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# Calculting NVP

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Deer Valley Lodge, a ski resort in the Wasatch Mountains of Utah, has plans to eventually add five new chairlifts. Suppose that one lift costs \$2 million, and preparing the slope and installing the lift costs another \$1.3 million. The lift will allow 300 additional skiers on the slopes, but there are only 40 days a year when the extra capacity will be needed. (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 200 days the lodge is open. Assume that the lift tickets at Deer Valley cost \$55 a day and the added cash expenses for each skier-day are \$5. The new lift has an economic life of 20 years.

1. 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. What subjective factors would affect the investment decision?

#### Solution Preview

1. Assume that the before-tax required rate of return for Deer
Valley is 14%. Compute the before-tax NPV of the new lift and
will be a profitable investment.

To calculate the Net Present Value (NPV) of the proposed investment,
we deduct the Present Value (PV) of the anticipated future cash flows
from the investment cost.

Since the cost of purchasing the lift is \$2,000,000 and the cost to
install it is \$1,300,000, the total investment comes to

\$2,000,000 + \$1,300,000 = \$3,300,000.

To calculate the PV, we must first compute the annual cash flow resulting
from the investment. If the new lift makes it possible to accommodate
300 more skiers for each of 40 days, then Deer Valley Lodge gains

300 * 40 = 12,000

skier-days annually.

Given that a lift ticket for one skier for one day costs \$55, the 12,000
additional skier-days make a positive contribution of

12,000 * \$55 = \$660,000

to the annual cash flow.

Now let us consider the annual costs arising from the purchase of the
lift. Operating costs are \$500 for each of 200 days, making a total of

200 * \$500 = \$100,000

annually.

Furthermore, each of the 12,000 skier-days results in additional expenses
of \$5, for an annual total of

12,000 * \$5 = \$60,000.

The net annual cash flow is therefore

\$660,000 - \$100,000 - \$60,000 = \$500,000.

To compute the PV, we begin with a value multiplier of 1.0 and divide
it each year by

100% + 14% = 114% = 1.14

to account for the 14% required rate of return.

For each of the 20 years in the economic life of the new lift, then,
we have the following adjusted net cash flow.

(1) \$500000.00 / (1.14 * 1.0000) = \$500000.00 / 1.1400 = \$438596.49

(2) \$500000.00 / (1.14 * 1.1400) = \$500000.00 / 1.2996 = \$384733.76

(3) \$500000.00 / (1.14 * 1.2996) = \$500000.00 / 1.4815 = \$337485.76

(4) \$500000.00 / (1.14 * 1.4815) = \$500000.00 / 1.6890 = \$296040.14

(5) \$500000.00 / (1.14 * 1.6890) = \$500000.00 / 1.9254 = \$259684.33

(6) \$500000.00 / (1.14 * 1.9254) = \$500000.00 / 2.1950 = ...

\$2.19