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 $1.74 million fully installed and has a 10 year life. It will be depreciated to a book value of $284,936.00 and sold for that amount in year 10.

b. The Engineering Department spent $49,835.00 researching the various juicers.

c. Portions of the plant floor have been redesigned to accommodate the juicer at a cost of $21,599.00.

d. The PJX5 will reduce operating costs by $407,610.00 per year.

e. CSD’s marginal tax rate is 34.00%.

f. CSD is 61.00% equity-financed.

g. CSD’s 19.00-year, semi-annual pay, 6.59% coupon bond sells for $997.00.

h. CSD’s stock currently has a market value of $21.12 and Mr. Bensen believes the market estimates that dividends will grow at 2.48% forever. Next year’s dividend is projected to be $1.73.

Answer 1

Following information is given in the question:

1. PJX5 cost is $1,740,000 with 10 years of useful life
2. Salvage value of PJX5 is $284,936
3. R&D cost is $49,835
4. Floor redesign cost is $21,599
5. Operating cost saving is $407,610 per year
6. Tax rate is 34%
7. 6.59% coupon bond pays semi-annual interest
8. Current value of stock is $21.12, dividend growth rate is 2.48%, next year dividend is $1.73

For calculating IRR of PJX5 we have to first calculate the Weighted Average Cost of Capital (WACC) of Caspian Sea Drinks, because for calculating IRR we have to use hit and trial method by putting two required rates of interest in the NPV of the project PJX5 and for that we should have a required rate to put in.

WACC = Cost of Equity * Weights of Equity + Cost of Debt * Weights of Debt

Where weights of equity is 61% and weights of debt 39%

Cost of Equity (Ke) can be calculated using Gordon Model of share valuation –

P0 = D1 / (Ke – g)

Where –

P0 = $21.12, D1 = $1.73 and g = 0.0248

21.12 = 1.73 / (Ke – 0.0248)

21.12 Ke – 0.5238 = 1.73

21.12 Ke = 2.2538

Ke = 0.1067 or 10.67%

Cost of Debt (Kd) can be calculated using after tax interest paid annually on bonds

Let us assume the face value of bond is $1000 since it is currently selling at $997

Interest rate is 6.59% paid semi-annually

Kd = [Interest * (1 – Tax rate)] / Face value of bond

Where –

Interest = $1000 * 6.59% * 2 = $131.80

Tax rate = 34% or 0.34

Face value = $1000

Kd = [131.8 * (1 – 0.34)] / 1000

Kd = 86.99 / 1000

Kd = 0.087 or 8.7%

Put thevalues of Ke and Kd in the WACC formula

WACC = Cost of Equity * Weights of Equity + Cost of Debt * Weights of Debt

WACC = 10.67 * 0.61 + 8.7 * 0.39

WACC = 6.51 + 3.39

WACC = 9.9%

Now we can estimate the IRR of PJX5 by assuming two rates and the two rate should be 9% and 14%, it means between these two rate the IRR shall stand.

Depreciation Calculation –

Depreciation = (Cost – Salvage value)/Life

Depreciation = ($1,740,000 – $284,936)/10

Depreciation = $145,506.40 per annum

Statement showing Annual Cash Flows

Particulars	Year 1 to 10
Operating cost saving	$          407,610.00
Depreciation	$       (145,506.40)
Earning before tax	$          262,103.60
Tax	$          (89,115.22)
Earning after tax	$          172,988.38
Depreciation	$          145,506.40
Cash Flows	$          318,494.78

Statement showing Net Present Value of PJX5 at 9% required rate

Period	Particulars	Amount (a)	Discounted Factor @ 9% (b)	Present Value (a * b)
0	Cost of PJX5	$    (1,740,000)	1	$     (1,740,000)
0	R&D cost	$          (49,835)	1	$          (49,835)
0	Floor design cost	$          (21,599)	1	$           (21,599)
1 to 10	Cash Flows	$          318,495	6.4177	$       2,044,004
10	Salvage value of PJX5	$          284,936	0.4224	$           120,357
	Net Present Value			$           352,927

Statement showing Net Present Value of PJX5 at 14% required rate

Period	Particulars	Amount (a)	Discounted Factor @ 14% (b)	Present Value (a * b)
0	Cost of PJX5	$    (1,740,000)	1	$     (1,740,000)
0	R&D cost	$          (49,835)	1	$           (49,835)
0	Floor design cost	$          (21,599)	1	$           (21,599)
1 to 10	Cash Flows	$          318,495	5.2161	$       1,661,301
10	Salvage value of PJX5	$          284,936	0.2697	$             76,847
	Net Present Value			$           (73,286)

Using two different rates of required rate of interest we got two NPV, now let us interpolate the IRR of the project.

Hence, IRR of PJX5 shall be calculated as follows –

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)]

IRR = 9 + [352927 / (352927 – (-73286))]

IRR = 9 + [352927 / 426213]

IRR = 9 + 0.83

IRR of PJX5 = 9.83%