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 IRR of the PJX5?

a. The PJX5 will cost $1.92 million fully installed and has a 10 year life. It will be depreciated to a book value of $144,039.00 and sold for that amount in year 10.

b. The Engineering Department spent $18,050.00 researching the various juicers.

c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $22,375.00.

d. The PJX5 will reduce operating costs by $313,116.00 per year.

e. CSD’s marginal tax rate is 31.00%.

f. CSD is 68.00% equity-financed.

g. CSD’s 19.00-year, semi-annual pay, 5.39% coupon bond sells for $961.00.

h. CSD’s stock currently has a market value of $24.22 and Mr. Bensen believes the market estimates that dividends will grow at 2.61% forever. Next year’s dividend is projected to be $1.62.

with steps if possible

Answer 1

Note :-

The Engineering Department spent $18,050.00 researching the various juicers&Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $22,375.00. are sunk cost.sunk costs are no longer relevant to future rational decision-making,so this cost is not consider to calculate the IRR.

Calcualtion of weighted average cost of capital:-

Cost of debt =[ i + ( D - NP) / n ] / ( D + NP)/2

Here I = annual interest payment = 1000 * 5.39% =$ 53.9

D = Face value = 1000

NP = Net proceeds = 961

Cost of debt before tax = [( 53.9 +( 1000 - 961)/19] / (1000+961)/2 = 0.057065

Cost of debt after tax = Cost of debt before tax * (1 - tax rate)

= 0.057065* (1 -0.31)

Cost of debt after tax =3.9375%

Cost of equity :-

Cost of equity = D1 / Po + g

Here

D1 = next year dividend

Po =market value g = gwoth rate

cost of equity =( 1.62 /24.22 ) +0.0261

Cost of equity = 0.0929869

Cost of equity = 9.2987%

Weighted average cost of capital = Cost of debt after tax * Weight of debt + Cost of Equity * Weight of equity

= 3.9375% * 0.32 + 9.2987% * 0.68

weighted average cost of capital = 7.583116%

weighted average cost of capital = 7.58%

Initial investment = cost of machine

Initial investment = 1,920,000

Depreciation =( 1,920,000 - 144,039) / 10 = 177,596.1 per year

Increase in cash flows:-

Particulars	amount
Reduce in operating cost	313,116
Less - Depreciation	177,596.10
increase in profit before rax	135,519.9
less-Tax@31%	42011.169
Profit after tax	93,508.73
Add- Depreciation	177,596.10
Increase in cash flows	271,104.83

Here Operating cash flow are same amount for all ten years. that is $ 271,104.83 per years and terminal cash inflows at end of 10 years that is 144,039 on sale of machinery.

Here IRR calculated between two I.e, 7.58% & 9%

NPV at 7.58% = present value of cash inflows - initial investment

= [ 271,104.83 * PVAF ( 7.58% , 10Years) + 144,039 * PVF ( 7.58% ,10 years)] - $ 1,920,000

= [ 271,104.83 * 6.8391 + 144,039 *0.4816 ] - $ 1,920,000

=$ 1,923,475.86 - 1,920,000

NPV at 7.58% = 3,475.86

NPV at 9% = present value of cash inflows - initial investment

= [ 271,104.83 * PVAF ( 9% , 10Years) + 144,039 * PVF ( 9% ,10 years)] - $ 1,920,000

= [ 271,104.83 * 6.4177 + 144,039 *0.4224 ] - $ 1,920,000

= 1,739,858.006 +60,843.631 - 1,920,000

NPV at 9% = -119,298.36

Calculation of IRR:-

IRR = Lower rate +[ NPV at lower rate / (NPV at lower rate - NPV at higher rate)] * ( Higher rate - Lowe rate)

IRR = 7.58% + [ 3,475.86 / ( 3,475.86 - (-119,298.36))] * ( 0.09 - 0.0758)

IRR = 7.618%