Coursecodebco126 Coursenamemathematicsoffinancetaskbrief ✓ Solved
COURSE CODE BCO126 COURSE NAME MATHEMATICS OF FINANCE Task brief & rubrics Final Amed Assignment Task This summa)ve assignment is divided in a portafolio of 3 exercises. This is an individual assignment. You have to answer the following ques)ons: QUESTION 1. A new piece of machinery needs to be purchased. The following )meline shows the cash flow of a 5-year project.
Based solely on this informa)on, would you recommend accep)ng or rejec)ng the project? Jus)fy your response technically. QUESTION 2. You have invented an intelligent device that can increase the efficiency of the produc)on chain by 10% for a building materials produc)on company. You intend to sell it in exchange for a perpetual payment that will start at ,000 and grow at a rate of 3% each year.
What is the present value of this perpetuity, if the discount rate is 6%? QUESTION 3. Your Aunt Annie is asking for your advice. She will receive a 4-year annuity star)ng at 0 but increasing by 8% per year. At the end of each year, Aunt Annie likes to deposit the money earned into her bank savings account.
Let's assume that her accounts earn interest at a compounded rate of 5% per year. a) A]er 4 years, what would her account be worth? b) Draw the )meline for the Future Value of this ordinary Annuity. FormaliAes: • Font: Arial 12,5 pts. • Text alignment: Jus)fied. Submission: Mid-term: Week 12 – Via Moodle (Turni)n). Submission deadline Sunday 2nd May 2021. Weight: This assignment count as 40% of your total grade in this subject.
These summa)ve assignments evaluate the following learning outcomes: o Outcome 1: Understand the concept of )me value of money; o Outcome 2: Define the concept of rate of return of a project in finance; o Outcome 3: Dis)nguish between simple and compound interest rates; o Outcome 4: Assess the present value of future cash flows and the future value of regular savings, annually and periodically; o Outcome 5: Demonstrate an ability to apply the technical skills related to the course in a prac)cal context; o Outcome 6: Understand the process of investments appraisal and projects classifica)on; o Outcome 7: Determine percentage calcula)ons and discoun)ng. Rubrics for each quesAon Descriptor 29-33 The student uses the proper formulas, completes the calcula)ons correctly, arrives to the right result, draws the graph correctly when required .9 The student uses the right formula, but applies it wrongly (minor errors, figures in the wrong place…) and then, of course, the result is wrong .9 The student demonstrates a fair understanding of the meaning of the data given and of the ques)on asked, but he/she is not able to iden)fy the formula to be used, does larger errors and/or the calcula)ons are wrong.
18- 20,8 The student demonstrates some understanding of the concepts but he/ she is not able to relate the data given in any way 9- 17,9 The student demonstrates insufficient understanding of the concepts and does not men)on any relevant ideas or concepts, but he/she done not leave it blank 3- 8,9 The student leaves the ques)on blank or cheats. Professional Presentation Research Activity · · · Why is important that you know how to create an effective presentation? · What common mistakes do people make when presenting information to a group? · What tips did you learn about effective PowerPoint presentations? Assignment Instructions Write a one-page paper (not to exceed 250 words). You will be graded on the following: · Quality of your response. · Coherence and organization. · Mechanics. The specific course outcome associated with this assignment is: · Develop a professional development strategy that fosters career readiness skills for masters-prepared health care administrators.
Paper for above instructions
QUESTION 1: Recommendation on Machinery Purchase
To determine whether to accept or reject the project involving the purchase of a new piece of machinery, we must analyze its cash flows over the project’s lifespan. Assuming a cash flow timeline has been provided, we will typically compute the Net Present Value (NPV) using the formula:
\[
\text{NPV} = \sum \frac{C_t}{(1 + r)^t} - C_0
\]
Where:
- \(C_t\) = Cash inflow during the period \(t\)
- \(r\) = discount rate (opportunity cost of capital)
- \(C_0\) = initial investment
If the NPV is greater than zero, it signifies that the project adds value, and we should accept it. Conversely, if NPV is less than or equal to zero, rejecting the project is prudent.
Let’s assume the cash flows from the project are \([-C_0, C_1, C_2, C_3, C_4, C_5]\). Suppose the discount rate is 10%. If for example, the cash flows are:
- Year 0: -0,000
- Year 1: ,000
- Year 2: ,000
- Year 3: ,000
- Year 4: ,000
- Year 5: ,000
Calculation of NPV
Using the above data:
\[
\text{NPV} = \left(\frac{30,000}{(1 + 0.1)^1}\right) + \left(\frac{40,000}{(1 + 0.1)^2}\right) + \left(\frac{50,000}{(1 + 0.1)^3}\right) + \left(\frac{25,000}{(1 + 0.1)^4}\right) + \left(\frac{10,000}{(1 + 0.1)^5}\right) - 100,000
\]
1. Calculate each term:
- Year 1: \( \frac{30,000}{1.1} = 27,272.73 \)
- Year 2: \( \frac{40,000}{1.21} = 33,057.85 \)
- Year 3: \( \frac{50,000}{1.331} = 37,570.09 \)
- Year 4: \( \frac{25,000}{1.4641} = 17,067.71 \)
- Year 5: \( \frac{10,000}{1.61051} = 6,211.18 \)
2. Summing these values gives:
\[
27,272.73 + 33,057.85 + 37,570.09 + 17,067.71 + 6,211.18 = 121,179.56
\]
3. Finally, calculating NPV:
\[
\text{NPV} = 121,179.56 - 100,000 = 21,179.56
\]
Since the NPV is greater than zero, we recommend accepting the project, as it is expected to generate value for the company.
References for Question 1
1. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance. McGraw-Hill Education.
2. Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
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QUESTION 2: Present Value of a Perpetuity
To find the present value of a perpetuity, we utilize the formula:
\[
PV = \frac{C}{r - g}
\]
Where:
- \(C\) = initial cash flow (,000)
- \(r\) = discount rate (6%)
- \(g\) = growth rate (3%)
Substituting in the values:
\[
PV = \frac{10,000}{0.06 - 0.03} = \frac{10,000}{0.03} = 333,333.33
\]
Thus, the present value of the perpetuity is 3,333.33.
References for Question 2
1. Zvi Bodie, Alex Kane, & Alan J. Marcus. (2014). Investments. McGraw-Hill Education.
2. Moyer, R. C., & Harris, M. S. (2004). Analysis of Financial Statements. Wiley.
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QUESTION 3: Aunt Annie's Annuity and Future Value Calculation
Part (a): Future Value of Annuity
Aunt Annie's annuity starts at 0 and increases by 8% annually for 4 years, with an interest rate of 5%.
The future value of an increasing annuity can be calculated using:
\[
FV = P \frac{(1 + g)^n - (1 + r)^n}{g - r}
\]
Where:
- \(P\) = first payment (0)
- \(g\) = growth rate (8%)
- \(r\) = interest rate (5%)
- \(n\) = number of years (4)
Substituting the values:
\[
FV = 800 \cdot \frac{(1 + 0.08)^4 - (1 + 0.05)^4}{0.08 - 0.05}
\]
Calculating each component:
- \((1 + 0.08)^4 = 1.3605\)
- \((1 + 0.05)^4 = 1.2155\)
Substituting these back gives:
\[
FV = 800 \cdot \frac{1.3605 - 1.2155}{0.03} = 800 \cdot \frac{0.145}{0.03} \approx 800 \cdot 4.8333 \approx 3,866.67
\]
After 4 years, Aunt Annie's account would be worth approximately