II-64 Investment Before and After Taxes Deer Valley Lodge, a ski area near Salt
ID: 2648624 • Letter: I
Question
II-64 Investment Before and After Taxes Deer Valley Lodge, a ski area near Salt Lake City, has plans to eventually add five new chairlifts. Suppose that one of the lifts costs $2.2 million, and preparing the slope and installing the lift costs another $1.48 million. The lift will allow 3(X) additional skiers on the slopes, but there are only 40 days a year when the lodge needs the extra capacity. (Assume that Deer Valley will sell all 300 lift tickets on those 40 days.) Running the new lift will cost $500 a day for the entire 2(X) days the lodge is open. Assume that lift tickets at Deer Valley cost $65 a day and added cash expenses for each skier-day are S9. The new lift has an economic life of 20 years. I. Assume that the before-tax required rate of return for Deer Valley is 14%. Compute the before- tax NPV of the new lift and advise the managers of Deer Valley about whether adding the lift will be a profitable investment. 2. Assume that the after-tax required rate of return for Deer Valley is 8%, the income tax rate is 40%, and the MACRS recovery period is 10 years. Compute the after-tax NPV of the new lift and advise the managers of Deer Valley about whether adding the lift will be a profitable investment. 3. subjective factors would affect the investment decision?Explanation / Answer
Initial Investment = Cost of lift + preparing and installing cost
= $2,200,000 + $1,480,000
= $3,680,000
Annual cash inflow = 300 skiers x 40 days x (65+9)
= 300 skiers x 40 days x 74 = 888,000
Annual cash outflow = $500 x 200 days
=$100,000
Net cash Inflow = annual cash inflow - annual cash outflow
= $888,000 - $100,000
= $788,000
After tax cashflow = $788,000 x 0.6 = $472,800
PV of after tax cash flows at 8%
= 472,800 x 9.8181 ( from present value of ordinary annuity table) or can be calculated by the given formula
= 1 - (1/ (1+i)n / i) = 4,641,998
NPV of tax saving is shown in the below table :
Therefore NPV after tax = PV of after tax cash flow + PV of MACRS Depreciation ( tax saving ) - Initial investment
$4,641,998 + $1,039,119 - $3,680,000 = 2,001,117
Hope this helps.
Year tax rate PV Factor @8% Depreciation at Macrs with recovery in 10 years = investment x macrs rate PV = a x b x c 1 0.4 0.9259259 $ 3,680,000 0.1 $368,000 $ 136,296.30 2 0.4 0.8573388 $ 3,680,000 0.18 $662,400 $ 227,160.49 3 0.4 0.7938322 $ 3,680,000 0.144 $529,920 $ 168,267.03 4 0.4 0.7350299 $ 3,680,000 0.1152 $423,936 $ 124,642.25 5 0.4 0.6805832 $ 3,680,000 0.0922 $339,296 $ 92,367.66 6 0.4 0.6301696 $ 3,680,000 0.0737 $271,216 $ 68,364.83 7 0.4 0.5834904 $ 3,680,000 0.0655 $241,040 $ 56,257.81 8 0.4 0.5402689 $ 3,680,000 0.0655 $241,040 $ 52,090.56 9 0.4 0.5002490 $ 3,680,000 0.0656 $241,408 $ 48,305.64 10 0.4 0.4631935 $ 3,680,000 0.0655 $241,040 $ 44,659.26 11 0.4 0.4288829 $ 3,680,000 0.0328 $120,704 $ 20,707.15 $1,039,119.00