Question

Problem 2

You are evaluating a project for The Ultimate recreational tennis racket, guaranteed to correct that wimpy backhand. You estimate the unit sales price of The Ultimate to be $500 and sales volume to be 1,000 units in year 1; 1,250 units in year 2, and 1,450 units in year 3. The project has a three year life. Variable costs amount to $225 per unit and fixed costs, excluding depreciation, are $110,000 per year. The project requires an initial investment of $170,000 which is depreciated straight-line to zero over the three-year project life. The expected scrap value of the asset at the end of year 3 is $35,000. Net working capital investment is initially lowered by $80,000 and it will be fully replaced at the end of the project’s life. The tax rate is 34% and the required return on the project is 10%. What is the NPV of this project? Accordingly what is your decision?

Answer 1

Computation of the Net Present Value:

S.No	Particulars	Amount
A	PV of the Annual Cash flow( wn:1)	$417,595.17
B	PV of the Salvage value of the machinary( wn:2)	$17,355.49
C	Initial outlay	($170,000)
D	Net Working Capital used( wn:3)	($19,896)
E	Net present value(A+B-C-D)	$245,054.66

Decision:Since NPV is positive $ 245054.66 , i will accept the project

Working Note:1:Computation of the present value of the Annual Cash flows

S.No	Particulars	Year 1	Year 2	Year 3	Total
A	No.of Units sold	1000	1250	1450	3700
B	Sale price per unit	$500	$500	$500	$500
C	Sale value(A*B)	$500,000	$625,000	$725,000	$1,850,000
D	Variable Cost per unit	$225	$225	$225	$225
E	Total Variable Cost(A*D)	$225,000	$281,250	$326,250	$832,500
F	Contribution(C-E)	$275,000	$343,750	$398,750	$1,017,500
G	Fixed Cost Excluding Depreciaton	$110,000	$110,000	$110,000	$330,000
H	Depreciation	$56,666.66	$56,666.66	$56,666.68	$170,000
I	Profit Before Tax(F-G-H)	$108,333.34	$177,083.34	$232,083.32	$517,500
J	Taxes @ 34%(I*0.34)	$36,833.34	$60,208.34	$78,908.33	$175,950.00
K	Profit After Tax(I-J)	$71,500.00	$116,875.00	$153,174.99	$341,550.00
L	Depreciation	$56,666.66	$56,666.66	$56,666.68	$170,000
M	Annual Cash flow(K+L)	$128,166.66	$173,541.66	$209,841.67	$511,550.00
N	Disc @ 10%	0.909090909	0.826446281	0.751314801
O	Discounted cash flow	$116,515.15	$143,422.86	$157,657.15	$417,595.17

Total pv of DCF is $ 417595.17

Working Note 2:Computation of Scrap value of the machinary

Particulars	Amount
Scrap value	$35,000
Taxes @ 34%	$11,900.00
Net value	$23,100.00

Note: Since the entire cost is recovered in the form of Depreciation, So at the time of sale of Asset capital gain tax is applicable. Since no Capital gain tax is specified in the question, assumed that normal tax rates will apply.

PV of Salvage value of machinary after year 3 is $ 23100/(1.10)^3

= $ 23100*0.75132

= $ 17355.492

Working Note 3:Computation of the Net Working Capital used

Present value of the working capital received after 3 years is $ 80000/(1.10)^3

= $ 80000*0.7513

= $ 60104

Particulars	Amount
Initial Outflow	$80,000
PV of the Working capital received after 3 years	$60,104
Net Working Capital used	$19,896

So Net working Capital used is $ 19896.