Engineering
Empire Beauty School Engineering Nominal and Effective Interest Rates Questions

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Topics: • • • Nominal and effective interest rates Bond value as an example of present worth (PW) Chapter 6: Comparison and selection amongst alternatives based on PW, AW, IRR, and Incremental Analysis Instructions: • For full credit, begin each calculation with an appropriate formula, show accurate calculations and appropriate units, and clearly identify your answers. The submissions are recommended to be computer generated. You can write mathematical equations in MS Word and export them to pdf file. See https://support.office.com/en-us/article/Write-insert-or-change-an-equation-1d01cabcceb1-458d-bc70-7f9737722702 • • • Please be sure your work is neat and legible, not scribbled or squeezed into the white spaces and margins of the assignment sheet. Identify your answers clearly. Answer all sub questions (if any) of a problem for full credit for that problem. 1. Try Your Skills 4-MMM Compute the effective annual interest rate in each of the following situations. (See section 4.14 of the textbook) (a) 5.75% nominal interest, compounded quarterly (b) 5.75% nominal interest, compounded daily 2. Exercise 4-100 Find the interest rates in the following situations. (See section 4.14 of the textbook) (a) APR = 8%, compounded monthly. Find the effective annual interest rate. (b) Nominal rate is 10% compounded quarterly. Find the effective semi-annual rate. (c) The effective annual interest rate is 11.02% and compounding is monthly. Find the nominal interest rate. (d) r = 6% and compounding is monthly. Find the effective quarterly interest rate. 3. Try Your Skills 5-J What is the maximum price you will pay for a bond with a face value of $1,000 and a coupon rate of 14%, paid annually, if you want a yield to maturity of 10%? Assume that the bond will mature in 10 years and the first payment will be received in one year. (See section 5.3 of the textbook) 4. Exercise 5-10 A corporate bond pays 5% of its face value once per year. If this $5,000 10-year bond sells now for $5,500, what yield will be earned on this bond? Assume the bond will be redeemed at the end of 10 years for $5,000. (See section 5.3.2 of the textbook) 5. Try Your Skills 6O A stem cell research project requires expensive specialized laboratory equipment. For this purpose, three pieces of equipment and their associated cash flows (listed below) are under consideration. One piece of equipment must be selected, and the laboratory’s MARR is 15% per year. (See section 6.4 of the textbook) EOY A B C 0 −136,500 −$84,000 −$126,000 1-4 −$12,500 −$28,500 −$15,500 5 −$10,000 −28,500 −15,500 (a) Use the PW method to rank-order the economic attractiveness of the three projects. (b) Determine the interest rate at which the laboratory would be indifferent between Equipment B and Equipment C. 6. Try Your Skills 6-U A municipal police department has decided to acquire an unmanned drone for aerial surveillance of a high-crime region of their city. Three mutually exclusive drones are being studied and their data are provided below. All alternatives are expected to have negligible market (salvage) values at the end of five years. The police department’s MARR is 8% per year. Which drone should be selected? (See section 6.4 of the textbook) Alternative Capital Investment Annual Expenses A $740,000 $361,940 B $1,840,000 $183,810 C $540,000 $420,000 7. Try Your Skills 6AA Two insulation thickness alternatives have been proposed for a process steam line subject to severe weather conditions. One alternative must be selected. Estimated savings in heat loss and insulation cost are given below. Thickness Installed Cost Annual Savings Life 2 cm $20,000 $5,000 4 years 5 cm $40,000 $7,000 6 years Which thickness would you recommend for a MARR = 15% per year and negligible market (salvage) values? The study period is 12 years. (See section 6.5 of the textbook) 8. Exercise 6-5: Your company is environmentally conscious and is considering two heating options for a new research building. What you know about each option is below, and your company will use an annual interest rate (MARR) of 8% for this decision. Which is the lower cost option for this company? (See sections 4.12 and 6.4 of the textbook) Hint: Consider a 20-year study of equivalent present worth. If 𝑓 ̅ ≠ 𝑖 we can find the present value of a geometric series by using the formula 𝑃𝑊 = ̅ 𝑁)] 𝐴1 [1 − (𝑃⁄𝐹 , 𝑖%, 𝑁)(𝐹 ⁄𝑃 , 𝑓%, 𝑖 − 𝑓̅ Where A1 is the initial cash flow in the series Gas Heating Option: The initial equipment and installation of the natural gas system would cost $225,000 right now. The maintenance costs of the equipment are expected to be $2,000 per year, starting next year, for each of the next 20 years. The energy cost is expected to be $5,000 starting next year and is expected to rise by 5% per year for each of the next 20 years due to the price of natural gas increasing. Geothermal Heating Option: Because of green energy incentive provided by the government, the geothermal equipment and installation are expected to cost only $200,000 right now, which is cheaper than the gas lines. There would be no energy cost with geothermal, but because this is a relatively newer technology the maintenance is expected to be $10,000 per year, starting next year, for each of the next 20 years. 9. Exercise 6-7: Fiesta Foundry is considering a new furnace that will allow them to be more productive. Three alternative furnaces are under consideration. Furnace A Furnace B Furnace C Initial investment $450,000 $400,000 $300,000 Annual revenues * $80,000 $70,000 $70,000 Annual cost * $10,000 $8,000 $13,000 Salvage value $50,000 $40,000 $35,000 Life of asset 15 years 15 years 15 years * Annual revenue and cost figures are increases over the “do nothing” alternative. Perform an incremental analysis of thee alternative using the IRR method for each increment of cash flows. The MARR is 12% per year. (See section 6.4 of the textbook) 10. Exercise 6-86: Consider the mutually exclusive alternatives given in the table below. The MARR is 10% per year. Capital investment (thousands) Uniform annual savings (thousands) Useful life (years) Alternative X Alternative Y Alternative Z $500,000 $250,000 $400,000 $131,900 $40,690 $44,050 5 10 20 Assuming repeatability, which alternative should the company select? Hint: Compare the annual worth of the alternative. (See section 6.5 of the textbook) (a) Alternative X (b) Alternative Y (c) Alternative Z (d) Do nothing Factor Name (F/P, i, N) Single payment compound amount factor Moves a single payment to N periods later in time (P/F, i, N) Single payment present worth factor Moves a single payment to N periods earlier in time (A/F, i, N) Sinking Fund factor Takes a single payment and spreads into a uniform series over N earlier periods. The last payment in the series occurs at the same time as F. (F/A, i, N) Uniform Series Compound Amount factor Takes a uniform series and moves it to a single value at the time of the last payment in the series. Capital Recovery Factor Takes a single payment and spreads it into a uniform series over N later periods. The first payment in the series occurs one period later than P. Uniform Series Present Worth Factor Takes a uniform series and moves it to a single payment one period earlier than the first payment of the series. Arithmetic Gradient Present Worth Factor Takes a arithmetic gradient series and moves it to a single payment two periods earlier than the first nonzero payment of the series. Arithmetic Gradient to Uniform Series Factor Takes a arithmetic gradient series and converts it to a uniform series. The two series cover the same interval, but the first payment of the gradient series is 0. (A/P, i, N) (P/A, i, N) (P/G, i, N) (A/G, i, N) Formula Purpose ...
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Final Answer

