Question

Caspian Sea Drinks is considering the purchase of a plum juicer – the PJX5. There is no planned increase in production. The PJX5 will reduce costs by squeezing more juice from each plum and doing so in a more efficient manner. Mr. Bensen gave Derek the following information. What is the NPV of the PJX5?

a. The PJX5 will cost $2.47 million fully installed and has a 10 year life. It will be depreciated to a book value of $209,348.00 and sold for that amount in year 10.

b. The Engineering Department spent $42,382.00 researching the various juicers.

c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $17,121.00.

d. The PJX5 will reduce operating costs by $496,430.00 per year.

e. CSD’s marginal tax rate is 20.00%.

f. CSD is 70.00% equity-financed.

g. CSD’s 19.00-year, semi-annual pay, 5.68% coupon bond sells for $984.00.

h. CSD’s stock currently has a market value of $22.13 and Mr. Bensen believes the market estimates that dividends will grow at 2.04% forever. Next year’s dividend is projected to be $1.48.

Answer 1

Note :- Here The Engineering Department spent $42,382 researching the various juicers is sunk cost. So, it is not to consider the cash outflows for calculation of NPV.

Calculation of initial cash outlay:-

Initial investment = cost of machine +cost of redesigned of floor for machine
Initial investment = $ 2,470,000  + $ 17,121 = $ 2,487,121

Calculation of the discouting rate i.e, WACC

calculation of cost of debt:-

Cost of debt before tax =[ interest amount + ( redemption value - net proceeds)/ n ] / ( Redemption value + net proceeds ) / 2

Cost of debt before tax = [56.8 + ( 1000 - 984)/19] / (1000+984)/2 = 5.81%

Cost of debt after tax = cost of debt before tax * (1- tax rate ) = 5.810696% * (1-0.20) = 4.648557%

Cost of debt after tax = 4.648557%

Calculation of cost of equity:-

Cost of equity =( D1 / market price ) + g

= 1.48/ 22.13 + 0.0204 = 8.72775% =

weight of equity = 0.70

Weight of debt = 1- weight of equity = 1- 0.70 = 0.30

WACC = cost of debt( after tax ) * weight of debt + cost of equity * weight of equity
WACC = 4.648557% * 0.30 + 8.72775* 0.70 =7.503995 % = 7.50%

Therefore, Discounting rate = 7.50%

Calculation annual depreciation amount :-

Depreciation =( Cost of machine - salvage value )/ no of years of machinery life

Depreciation = (2,470,000 - 209,348) / 10 year = $ 226,065.2 per year.

Calculation of Annual cash inflows:-

Particulars	amount
Annual cost savings	$ 496,430
Less- Depreciation	($ 226,065.2)
Profit before tax	$ 270,364.8
Less- Tax @20%	($ 54,072.96)
Profit after tax	$ 216,291.84
Add- Depreciation	$ 226,065.2
Annual Cash inflows after tax	$ 442,357.04

Calcualtion of the NPV of the Project :-

Calculation of the Salvage value of the PJX5 after tax:-

NPV = Present value of cash inflows - (present value of cash out flows or initial investment )

Sale proceeds in 10th year - $ 209,348
Less- Book value - $( 209,348) [ 2,470,000 - 226,065.2 *10]
gain on sale of PJX5 - 0

There is no gain in sale of PJX5 in 10th year, So, is no tax.

Therefore salvage value = $ 209,348

Cash inflows upto 9 year constant that is $ 442,357.04 per year, So, we use present value of annuity factor to bring it into present value of all nine years cash inflows.

Cash inflows for the 10th year is = Annual cash inflows + sale of proceeds of PJX5 = $ 442,357.04 + $ 209,348

Cash inflows for the 10th year = $ 651,705.04, we use present value factor to bring it into the present value of 10th year cash inflows.

Present value of cash inflows = $ 442.357.04 * PVAF (9years, 7.50%)+ 651,705.04 * PVF(10th year, 7.50%)

Present value of cash inflows = $ 442,357.04 *[ (1 - (1+r)n) / r ] + 651,705.04 * 1/(1+r)10

= $ 442.357.04 * [ (1- (1+0.075)9 ) / 0.075} + 651,705.04 * 1/(1+0.075)10

= $ 442,357.04 * 6.37888707 + 651,705.04 * 0.48519393

= $ 2,821,745.6 + 316,203.33

Present value of cash inflows =$ 3,137,948.93

Initial investment = $ 2,487,121 (calculated above)

NPV = Present value of cash inflows - initial investment

NPV = $ 3,137,948.93 - $ 2,487,121

Net present value =$ 650,827.93