You Are The Managing Partner Of A Marketing Consulting Firm ✓ Solved

You are the managing partner of a marketing consulting firm that specializes in athletics and sports management Your firm includes the following departments legal public relations accounting management consulting talent representation and event management

You are the managing partner of a marketing consulting firm that specializes in athletics and sports management. Your firm includes the following departments: legal, public relations, accounting, management consulting, talent representation, and event management.

Assuming the market rate of interest is 10%, calculate the selling price for each bond issue. If required, round your intermediate calculations and final answers to the nearest dollar.

Situation: Selling Price of the Bond Issue

  • a. 640 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments
  • b. 640 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments
  • c. 830 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments
  • d. 1,950 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments

Use the appropriate present value table: PV of $1 and PV of Annuity of $1 (See Above).

Sample Paper For Above instruction

Introduction

Determining the selling price of bonds based on market interest rates requires understanding of present value calculations. Bonds issued with different terms, face values, and payment structures must be evaluated to establish their fair market value. In this paper, we will calculate the selling prices for four different bond issues using a 10% market interest rate, by applying present value tables for both lump sum (PV of $1) and annuities (PV of an $1).

Understanding Bond Valuation

The market value of bonds is essentially the present value of their future cash flows, which include periodic interest payments and the face value repayment at maturity. These cash flows are discounted using the current market rate of interest, which reflects investor expectations and the risk profile of the bond issuer.

Calculations for Each Bond Issue

Bond Issue A: 640 Bonds; $1,000 Face Value; 8% Stated Rate; 5 Years; Annually

Interest payments per bond = $1,000 x 8% = $80

Number of bonds = 640

Total annual interest payments = 640 x $80 = $51,200

Since interest is paid annually, we use the PV of an annuity of $1 for 5 years at 10% = 3.79 (from PV annuity table), and PV of $1 for 5 years at 10% = 0.621 (from PV of $1 table).

Present value of interest payments = $51,200 x 3.79 = $193,888

Present value of face value = $640,000 x 0.621 = $397,440

Total bond price = $193,888 + $397,440 = $591,328

Bond Issue B: 640 Bonds; $1,000 Face Value; 8% Stated Rate; 5 Years; Semiannual Payments

Interest payment per period = $1,000 x 8% / 2 = $40

Total payments per period = 640 x $40 = $25,600

Number of periods = 5 x 2 = 10

PV of an ordinary annuity of $1 for 10 periods at 10%/2 = 4.92

PV of $1 for 10 periods at 10%/2 = 0.613

Present value of interest payments = $25,600 x 4.92 = $125,952

Present value of face value = $640,000 x 0.613 = $392,320

Total bond price = $125,952 + $392,320 = $518,272

Bond Issue C: 830 Bonds; $1,000 Face Value; 8% Stated Rate; 10 Years; Semiannual Payments

Interest per period = $1,000 x 8% / 2 = $40

Total payments per period = 830 x $40 = $33,200

Number of periods = 10 x 2 = 20

PV of an annuity of $1 for 20 periods at 10%/2 = 12.46

PV of $1 for 20 periods = 0.1486

Present value of interest payments = $33,200 x 12.46 = $413,332

Present value of face value = $830,000 x 0.1486 = $123,638

Total bond price = $413,332 + $123,638 = $536,970

Bond Issue D: 1,950 Bonds; $500 Face Value; 12% Stated Rate; 15 Years; Semiannual Payments

Interest per period = $500 x 12% / 2 = $30

Total payments per period = 1,950 x $30 = $58,500

Number of periods = 15 x 2 = 30

PV of an annuity of $1 for 30 periods at 10%/2 = 15.09

PV of $1 for 30 periods = 0.2314

Present value of interest payments = $58,500 x 15.09 = $882,765

Present value of face value = $975,000 x 0.2314 = $225,915

Total bond price = $882,765 + $225,915 = $1,108,680

Conclusion

Calculating the bond prices involves applying present value calculations based on the respective cash flow timings, payment amounts, and the prevailing market interest rate. The differences among the bonds stem from their durations, payment frequencies, and face values. These calculations facilitate accurate bond valuation, ensuring that the bonds are priced fairly in the market, aligning with investor expectations and risk assessment.

References

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