## Capital Budgeting and Investment Analysis

## Question 1 : Engine System Comparison.

**An airline is considering two types of engine systems for use in its planes: System A costs $400,000 and uses 50,000 gallons of fuel per 1,000 hours of operation at the average load encountered in passenger service. System B costs $600,000 and uses 40,000 gallons of fuel per 1,000 hours of operation at the average load encountered in passenger service. Both engine systems have the same life and the same maintenance and repair record, and both have a three-year life before any major overhaul is required. Each system has a salvage value of 10% of the initial investment. The jet fuel costs $5 per gallon currently and fuel consumption is expected to increase at the rate of 5% per year because of degrading engine efficiency. Assume 2,000 hours of operation per year and an interest rate of 12%. Compute the cash flow and the balance for both systems.**

## Answer

To compare the two engine systems, we need to calculate the cash flow and the balance for each system.

an additional assumption that the fuel consumption rate will increase by 5% each year:

For System A:

- Initial Cost: $400,000
- Fuel cost in year 1: 50,000 gallons/1,000 hours x 2,000 hours/year x $5/gallon = $500,000
- Salvage Value: 10% of initial cost = $40,000
- Fuel consumption rate in year 2: 50,000 gallons/1,000 hours x 2,000 hours/year x 1.05 = 105,000 gallons/year
- Fuel cost in year 2: 105,000 gallons/year x $5/gallon = $525,000
- Fuel consumption rate in year 3: 50,000 gallons/1,000 hours x 2,000 hours/year x 1.05^2 = 110,250 gallons/year
- Fuel cost in year 3: 110,250 gallons/year x $5/gallon = $551,250
- Cash flow in year 1: $2,000,000 – $860,000 = $1,140,000
- Cash flow in year 2: $2,000,000 – $525,000 – $40,000/(1+12%) + $1,140,000/(1+12%)^2 = $692,736
- Cash flow in year 3: $2,000,000 – $551,250 – $40,000/(1+12%)^2 + $692,736/(1+12%)^3 = $737,686
- Balance in year 3: -$400,000 + $737,686 = $337,686

For System B:

- Initial Cost: $600,000
- Fuel cost in year 1: 40,000 gallons/1,000 hours x 2,000 hours/year x $5/gallon = $400,000
- Salvage Value: 10% of initial cost = $60,000
- Fuel consumption rate in year 2: 40,000 gallons/1,000 hours x 2,000 hours/year x 1.05 = 84,000 gallons/year
- Fuel cost in year 2: 84,000 gallons/year x $5/gallon = $420,000
- Fuel consumption rate in year 3: 40,000 gallons/1,000 hours x 2,000 hours/year x 1.05^2 = 88,200 gallons/year
- Fuel cost in year 3: 88,200 gallons/year x $5/gallon = $441,000
- Cash flow in year 1: $2,000,000 – $940,000 = $1,060,000
- Cash flow in year 2: $2,000,000 – $420,000 – $60,000/(1+12%) + $1,060,000/(1+12%)^2 = $740,469
- Cash flow in year 3: $2,000,000 – $441,000 – $60,000/(1+12%)^2 + $740,469/(1+12%)^3 = $785,181
- Balance in year 3: -$600,000 + $785,181 = $185,181

**Based on these calculations, System B has a higher initial cost but lower fuel cost, resulting in a higher cash flow and balance compared to System A. Therefore, System B may be the more favorable choice.**

## Question 2: Impact of a specific industry (coal mining) on the local housing market.

**A company mines 390,000 tons of coal per year in a rural county. The coal is worth $75 per ton. The average price for a 2,000-squak-loot house with thene bedrooms more than 20 im aweay from the mining site in Bis county is $220,000. The averago price for a similar, 2,000 -square-foot house with thee bedrocms wilhin 4 km of the mine is 8 percent fowee. Using comparative statics, what is the eflect of mining on home prises in this county? Mining changes the price of a 2,000-square-foot home (with three bedrooms) by 5 (Round your rosponse to fwo docimal pleces and use a negative sign if nocessary)**

**Answer**:

A company mines 390,000 tons of coal per year in a rural county. The coal is worth $75 per ton, so the total value of coal mined by the company per year is:

390,000 tons/year x $75/ton = $29,250,000/year

The average price for a 2,000-square-foot house with three bedrooms more than 20 miles away from the mining site in the county is $220,000. This represents the baseline price of such a house in the county.

The average price for a similar, 2,000-square-foot house with three bedrooms within 4 km of the mine is 8% lower than the baseline price:

New Price = Old Price – 0.08 x Old Price New Price = 0.92 x $220,000 New Price = $202,400

So the price of a house within 4 km of the mine is $202,400.

Assuming that a 1% increase in coal production leads to a 5% decrease in home prices, a 100% increase in coal production would lead to a 500% decrease in home prices. This can be calculated as follows:

% Change in Price = (-500% x $202,400) / $220,000 % Change in Price = -$460

Therefore, a 100% increase in coal production (i.e., doubling the current production of 390,000 tons/year) would lead to a 460% decrease in the price of a 2,000-square-foot house with three bedrooms within 4 km of the mine. This translates to a price reduction of $202,400 x 4.6 = -$931,840.

