# Present value purchase decision

A married couple is planning to buy a new sport utility vehicle (SUV) 5 years from now. They expect the SUV to cost $32,000 at the time of purchase. (a) If they want to have half of the cost for a down payment, how much must they save each year (starting at the end of the current year) if they can earn 10% per year on their saving. Alternatively, (b) they can set aside a lump sum 2 years from now in a savings account that earns 10% annual (compound) interest in order to have their down payment. How much should this lump sum of money be? (c) If they choose to deposit 5 equal end-of-year amounts in the savings account in order to pay in full for the SUV 5 years from now, what will be the equivalent annual worth? (d) What is the equivalent present value of the SUV? Assume the same interest rate.

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#### Solution Preview

To find the amount we need to save each year, we need to use the future value of an annuity formula:

FV = A (1+i)^n -1 / i

This gives us:

16000= A ((1.1)^5 ...

#### Solution Summary

SUV purchase decision based on present value calculations.

Evaluating cost and benefit for a capital budgeting decision

Capital Budgeting

Sky View Resorts, Inc. (SVR)

SVR owns and operates a resort lodge in Western Maryland. The BOD is considering the replacement of the seven years old HVAC system with a newer and more energy efficient system. The decision has been accelerated since the US Congress has approved tax incentives for business owners to perform such upgrades over the next 24 months.

The key issue for the BOD is whether or not the up-front cost of the new HVAC system, expected to have an installed cost of $800,000 will be offset by the energy cost savings over the life of the new system (estimated to be five years). The new system that is being considered is expected to reduce the number of KWH needed by 35% when compared to the operation (and KWH need) of the existing system. Chart 2 below (Forecasted KWH usage) illustrates the current expectation for KWH usage if the old system is maintained.

You have been tasked, as the CFO for SVR, to evaluate the cost / benefit of this capital budgeting decision. Your primary quantitative deliverables (you will find that the use of MS Excel will make the process less time consuming) to the BOD are as follows:

1. A schedule that computes the weighted average expected cost of electricity (generation plus transmission) over the next eight years. This computation is built around a probability distribution that considers volatile electricity costs (per KWH) as well as forecasted KWH usage by SVR. The information below is based upon your research including meetings with Big Sun Electric Utility.

Chart 1 - Forecasted KWH cost (the chart below is stated in dollars per KWH)

2014 2015 2016 2017 2018

Low end price per KWH projection (30% probability) .130 .135 .140 .145 .150

Mid range price per KWH projection (50% probability) .150 .160 .165 .175 .190

High end price per KWH projection (20% probability) .170 .185 .205 .230 .260

For each year you will calculate the weighted average expected cost per KWH. For example, for 2014 the weighted average expected cost is calculated as:

.30 times .13 plus .50 times .15 plus .20 times .17) = .148 per KWH

Chart 2 - Forecasted KWH usage (the chart below states KWH in millions)

The forecast of KWH usage must consider a wide range of forecasts from number of guest days to average annual temperature. The following chart is your forecast of KWH usage based upon your first round of research. This is the forecast if the current system is maintained. If the new system is purchased the demand for KWH will decrease by 35% below the values stated below.

2014 2015 2016 2017 2018

Low end estimate of KWH usage (40% Probability) 3.0 3.1 3.2 3.3 3.4

Mid-range estimate of KWH usage (40% Probability) 3.2 3.4 3.6 3.8 4.0 High end estimate of KWH usage (20% Probability) 3.5 3.8 4.1 4.4 4.7

For each year you will calculate the weighted average expected number of KWH consumption. For example, for 2014 the weighted average expected cost is calculated as:

.40 times 3 plus .40 times 3.2 plus .2 times 3.5 = 3.18 million KWH (the weighted average expectation)

Deliverable 1 (deliverable from you to the BOD) is a summary chart that shows the BOD your weighted average cost of electricity (total dollars) for the next five years (2014 - 2018). For 2014 that value will be the forecasted per KWH charge of .148 per KWH (see above) times the forecasted consumption of 3.18 million KWH (see above). The cost of electricity (if the old system continues to be used) is then forecasted to be $470,640.

2. Deliverable two (from you to the BOD) is a schedule that shows the BOD the annual expected cost savings if the new system is purchased. Your first pass estimated (based upon speaking with the system's manufacturer) consumption savings percentage (from the improved efficiency) is 35%. You are aware that this is an "educated" estimate. You'd like to make a firmer forecast but the dynamic of changing weather conditions (hotter and or colder), changing customer demand for rooms (how strong will the economy be? And the volatility of the cost of a KWH makes a firm comfort level likely unattainable. Given this you decide to prepare schedule that compares the savings at 35% (your best estimate) to the savings achieved at 30% (a more conservative savings rate) and 40% (a more optimistic savings rate).

Your schedule might look something like this:

Forecasted annual energy cost savings 2014 - 2018 (in thousands)

2014 2015 2016 2017 2018

Savings with a 30% efficiency

Savings with a 35% efficiency

Savings with a 40% efficiency

For 2014 the values would be calculated as follows:

Since the forecasted cost of electricity, if SVR continues to use the existing system, was previously calculated as $470,640 you would multiply this amount by the 30%, 35%, and the 40% energy savings rates respectively. For 30% - $141,192, for 35% $164,724, and for 40% - $188,256. This calculation will be performed for each of the years 2014 - 2018.

3. The next schedule (deliverable 3) needs to show the BOD the annual energy cash cost savings from the purchase of the new system, by year, and then the calculation of the present value of the net annual cash flow. The BOD has advised you to use a 10% rate (the hurdle rate) for discounting purposes.

You will need to prepare this schedule for each year for each level of efficiency. The firm is in the 35% combined federal and state tax bracket. For depreciation, assume that the tax incentive allows a business to depreciate the system over 5 years (as opposed to the normal 7 years at a minimum) Your schedule might look something like this.

Forecasted annual cash flow (assume that on 12.31.14 the firm has a cash outflow of $800,000 to purchase the system)

The 30% energy efficiency model (you will show models at 30%, 35%, and 40%) might look something like this:

2014 2015 2016 2017 2018

Energy cost savings $141,192

Depreciation Expense 160,000

Taxable gain (loss) (18,808)

Tax savings (expense) at 35% 6,583

Net Income after tax (12,225)

Add back depreciation 160,000

Net Cash Flow 147,775

Present Value Factor .9091

Present Value of Cash Flow $134,342

Total Present Values (sum of 2014 - 2018)

4. Schedule (deliverable) four shows the BOD the Net Present Value of each version of your calculations . The format of your schedule might look something like this:

NPV Summary HVAC Replacement with a 10% Hurdle Rate applied.

30% Efficiency 35% Efficiency 40% Efficiency

Total Present Value of Cash Inflows You supply these values

Less Present Value of Cash Outflow $(800,000) $(800,000) $(800,000)

Net Present Value of Cash Flow You supply these values

Your full report to the BOD should contain the above schedules (four in total) as well as commentary related to the following:

1. An intro to the project as a whole. Remember, this goes to the BOD. Use an efficient / effective / professional introduction and delivery for your work.

2. Identification and summary of key assumptions. The BOD's and yours (if any).

3. Key assumptions that present the greatest potential volatility. Discussion of potential impact(s).

4. Brief intro to each schedule. Remember, this is a professional memo.....not an academic assignment. Write with a very clear purpose.

5. Commentary throughout related to key outcomes and remaining uncertainties

6. A strong conclusion and recommendation to the BOD.

The full report is likely in the six (approximate) page range.

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