Hi doodle4me!!
The total initial investment I is:
I = $100,000
For each year i = 1 to 6,
the depreciation Di is:
D1 = 0.20 * $100,000 = $20,000
D2 = 0.32 * $100,000 = $32,000
D3 = 0.19 * $100,000 = $19,000
D4 = 0.12 * $100,000 = $12,000
D5 = 0.11 * $100,000 = $11,000
D6 = 0.06 * $100,000 = $ 6,000
Lugar depreciates the 100% of the initial investment.
Salvage value SV is:
SV = $10,000
Book value BV is zero:
BV = depreciable asset - total amount depreciated =
= $100,000 - $100,000 = $0
The revenues R for each year are:
R = $90,000
The expenses E for each year are:
E = $50,000
Then for each year (R-E) or Net Operating Profit is:
R - E = $40,000
Tax rate T is 0.40 and Tax calculation for each year:
Ti = T * (R - E - Di) = with T = 0.4
= 0.4 * ($40,000 - Di) =
= $16,000 - 0.4 * Di
Then:
T1 = $16,000 - 0.4 * $20,000 = $8,000
T2 = $16,000 - 0.4 * $32,000 = $3,200
T3 = $16,000 - 0.4 * $19,000 = $8,400
T4 = $16,000 - 0.4 * $12,000 = $11,200
T5 = $16,000 - 0.4 * $11,000 = $11,600
T6 = $16,000 - 0.4 * $6,000 = $13,600
The cash flow formula is:
CF = Net Operating Profit - Taxes
Recall that (R - E) is the Net Operating Profit for each year, then:
CFi = R - E - Ti = $40,000 - Ti
We have that:
CF1 = $40,000 - $8,000 = $32,000
CF2 = $40,000 - $3,200 = $36,800
CF3 = $40,000 - $8,400 = $31,600
CF4 = $40,000 - $11,200 = $28,800
CF5 = $40,000 - $11,600 = $28,400
CF6 = $40,000 - $13,600 = $26,400
For the last year we must consider the Terminal cash flow (TCF):
TCF = SV - T*(SV-BV) =
= $10,000 - 0.4*($10,000) =
= $6,000
We will use WACC as the required rate of return:
r = WACC
Why we use WACC as required rate of return?
"Broadly speaking, the assets of a company are financed by either debt
or equity. WACC is the average of the cost of each of these sources of
financing weighted by their respective usage in the given situation.
By taking a weighted average, we can see how much interest the company
has to pay for every dollar it borrows.
A firm's WACC is the overall required return on the firm as a whole.
It is the appropriate discount rate to use for cash flows similar in
risk to the overall firm."
From "Investopedia: Weighted Average Cost of Capital - WACC":
http://www.investopedia.com/terms/w/wacc.asp
The Present Value (PV) formula for this 6 years project is:
CF1 CF2 CF6 TCF
PV = --------- + ---------- +...+ ---------- + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^6 (1 + r)^6
Net Present Value (NPV):
NPV = PV - I
Using the calculator we find that:
PV = $138,839.59
NPV = $138,839.59 - $100,000 = $38,839.59
----------------------------------------------------------
I hope that this helps you. If you find something unclear with theory
or (may be) a mistake in a calculation, please request for an answer
clarification, I will be glad to offer further assistance before you
rate this answer.
Best regards.
livioflores-ga |
