Question

Fairfax Pizza is considering buying a new oven. The new oven would be purchased today for 17,600 dollars. It would be depreciated straight-line to 1,200 dollars over 2 years. In 2 years, the oven would be sold for an after-tax cash flow of 1,700 dollars. Without the new oven, costs are expected to be 11,700 dollars in 1 year and 15,200 in 2 years. With the new oven, costs are expected to be -500 dollars in 1 year and 9,300 in 2 years. If the tax rate is 50 percent and the cost of capital is 11.22 percent, what is the net present value of the new oven project?

Answer 1

Steep 1:Computation of Savings in Cost

S.No	Particulars	Year 1	Year 2
A	Expected cost withoutnew oven	$11,700	$15,200
B	Expected cost Under new oven	($500)	$9,300
C	Savings in Cost due to Purchase of new Oven ( A-B)	$12,200	$5,900

Note: Savings in Cost is treated as income.So it is one kind of Cash inflow to the Firm

Step 2:Computation of Annual of Operating Cashflows

S.No	Particulars	Year 1	Year 2
A	Savings in Cost	$12,200	$5,900
B	Depreciation	$8,200	$8,200
C	Profit Before Tax ( A-B)	$4,000	($2,300)
D	Tax @ 50% on C	$2,000.0	($1,150.0)
E	Profit after Tax ( C-D)	$2,000.0	($1,150.0)
F	Annual Cash flow ( E+B)	$10,200.0	$7,050.0

Given in Two years the oven is depreciated straightline to $ 1200 dollars

Computation of Depreciation under straight line method

* Depreciation = (Cost of Asset -Expected salvage value)/ Useful life.

= ($ 17600-$ 1200)/2

= $ 8200

Step 3:Computation of Present value of Operating cash flow

Year	Amount	Disc @11.22%	Discounting factor	Discounted cashflow( Cashflow* Discounting factor)
1	$10,200.0	1/( 1.1122)^1	0.89912	$9,171.01
2	$7,050.0	1/( 1.1122)^2	0.80841	$5,699.32
	Total			$14,870.34

Hence Present value of Operating cashflow is $ 14870.34

Step 4:Computation of Present value of Terminal cash flow

After Tax proceeds from the sale of oven at the end of year 2 = $ 1700

Present value of after Tax proceeds= Future value / ( 1+i)^n

Here I = Rate of interest and n = No.of years.

Present value of after Tax proceeds= Future value / ( 1+i)^n

= $ 1700/ ( 1+0.1122)^2

= $ 1700/ ( 1.1122)^2

= $ 1700/1.23699

= $ 1374.30

Step 5:Computation of NPV

S.No	Particulars	Amount
A	PV of Operating cash flows	$14,870.34
B	PV of Terminal cashflows	$1,374.30
C	Total PV of Cashinflows( A+B)	$16,244.64
D	Initial outlay	$17,600
E	Net Present value( C-D)	($1,355.36)

* NPV = PV of cash inflows - initial outlay

Hence NPV of a new oven is -$ 1355.36

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