Deer Valley Lodge
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I am asked to compute the before-tax Net Present Value or NPV of a new ski lift for Deer Valley Lodge and advise the management there of the profitability. Before I am able to make this calculation there are a few calculations that I will need to make first. First the total amount of the investment, this will be the cost of a lift itself $2 million plus the cost of preparing the slope and installing the lift $1.3 million. Thus the investment amount for one lift is $3.3 million.
Next I will need to find out the yearly net income from the investment. This will be gross ticket sales minus the total expenses. Deer Valley expects 300 skiers per day for 40 days at $55.00 per ticket, giving us $660,000 in ticket sales. In order to figure the total expenses I need to separate the fixed and variable expenses. Fixed expenses are those that will be there everyday the lodge is open regardless of the number of skiers. The Lodge is open 200 days per year and the cost of running the new lift is $500 per day for the entire 200 days giving us $100,000 in fixed costs. Variable costs are the expenses based on the number of customers. There is an additional $5 expense per skier per day associated with the new lift. If there are 300 skiers multiplied by $5 each multiplied by the 40 days that they are expected to be on the lift, we will have $60,000 in variable expenses. Fixed costs of $100,000 plus the variable costs of $60,000 will give us $160,000 in total expenses. The gross ticket sales of $660,000 minus the total expenses of $160,000 give us a yearly net income of $500,000.
The new lift has an economic life of 20 years and we would like to make 14% on our investment. The NPV factor of 14% at 20 years is 6.6231. By multiplying our net yearly income or our annuity of $500,000 times the NPV factor of 6.6231 we will have a NPV of $3,311,550.
When comparing the NPV to the amount of the investment I find that there will be a before tax profit of $11,550, meaning that this could be a good investment.
I am now asked to compute the after-tax NPV of a new lift and again advise the management of the profitability. Our income tax rate is 40% leaving us with 60% of our net yearly income. Our net yearly income is $500,000 by multiplying that times 60%, our percentage that we will have left after taxes, we end up with $300,000.
Our rate of return will drop to 8% since we will be expecting a lower rate of return after taxes. The NPV factor for 20 years @ 8% is 9.8181. By multiplying the NPV factor of 9.8181 times our after tax annuity of $300,000 we have a NPV of $2,945,430.00 for our after tax net income.
Next I need to find the NPV of the tax savings from the depreciation of the investment. The amount of money that we save on taxes will be the amount of the deduction times the tax rate. I will be able to deduct the total investment over 10 years as depreciation. To find the tax savings on the investment I multiply the investment amount of $3.3 million times the tax rate of 40% to find the tax savings of $1,320,000.00. I then multiply the tax savings times the NPV factor of .7059, the discount rate of 8% at 10 years, to find $931,788.00, the NPV of the tax savings.
Now to find the total NPV of the after-tax income