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Topics:




Nominal and effective interest rates
Bond value as an example of present worth (PW)
Chapter 6: Comparison and selection amongst alternatives based on PW, AW, IRR, and
Incremental Analysis

Instructions:


For full credit, begin each calculation with an appropriate formula, show accurate
calculations and appropriate units, and clearly identify your answers. The submissions are
recommended to be computer generated. You can write mathematical equations in MS
Word and export them to pdf file. See
https://support.office.com/en-us/article/Write-insert-or-change-an-equation-1d01cabcceb1-458d-bc70-7f9737722702





Please be sure your work is neat and legible, not scribbled or squeezed into the white
spaces and margins of the assignment sheet.
Identify your answers clearly.
Answer all sub questions (if any) of a problem for full credit for that problem.

1. Try Your Skills 4-MMM Compute the effective annual interest rate in each of the following
situations. (See section 4.14 of the textbook)
(a) 5.75% nominal interest, compounded quarterly
𝑟 𝑛
((1 + ) − 1) ∗ 100
𝑛
. 0575 4
) − 1) ∗ 100 = 𝟓. 𝟖𝟕𝟓%
((1 +
4
(b) 5.75% nominal interest, compounded daily
𝑟 𝑛
((1 + ) − 1) ∗ 100
𝑛
. 0575 365
) − 1) ∗ 100 = 𝟓. 𝟗𝟏𝟖%
((1 +
365

2. Exercise 4-100 Find the interest rates in the following situations. (See section 4.14 of the
textbook)
(a) APR = 8%, compounded monthly. Find the effective annual interest rate.
𝑟 𝑛

((1 + 𝑛) − 1) ∗ 100

. 08 12
) − 1) ∗ 100 = 𝟖. 𝟑%
((1 +
12
(b) Nominal rate is 10% compounded quarterly. Find the effective semi-annual rate.
𝑛

((1 +

𝑟 2
)
𝑛

− 1) ∗ 100
4

. 10 2
) − 1) ∗ 100 = 𝟓. 𝟏%
((1 +
4
(c) The effective annual interest rate is 11.02% and compounding is monthly. Find the
nominal interest rate.
1

Monthly = ((1 + 𝑟)𝑛 − 1) ∗ 100
1

Monthly = ((1 + .1102)12 − 1) ∗ 100 = .875%
Nominal = 12 ∗ .0875 = 𝟏𝟎. 𝟓%
(d) r = 6% and compounding is monthly. Find the effective quarterly interest rate.
𝑟 𝑛

Monthly = ((1 + 𝑛) − 1) ∗ 100
.06 12

Monthly = ((1 + 12 )

− 1) ∗ 100 = 6.168%

Quarterly = .06168/4 = 1.54%

3. Try Your Skills 5-J
What is the maximum price you will pay for a bond with a face
value of $1,000 and a coupon rate of 14%, paid annually, if you want a yield to maturity of
10%? Assume that the bond will mature in 10 years and the first payment will be received in
one year. (See section 5.3 of t...

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Rice University

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