Question

Scholastic Co. is evaluating different equipment. Machine A costs $85,000 has a four-year life, and costs $45,000 per year to operate. The machine will be depreciated using straight-line and the relevant discount rate is 8%. The machine will have a salvage value of $20,000 at the end of the project's life. The firm has a tax rate of 21%. Calculate the NPV of the project. (Enter a negative value and round to 2 decimals)

Answer 1

Computation of Annual Cashoutflow

Year	Operating Expenses	Depericiation	Total expenses( Operating expenses+ Depreciation)	Tax shield @ 21% on total expenses	Cash outflow( Operating expenses- Tax shield on expenses)
1	$45,000	$16,250	$61,250	$ 61250*0.21= $ 12862.50	$ 45000-$ 12862.5= $ 32137.5
2	$45,000	$16,250	$61,250	$ 61250*0.21= $ 12862.50	$ 45000-$ 12862.5= $ 32137.5
3	$45,000	$16,250	$61,250	$ 61250*0.21= $ 12862.50	$ 45000-$ 12862.5= $ 32137.5
4	$45,000	$16,250	$61,250	$ 61250*0.21= $ 12862.50	$ 45000-$ 12862.5= $ 32137.5

Computation of Present value of future cashoutflows

We know that Present value of Ordinary Annuity = C * [ {1-( 1+i) ^-n} /i]

Here C = Cash flow per period

I = Rate of interest

n = No. of years

Present value of Future cashoutfllow in year 1 to 4 = C * [ {1-( 1+i) ^-n} /i]

= $ 32137.5[ { 1-( 1.08)^-4} /0.08]

= $ 32137.5 [ { 1-0.73503} /0.08]

= $ 32137.5 { 0.26497/0.08}

= $32137.5*3.31213

= $ 106443.5779

Total PV of Cashoutflow = Initial outlay + PV of Cashoutflow arising in year 1 to 4

= $ 85000+ $ 106443.5779

= $ 191443.58

Compuation of Book value of Equipment

Book value = Cost of Asset - Accumulated depreciation

=$ 85000-4( $ 16250)

= $ 85000-$ 65000

= $ 20000

Since Book value and Salvage value are same there is no tax on salvage value

Computation of Present value of Terminal cashflows

PV of Terminal Cashflow = Future Value / ( 1+i) ^n

Here I = Interest rate and n = No.of years

PV of terminal cash flow = $20000/ ( 1.08)^4

= $ 20000/1.36049

= $ 14700.5858

Computation of NPV

S.No	Particulars	Amount
A	PV of Cashinflows	$0
B	PV of Terminal Cashflows	$14,700.5858
C	Total Pv inflows	$14,700.5858
D	PV of Cashoutflows	$191,443.58
E	Net Present value ( C-D)	($176,742.9921)

* NPV = PV of Cashinflows - PV of Cashoutflows

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