Answer:
The maximum price that Truck-or-Treat should be willing to pay for the purchase of the new trucks if it remains an unlevered company is $510,702.49.
Explanation:
Let:
x = Maximum price for the new truck = initial investment = ?
AEBTD = Annual earnings before taxes and depreciation = $220,000
T = Tax rate = 21%, or 0.21
n = Number of years = 5
Since the it is assumed that Truck-or-Treat remains an unlevered company, this implies the required annual rate of return on Truck-Or-Treat's unlevered equity of 15 percent is the relevant rate of return to use.
Therefore, we have:
r = required annual rate of return = 15%, or 0.15
D = Annual depreciation = Maximum price for the new truck / Number of useful years = x / 5 = 0.2x
P = Annual cash flow = ((AEDTD - D) * (1 - T)) + D = ((220000 - 0.2x) * (1 - 0.21)) + 0.2x = ((220000 - 0.2x) * 0.79) + 0.2x = 173,800 - 0.158x + 0.2x = 173,800 - 0.042x
Using the formula for calculating the present value (PV) of an ordinary annuity, we have:
PVP = Present value of annual cash flow = P * ((1 - (1/(1 + r))^n) / r) = (173,800 - 0.042x) * ((1 - (1/(1 + 0.15))^5) / 0.15) = (173,800 - 0.042x) * 3.3521550980114 = 582,604.56 - 0.140790514116479x
For the NPV of this unlevered truck project to be equal to $0, we must have:
x = PVP
That is:
x = 582,604.56 - 0.140790514116479x
Solving for x, we have:
x + 0.140790514116479x = 582,604.56
x(1 + 0.140790514116479) = 582,604.56
x1.140790514116479 = 582,604.56
x = 582,604.56 / 1.140790514116479 = $510,702.49
Therefore, the maximum price that Truck-or-Treat should be willing to pay for the purchase of the new trucks if it remains an unlevered company is $510,702.49.
