PA11-3 Comparing, Prioritizing Multiple Projects [LO 11-1, 11-2, 11-3, 11-6]

Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume straight line depreciation method is used.   

Project 1: Retooling Manufacturing Facility

This project would require an initial investment of $5,750,000. It would generate $1,027,000 in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $1,216,000.

Project 2: Purchase Patent for New Product

The patent would cost $4,030,000, which would be fully amortized over five years. Production of this product would generate $866,450 additional annual net income for Hearne.

Project 3: Purchase a New Fleet of Delivery Trucks

Hearne could purchase 25 new delivery trucks at a cost of $205,000 each. The fleet would have a useful life of 10 years, and each truck would have a salvage value of $6,800. Purchasing the fleet would allow Hearne to expand its customer territory resulting in $1,101,900 of additional net income per year.


Required:
1. Determine each project's accounting rate of return. (Round your answers to 2 decimal places.)

       

2. Determine each project's payback period. (Round your answers to 2 decimal places.)

       

3. Using a discount rate of 10 percent, calculate the net present value of each project. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

       

4. Determine the profitability index of each project and prioritize the projects for Hearne. (Round your intermediate calculations to 2 decimal places. Round your final answers to 4 decimal places.)

    

PA11-3 Comparing, Prioritizing Multiple Projects [LO 11-1, 11-2, 11-3, 11-6]

Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume straight line depreciation method is used.   

Project 1: Retooling Manufacturing Facility

This project would require an initial investment of $5,750,000. It would generate $1,027,000 in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $1,216,000.

Project 2: Purchase Patent for New Product

The patent would cost $4,030,000, which would be fully amortized over five years. Production of this product would generate $866,450 additional annual net income for Hearne.

Project 3: Purchase a New Fleet of Delivery Trucks

Hearne could purchase 25 new delivery trucks at a cost of $205,000 each. The fleet would have a useful life of 10 years, and each truck would have a salvage value of $6,800. Purchasing the fleet would allow Hearne to expand its customer territory resulting in $1,101,900 of additional net income per year.


Required:
1. Determine each project's accounting rate of return. (Round your answers to 2 decimal places.)

       

2. Determine each project's payback period. (Round your answers to 2 decimal places.)

       

3. Using a discount rate of 10 percent, calculate the net present value of each project. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

       

4. Determine the profitability index of each project and prioritize the projects for Hearne. (Round your intermediate calculations to 2 decimal places. Round your final answers to 4 decimal places.)

PA11-3 Comparing, Prioritizing Multiple Projects [LO 11-1, 11-2, 11-3, 11-6]

Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume straight line depreciation method is used.   

Project 1: Retooling Manufacturing Facility

This project would require an initial investment of $5,500,000. It would generate $982,000 in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $1,156,000.

Project 2: Purchase Patent for New Product

The patent would cost $3,855,000, which would be fully amortized over five years. Production of this product would generate $732,450 additional annual net income for Hearne.

Project 3: Purchase a New Fleet of Delivery Trucks

Hearne could purchase 25 new delivery trucks at a cost of $180,000 each. The fleet would have a useful life of 10 years, and each truck would have a salvage value of $6,300. Purchasing the fleet would allow Hearne to expand its customer territory resulting in $855,000 of additional net income per year.


Required:
1. Determine each project's accounting rate of return. (Round your answers to 2 decimal places.)

       

2. Determine each project's payback period. (Round your answers to 2 decimal places.)

       

3. Using a discount rate of 10 percent, calculate the net present value of each project. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

       

4. Determine the profitability index of each project and prioritize the projects for Hearne. (Round your intermediate calculations to 2 decimal places. Round your final answers to 4 decimal places.)

    

PA11-3 Comparing, Prioritizing Multiple Projects [LO 11-1, 11-2, 11-3, 11-6] Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume straight line depreciation method is used. Project 1: Retooling Manufacturing Facility This project would require an initial investment of $5,600,000. It would generate $1,000,000 in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $1,180,000. Project 2: Purchase Patent for New Product The patent would cost $3,925,000, which would be fully amortized over five years. Production of this product would generate $785,000 additional annual net income for Hearne. Project 3: Purchase a New Fleet of Delivery Trucks Hearne could purchase 25 new delivery trucks at a cost of $190,000 each. The fleet would have a useful life of 10 years, and each truck would have a salvage value of $6,500. Purchasing the fleet would allow Hearne to expand its customer territory resulting in $950,000 of additional net income per year. Required: 1. Determine each project's accounting rate of return. (Round your answers to 2 decimal places.) 2. Determine each project's payback period. (Round your answers to 2 decimal places.) 3. Using a discount rate of 10 percent, calculate the net present value of each project. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.) 4. Determine the profitability index of each project and prioritize the projects for Hearne. (Round your intermediate calculations to 2 decimal places. Round your final answers to 4 decimal places.)

Consider the following quarterly time series.

a. Construct a time series plot. What type of pattern exists in the data?

b. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data.

Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise.

c. Compute the quarterly forecasts for next year based on the model developed in part (b).

(that is for all the four quarters next year)

Q.4 A researcher is interested in whether people’s level of loneliness would vary as a function of their relationship status (single vs. in a relationship), and how such difference might depend on whether people own a pet or not. She recruited a group of participants, asking them about their relationship status, pet ownership, and the perceived level of loneliness. The data are as below, with a higher number denoting greater level of loneliness:

Conduct a proper statistical test by hand calculation to test the hypotheses in b., with 5% as the level of significance (α). (For this exercise, the data assumptions of your chosen statistical test can be taken as reasonably met.) Show your calculation formulae and steps. In case you decide to conduct an ANOVA, you are not required to conduct any post-hoc comparisons. Decide whether to reject the null hypothesis or not for each effect and state the basis of your decision.

2
Question # 1 (15%)
An experiment is conducted to observe the room temperature. Assume the temperature can vary
from 0 oF to 100 oF. A collection of 6 measurements of temperature in a classroom during May is
given below.
Meas. # 1 2 3 4 5 6
--------------------------------------------------------------------------------
Temperature 64 59 61 58 66 60 oF
(a) Define the sample space for the measurements.
(b) Find at least two statistical measures for location. Indicate which one is preferred.
(c) Find the variance and standard deviation.
(d) Construct the boxplot and indicate 1) the normal range of data and 2) if there is any outlier.

Suppose McDonald’s 2020 financial statements contain the following selected data (in millions).

(a1) Compute the following values.

2. Let X1 and X2 have the joint pdf

   f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere

3. (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1.
   (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1.
   (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2).
   (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).

Please answer with a solution. Thank You!

1) Given a differential equation (1−2x²−2y)dy−(4x³+4xy)dx = 0. Is it an exact equation? Justify your answer. Solve the equation.

2) Given a differential equation (y³ − y² sinx − x)dx + (3xy² + 2y cos x)dy = 0. Is it an exact equation? Justify your answer. Solve the equation.

3) Solve the linear equation of order one: dy/dx + (1 + 2/x)y = x^-2e^x

4) Solve the linear equation of order one: xdy/dx − 2y = x⁴e^{x^2}