Question

Caspian Sea Drinks is considering the production of a diet drink. The expansion of the plant and the purchase of the equipment necessary to produce the diet drink will cost $25.00 million. The plant and equipment will be depreciated over 10 years to a book value of $3.00 million, and sold for that amount in year 10. Net working capital will increase by $1.45 million at the beginning of the project and will be recovered at the end. The new diet drink will produce revenues of $9.32 million per year and cost $2.32 million per year over the 10-year life of the project. Marketing estimates 10.00% of the buyers of the diet drink will be people who will switch from the regular drink. The marginal tax rate is 35.00%. The WACC is 13.00%. Find the IRR (internal rate of return).

Answer 1

Caspian Sea Drinks is considering the production of a diet drink.

The expansion of the plant and the purchase of the equipment necessary to produce the diet drink will cost $25.00 million

The plant and equipment will be depreciated over 10 years to a book value of $3.00 million,and sold for that amount in year 10

Net working capital will increase by $1.45 million at the beginning of the project and will be recovered at the end.

The new diet drink will produce revenues of $9.32 million per year and cost $2.32 million per year over the 10-year life of the project

The marginal tax rate is 35.00%. The WACC is 13.00%.

Marketing estimates 10.00% of the buyers of the diet drink will be people who will switch from the regular drink  = It is actually irrelevant here doesn’t consider

Find the IRR (internal rate of return).

IRR

IRR is the rate at which NPV of the project become zero, Computing the internal rate of return (IRR) for a possible investment is time-consuming and inexact. IRR calculations must be performed via guesses, , and trial and error. Essentially, an IRR calculation begins with two random guesses at possible values and ends with either a validation or rejection. If rejected, new guesses are necessary.

0 = PV of cash inflow - PV of cash outflow

We can solve through this trail and error method

For calculating IRR, we need two NPV with their discount rate. One of them is positive and one of them negative. And discount rate used for those NPVs are one of them lower than IRR and one of them Higher than IRR

The first step is to make guesses at the possible values for lower discount rate and higher discount rate to determine

For correcting the Guess, just use fake payback period and check the closest value of the result in the Present value of annuity $ 1 factor table’s use full life of the assets year (n) period row and find the correspondent rate on top of that row. Use this rate as apprpx.IRR and take two rate, one is lower than this rate and one is higher than this rate

So first calculate Fake payback period

Fake payback period = initial investment / average CF

Here,

initial investment = equipment cost + increase in net working capital

initial investment = 25000000 + 1450000 = 26450000

average CF

Operating cash flow year 1 to 10

items	Years 1 to 10
Revenue	9320000
- cost	2320000
= Earning before tax	7000000
- Tax exp @ 35%	2450000
= Earning after tax (excluding dep.)	4550000
+ depreciation tax shield (calculation is below)	770000
= operating cash flow	5320000

depreciation tax shield = depreciation exp. * tax rate

  depreciation exp = depreciable base / useful life

    depreciable base = cost of equip - end book values

    depreciable base = 25000000 - 3000000 = 22000000

  depreciation exp = 22000000 / 10 = 2200000

depreciation tax shield = 2200000 * 35% = 770000

Terminal non operating cash flow

Salvage value = 3000000

Book value = 3000000

No gain or loss so there is no tax effect

Net cash received from proceeds = 3000000

Release of net working capital = 1450000

  Net terminal cash flow = 3000000 + 1450000 = 4450000

So the average cash flow - = (( 5320000 *10 ) + 4450000 )) / 10 = 5765000

Fake payback period = 26450000 / 5765000 = 4.588

Look In the table’s n=10 period row and find the closest value of 4.588 and its rate on top of that column

Closest value = 4.6586      aand its correspondent rate is   17%

So, pretend that 17% is the approx. IRR, take two rate, one is below 17% and one is higher than 17% . I have taken here 13% and 22%

one is below 17% = for this, I take the company WACC of 13%

Use 13% discount rate and find the NPV of the project. It should be positive.

NPV @ 13%

Year	CF	PV factor $1 @ 10%	CF * PV factor $1 @ 20%
0	- $ 26450000	(1 / 1+13%)0 = 1	- $ 26450000
1 to 10 year operating cash flow	5320000	(1 / 1+13%)10GT = 5.426	28867615.29
Terminal cash flow	4450000	(1 / 1+13%)10 = 0.294588	1310918.15

NPV = PV of CF - initial investment

NPV = 28867615.29 + 1310918.15 - 26450000 = 3728533.44 (positive NPV)

One of thing that if we get a positive NPV, the discount rate used here be lower than IRR

Use 22% discount rate and find the NPV of the project. It should be negative.

NPV @ 22%

Year	CF	PV factor $1 @ 10%	CF * PV factor $1 @ 20%
0	- $ 26450000	(1 / 1+22%)0 = 1	- $ 26450000
1 to 10 year operating cash flow	5320000	(1 / 1+22%)10GT = 3.9232	20871340.53 0.21057
Terminal cash flow	4450000	(1 / 1+22%)10 = 0.13689	609202.54

NPV = PV of CF - initial investment

NPV = 20871340.53 + 609202.54 - 26450000 = - 4969456.81 (negative NPV)

One of thing that if we get a negative NPV, the discount rate used here be higher than IRR

So we can conclude that the actual correct IRR is between 10% and 22%

***Next use a formula to find correct IRR

IRR = Lower discount rate + (NPV @ Lower discount rate / Difference between two NPV ) * ( Higher discount rate - Lower discount rate)

Here,

Lower discount rate = 13%

NPV @ Lower discount rate = 3728533.44

Difference between two NPV = NPV @ Lower discount rate - NPV @ Higher discount rate

Difference between two NPV = 3728533.44 - (- 4969456.81 ) = 8697990

NPV @ Higher discount rate = - 4969456.81

Higher discount rat = 22%

Put the values in to the formula

IRR = 13% + ( 3728533.44  / 8697990 ) * ( 22% - 13%)

IRR = 13% + ( 0.4286 * 9)

IRR = 13% + 3.858 = 16.858%

The correct IRR is =   16.858%

The project IRR is greater than WACC, The project will be taken.

There is some difference in calculation