Homework Assignment Please Explain Each Answer Due On Monday
Homework Assignmentplease Explain Each Answer Due On Monday At 7amch
Explain each answer thoroughly, demonstrating understanding of core concepts, calculations, and implications. Address each problem individually, providing detailed explanations, calculations, and reasoning behind the answers. Use relevant financial formulas, tables, and concepts such as present value, future value, interest rates, and elasticity where applicable. Incorporate proper citations and references for any external data or formulas used. Present your responses in a clear, logical, and organized manner appropriate for an academic setting.
Paper For Above instruction
Question 1: Tommy John is set to receive $1,000,000 in three years, with a current market interest rate of 10%.
a. The present value (PV) of this future sum can be calculated using the present value table in Exhibit 8, which provides discount factors for different interest rates and periods. The formula for PV is:
PV = Future Value / (1 + r)^n
Where r is the annual interest rate (10% or 0.10), and n is the number of years (3). Using the present value factor from the table, which at 10% for 3 years is approximately 0.7513, the PV is:
PV = $1,000,000 × 0.7513 ≈ $751,300
Rounded to the nearest dollar, the present value is approximately $751,300.
b. The present value is less than the future $1,000,000 due to the fundamental principle of the time value of money. The primary reasons include:
- Inflation: reduces the purchasing power of future dollars, making future sums less valuable today.
- Interest accumulation: money today can be invested to earn interest, so a dollar today is worth more than a dollar in the future unless compensated by interest.
Because of these factors, the present value reflects the amount of money that, if invested today at the prevailing interest rate, would grow to the future sum.
Question 2:
Determining the present value of receiving $200,000 annually for four years at 7% interest.
a. Using successive computations and the present value table in Exhibit 8, the present value of each year's payment is calculated as:
- Year 1: PV = $200,000 × Present value factor at 7% for year 1
- Year 2: PV = $200,000 × Present value factor at 7% for year 2
- Year 3: PV = $200,000 × Present value factor at 7% for year 3
- Year 4: PV = $200,000 × Present value factor at 7% for year 4
Using the table, the factors are approximately 0.9346 for year 1, 0.8734 for year 2, 0.8163 for year 3, and 0.7629 for year 4. Therefore:
- Year 1: $200,000 × 0.9346 ≈ $186,920
- Year 2: $200,000 × 0.8734 ≈ $174,680
- Year 3: $200,000 × 0.8163 ≈ $163,260
- Year 4: $200,000 × 0.7629 ≈ $152,580
Total present value = sum of the above ≈ $677,440.
b. Using the present value of an annuity table in Exhibit 10 (assuming it has the factor for 4 periods at 7%), which is approximately 3.3872, we multiply the annual payment by this factor:
PV = $200,000 × 3.3872 ≈ $677,440
This confirms the previous calculation, simplifying the process for multiple payments.
c. The present value of these four installments ($800,000 total) is less than $800,000 because of the time value of money. Future payments are discounted back to the present, reflecting that money received earlier is more valuable than the same amount received later, due to earning potential and inflationary effects.
Question 3:
On January 1, 2016, you win a lottery with a prize of $50,000,000 paid in eight annual installments of $6,250,000 starting December 31, 2016. The current interest rate is 5%. To find the present value, we treat this as an annuity and use the present value of an annuity formula:
PV = Payment × Present value of annuity factor at 5% for 8 years
The annuity factor at 5% for 8 years from Table 2 is approximately 6.4632.
So, PV = $6,250,000 × 6.4632 ≈ $40,404,750.
This represents the current worth of the future installment payments, discounted at the prevailing interest rate.
Question 4:
The scenario is similar to question 3; therefore, the present value at 5% has already been calculated as approximately $40,404,750. The question asks whether the present value at 12% interest would be higher or lower than at 5%. Since increasing the discount rate raises the discounting effect, the present value at 12% would be less than at 5%. Therefore, the answer is:
· No
The present value decreases when the discount rate increases, because future payments are worth less in today's terms at higher interest rates.
Question 5:
Pinder Co. issues $25 million of bonds with a 7% coupon rate over five years, payable semiannually. The bonds' market rate is 9%. To determine the present value of these bonds, we consider two components: the present value of the coupon payments and the present value of the face value, both discounted at the market rate.
First, the semiannual interest payment is:
Coupon payment = (7% × $25,000,000)/2 = $875,000
Number of periods = 5 years × 2 = 10
Market interest rate per period = 9% / 2 = 4.5% or 0.045
Using the present value of an annuity formula, with the present value of an annuity factor for 10 periods at 4.5% (approximately 8.7903), the PV of interest payments is:
PV of coupons = $875,000 × 8.7903 ≈ $7,682,612.50
The face value is discounted as a lump sum using the present value factor for 10 periods at 4.5%, which is approximately 0.6292:
PV of face value = $25,000,000 × 0.6292 ≈ $15,730,000
Adding both components gives the total bond value:
Bond PV ≈ $7,682,613 + $15,730,000 ≈ $23,412,613
Thus, the market value of the bonds is approximately $23,412,613, reflecting the discount due to the higher market rate compared to the coupon rate.
References
- Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
- Higgins, R. C. (2018). Analysis for Financial Management. McGraw-Hill Education.
- Ross, S. A., Westerfield, R., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
- Damodaran, A. (2015). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
- Investopedia. (2023). Present Value (PV) Definition. https://www.investopedia.com/terms/p/presentvalue.asp
- Exhibit 8 & Exhibit 10 Data Tables from the textbook or course materials on financial calculations.
- Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance. Pearson.
- Moyer, R. C., McGuigan, J. R., & Kretlow, W. J. (2018). Contemporary Financial Management. Cengage Learning.
- Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies. Pearson.
- Palepu, K. G., & Healy, P. M. (2018). Business Analysis & Valuation: Using Financial Statements. Cengage Learning.