So the effect of mining on the price of a 2,000-square-foot house with three bedrooms within 4 km of the mine is a 460% decrease (i.e., a price reduction of $931,840). This is a substantial negative effect on home prices in the county.

## Question 3: Monopoly

a. **Complete the table below, which shows the costs and revenues of Solo the monopolist. (You may assume that the demand curve is a straight line.) Leave no cells blank – be certain to enter “0” wherever required. Quantity per Period Price TR MR MC TC 0 / / / / / 1 $32 $ $ $6 75 2 7 82 3 28 6 88 4 5 93 5 12 6 99 6 7 106 7 20 8 114 8 9 123 9 10 133 10 12 145 **

**b. What are the values of the profit-maximizing output, price, and total profit or loss? Output: Price: $ Total At what outout will total revenue be maximized, and what will be the value of total revenue?**

**a.**

Quantity per Period | Price | Total Revenue (TR) | Marginal Revenue (MR) | Marginal Cost (MC) | Total Cost (TC) |
---|---|---|---|---|---|

0 | / | / | / | / | 0 |

1 | $32 | $32 | $32 | $6 | $38 |

2 | $28 | $56 | $24 | $7 | $51 |

3 | $24 | $72 | -$4 | $6 | $60 |

4 | $20 | $80 | -$8 | $5 | $68 |

5 | $16 | $80 | $0 | $6 | $85 |

6 | $12 | $72 | $12 | $7 | $103 |

7 | $8 | $56 | $24 | $8 | $122 |

8 | $4 | $32 | $16 | $9 | $142 |

9 | $0 | $0 | -$32 | $10 | $163 |

10 | $0 | $0 | $0 | $12 | $185 |

The table provided shows the costs and revenues of Solo the monopolist at different levels of output. It is assumed that the demand curve is a straight line, and the marginal cost of production increases as output increases due to diminishing returns to scale.

The table has several columns that show different aspects of Solo’s costs and revenues:

- Quantity per Period: This column shows the level of output that Solo produces in each period, ranging from 0 to 10 units.
- Price: This column shows the price that Solo charges for each unit of output. As a monopolist, Solo has market power and can set the price higher than the marginal cost of production.
- Total Revenue (TR): This column shows the total revenue that Solo earns from selling the corresponding quantity of output. It is calculated by multiplying the price by the quantity sold.
- Marginal Revenue (MR): This column shows the additional revenue that Solo earns from selling one more unit of output. As a monopolist, Solo faces a downward-sloping demand curve, which means that to sell an additional unit of output, Solo must lower the price of all units sold. As a result, the marginal revenue of Solo is less than the price of the good.
- Marginal Cost (MC): This column shows the additional cost that Solo incurs from producing one more unit of output. Due to diminishing returns to scale, Solo’s marginal cost of production increases as output increases.
- Total Cost (TC): This column shows the total cost that Solo incurs to produce the corresponding quantity of output. It is calculated by adding up the marginal cost of each unit produced.

**b.**

The table provides a detailed picture of Solo’s costs and revenues at different levels of output, which can be used to determine the profit-maximizing level of output, price, and total profit or loss.

The profit-maximizing output is 6, the price is $12, and the total profit is $3. Total revenue will be maximized at an output of 5, and the value of total revenue will be $80.

To determine the profit-maximizing level of output and price, we need to find the level of output at which marginal revenue equals marginal cost. At this level of output, Solo is producing the optimal amount of output where the marginal benefit from selling an additional unit equals the marginal cost of production.

From the table, we can see that at an output of 6 units, the marginal revenue is $12 and the marginal cost is $7. Therefore, this is the profit-maximizing level of output, and the price Solo charges for each unit is $12.

To calculate the total profit, we need to subtract the total cost from the total revenue. At an output of 6 units, the total revenue is $72 (6 units x $12 per unit), and the total cost is $69 (see the “TC” column for an output of 6). Therefore, the total profit is $3 ($72 – $69).

To determine the output level at which total revenue is maximized, we need to find the level of output at which the marginal revenue is zero. From the table, we can see that at an output of 5 units, the marginal revenue is zero. Therefore, this is the output level at which total revenue is maximized.

To calculate the value of total revenue at an output of 5 units, we simply need to multiply the price by the quantity sold. Since the price is $16 and the quantity sold is 5 units, the total revenue is $80 (5 units x $16 per unit).

## Question 3: Time value of money and annuities.

**Suppose you make 15 equal annual deposits of $ 1280 each into a bank account paying 14 % interest per year.The first deposit will be made one year from today.How much money can be Withdrawn from this bank account after the 15th deposit?**

Answer :

This is a problem of future value of an annuity with regular deposits. We can use the formula for future value of an annuity:

FV = PMT * ((1 + r)^n – 1) / r

where: FV = future value PMT = regular payment r = interest rate per period n = number of periods

In this case, PMT = $1280, r = 14% per year, and n = 15 years. However, we need to calculate the future value after all 15 deposits have been made, so we need to adjust n to take into account the fact that the first deposit will be made one year from today. Therefore, we use n = 14 instead of 15.

Plugging in the numbers, we get:

FV = $1280 * ((1 + 0.14)^14 – 1) / 0.14 FV = $44,704.63

Therefore, the amount of money that can be withdrawn from this bank account after the 15th deposit is $44,704.63.

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