Question

Dog Up! Franks is looking at a new sausage system with an installed cost of $507086. This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the sausage system can be scrapped for $73250. The sausage system will save the firm $170394 per year in pretax operating costs, and the system requires an initial investment in net working capital of $37679. If the tax rate is 32 percent and the discount rate is 11 percent, what is the NPV of this project?

Answer 1

NPV of the project=NPV of yearly savings after Tax @32%+NPV of tax shield on depreciation+ NPV of( scrap Value+ working capital reinvestment)- Initial investment

NPV of yearly savings after tax=PVIFA(11%,5)*$170394*(1-tax rate)

PVIFA(11%,5)=sum of present value factor for 5 years @ discounted rate                  11%=1/(1.11)+1/(1.11)²……..+1/(1.11)⁵=3.6979

For getting after tax value we have to multiply by (1-tax rate)(1-32%)=68%

Thus NPV of yearly savings=3.6979*170394*68%=$428,236……(1)

But franks will get tax shield on depreciation=PVIFA(11%,5)*{(installed cost-scrap value)/5}*32%

                                                                             =3.6979*{($507086-$73,250)/5}*32%

                                                          =3.6979*($433856/5)*32%

                                                        =3.6979*86767.2*32%=$102,618.4…..(2)                                                       

NPV of scrap value and reinvested working capital @ year end =PVIF(11%,5)*($73,250+$37,679)

Discounting factor @11% For 5^th year =1/(1.11)⁵ *$110929

                                                                       =0.5935*$110929=$65,830.96….(3)

Initial Investment=installed cost + initial working capital=$507,086+$37,679=$544,765….(4)

NPV of the project=(1)+(2)+(3)-(4)=$428,236+$102,618.4+$65,830.96-$544,765

                               =$51,920.31.

Since NPV is positive,project is acceptable.NPV can be calculated also by tabular method given below

YEAR	DF	Investment(P)	EBITDA	Depreciation	EBIT	TAX@32%	EAT	OCF=P+EAT+DEP	DF*OCF
0	1	-544765						-544765	$          (544,765.00)
1	0.9009		170394	86767.2	83626.8	26760.576	56866.224	143633.424	$            129,399.48
2	0.81162		170394	86767.2	83626.8	26760.576	56866.224	143633.424	$            116,576.11
3	0.73119		170394	86767.2	83626.8	26760.576	56866.224	143633.424	$            105,023.52
4	0.65873		170394	86767.2	83626.8	26760.576	56866.224	143633.424	$               94,615.79
5	0.59345	110929	170394	86767.2	83626.8	26760.576	56866.224	254562.424	$            151,070.41
	3.6959			433836					$               51,920.31