Question

1. You have the following cost and revenue information on a project that invests in the conversion of a coal-fired electricity generating plan into a gas-fired unit.

Cost of new equipment: $200 million.

The equipment will be depreciated over 8 years on a straight-line basis to zero book value.

Proceeds from the sale of old equipment which has a book value of $15 m is 40 million,

Expensable installation cost: 0.50 million.

Estimated Revenue from the sale of electricity in the first year: $65 million and it remains the same for all 5 years;

Cost of gas: $25 million;

Operating and other expenses: $4 million;

Initial working capital expenses: $1 million;

Project’s assets estimated resale value: $65 million.

The project is subject to a tax rate of 30%,

Anticipated clean-up expense: $1.0 million.

The investment is eligible for $1.0 million investment tax credit.

The weighted average cost of capital (WACC) of the project is 5%.

Using these data,

1. calculate the following cash flows associated with the project: (i) Net initial investment outlay; (ii) Net operating cash flows (NOCF) also known as CFAT and (iii) net salvage value, and
2. assuming that the net operating cash flows will remain the same for all 8 years, calculate the NPV and the IRR of the project.

Net initial investment outlay:

-I_o – W –(1-t)E₀ + [S_o – t(S₀-B₀] + I_c

Net operating cash flow:

(1-t)(R – C) + t(D)

Net salvage value:

S – t(S – B) – (1 – t)REX + W

Answer 1

Answer to A

i) Net Initial Investment

Net initial investment outlay:

-Io – W –(1-t)E0 + [So – t(S0-B0] + Ic

Where Io = Cost of New project - $200 Million

W= Change in Working Capital = $1 Million (as there is an increase in Working Capital therefore it is a cash outflow)

(1-t)Eo = Post Tax Expesnable Installation Cost = (1-0.30)*0.50 Million=$ 0.35 million (where t is Tax rate)

Ic = Investment Tax Credit = $ 1 Million (Cash Inflow)

[So – t(S0-B0] - Post Tax Proceeds of Old Plant where So is Sales Proceeds and Bo is the book value of old plant and T is Tax rate. (Cash Inflow)

Therefore [So – t(S0-B0] = [40-(40-15)*0.30=] =$32.5 Million

Now we compute the Initial Investment Outlay

= - $200 Million - $1 Million -$ 0.35 million +$ 1 Million +$32.5 Million

= $ 167.85 Million

ii) Net Operating Cash Flows

Net operating cash flow:

(1-t)(R – C) + t(D)

where R = Electricty Revenue = $ 65 Million

C = Cost of Gas + Operating and Other Expenses

= $ 25 Million + $ 4 Million = $ 29 Million

T = Tax Rate

T(D) is Depriciation Tax Shield, which is savings in tax due to depriciation

now, depricaition = Asset Value/ No. of Years of Use

=$ 200 Million / 8 Years = $25 Milllion

Now, Tax Shield on Depriciation = $25 Milllion*30% (Tax Rate)

= $ 7.5 Million

Therefore Net Operating Cash Flow = ($ 65 Million - $ 29 Million) (1-0.30) +$ 7.5 Million

= $ 32.7 Million

iii) Net salvage value:

S – t(S – B) – (1 – t)REX + W

Where S = Sale Proceeds = $ 65 Million

B= Book Value = $ 0 . As it is given that the machine needs to be depriciated to nill salvage value

(1 – t)REX = Post Tax Clean Up Expenses = (1-0.30)* $ 1 Million =$ 0.70 Million

and W = Change in Working Capital (Since the Working capital will be releazed at the end of the project life, it will be an inflow) = $ 1 Million

Therefore Net Salvage Value = $ 65 Million - (30%)($ 65 Million - 0) - $ 0.70 Million +$ 1 Million

= $ 45.8 Million

Answer to B

Now given that the operating Cash flows will remain same for all 8 years, we need to compute the present value of all such cash flows using the discount rate = 5%

Now,NPV = Initial Investment - PV of all Cash Inflows

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8
Initial Investment (A)	-167.85
Operating Cash Inflows (B)		32.7	32.7	32.7	32.7	32.7	32.7	32.7	32.7
Net Salvage Value ('C)									45.8
Net Cash Flows (D=A+B+C)	-167.85	32.7	32.7	32.7	32.7	32.7	32.7	32.7	78.5
Discount Factors @ 5% ('E)	1	0.943396	0.889996	0.839619	0.792094	0.747258	0.704961	0.665057	0.627412
Present Value of All Cash Flows (F=D*E)	-167.85	30.85	29.10	27.46	25.90	24.44	23.05	21.75	49.25
Now NPV Is Summation of All the above Cash Flows			63.95

Therefore NPV of the project = $ 63.95 Million

Now IRR is the rate of Return where NPV is 0

Therefore Internal Rate of Return can be computed below using Ecxel

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8
Initial Investment (A)	-167.85
Operating Cash Inflows (B)		32.7	32.7	32.7	32.7	32.7	32.7	32.7	32.7
Net Salvage Value ('C)									45.8
Net Cash Flows (D=A+B+C)	-167.85	32.7	32.7	32.7	32.7	32.7	32.7	32.7	78.5
TO COMPUTE IRR USE THE FORMULA	=IRR(SELECT ALL THE CASH FLOWS)
IRR	14%

The same can also be computed using hit and trial method

Given that the NPV of the project is $ 65 Million when discounted using the WACC rate of 5%. Now IRR has to be a higher rate if we need the NPV 0. So when Disounting the cashflows using rate of 14 % we get the NPV 0 therefore IRR of the project = 14%