Your Initials: A firm expects for the next several years to have 39% federal inc

Question

Your Initials: A firm expects for the next several years to have 39% federal inconne tax. A new project is sed that will bring $30,000 in revenues per year and will cost $10,0 per year. If this new project necessitates a total initial investment of $50.000, and has zero salvage value at the end of its six-year life, find the IRR after income taxes are paid? Assume MACRS depreciation is use with a recovery period of five years. Hint: calculate the after tax cash flow first then find the IRR 30 points) Hint: start with i-10% and increment i by 10%.

Explanation / Answer

Ques 1.(a). P =38 + (2700/D) for D>=1

Let D is the quantity demanded .

Total Revenue TR = P.D = (38 + (2700/D))D = 38D+2700

Total Cost TC = 1000 + D2

Profit = TR-TC = 38D+2700 - 1000 - D2 = -D2 + 38D +1700 ......(1)

For maximixing Profit , differentiate Profit with respect to D and put it equal to zero .

d/dD = -2D+38 = 0

=> 2D=38

=>D=19

So, value of D that maximises profit per month is 19.

(b).For maximum Profit put value of D found in (a) in equation 1 .

-(19)2 + 38(19) + 1700 = -361 + 722 + 1700 = 2061

So associated maximum profit per month for D=19 is $2061.

(c).For unit price when D=19 , Put D=19 in P =38 + (2700/D)

=>P =38 + (2700/19) = 38 + 142.11 = 180.11

So, unit price when D=19 is $180.11 .

(d). At Break even point Profit is zero so

Putting equation (1) =0 we get ,

-D2 + 38D +1700 = 0

D2 - 38D -1700 = 0

Solving the quadratic equation we get ,

D1= 64.40 & D2= -26.4

Since D>=1 Therefore D= 64.40

At D= 64.40 , P = 38 + (2700/64.40) = $79.93

So , Break even point is (79.93,64.40) .

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