) + ($32,710/1.520875) + ($32,710/1.749006) + ($32,710/2.011357) + ($13,990/2.313061) + ($13,990/2.66002) + ($13,990/3.059023) + ($13,990/3.517876) + ($25,490/4.045558)

= $56,807.54

Since the NPV of purchasing new machinery is positive, Signs for Fields Machinery should purchase it.

b) The current salvage value of $9,000 will increase the initial investment cost by same amount resulting in lesser NPV. However, since the NPV of purchasing new machinery is way more than $9,000, it would still result in positive NPV resulting in the same decision.

c) IRR:

IRR stands for internal rate of return, at which NPV is zero. It is calculated using below given formula.

Formula for IRR: 0 = -Initial Investment + [(Cash Inflow₁)/(1+IRR)¹] + [(Cash Inflow₂)/(1+IRR)²] + [(Cash Inflow₃)/(1+IRR)³]…..+ [(Cash Inflow_n)/(1+IRR)ⁿ]

0 = -$79,000 + [($32,710)/(1+IRR)] + [($32,710)/(1+IRR)²] + [($32,710)/(1+IRR)³] + [($32,710)/(1+IRR)⁴] + [($32,710)/(1+IRR)⁵] + [($13,990)/(1+IRR)⁶] + [($13,990)/(1+IRR)⁷] + [($13,990)/(1+IRR)⁸] + [($13,990)/(1+IRR)⁹] + [($25,490)/(1+IRR)¹⁰]

IRR = 35.65%

PI stands for Profitability Index, which tells us about the profitability of a project / investment in terms of ratio.

Formula for PI = (NPV + Initial Investment) / Initial Investment

PI = ($56,807.54 + $79,000) / $79,000 = 1.7191