Module 9 Critical Thinking Assignment: Valuation And Charact ✓ Solved

Module 9 Critical Thinking Assignment Valuation and Character

Complete the problems in an Excel spreadsheet. Be sure to show your work to receive credit; no hard keys.

Problem 9.1: Bond Valuation Calculate the value of bond that matures in 10 years and 1,000 SAR par value. The coupon rate is 8% and the market's required yield to maturity is 12%.

Problem 9.2: Yield to Maturity A bond's market price is 850 SAR. It has a 1000 par value, will mature in 8 years, and the coupon rate 8 percent annually. What is the bond's yield to maturity? What happens to the bond's yield to maturity if the bond matures in 16 years? What is mature in 5 years?

Problem 9.3: Bond Valuation w/Semiannual Coupon Payment A bond matures in 10 years with 1,000 SAR par value. The coupon rate is 8% and the market's required yield to maturity is 12%. What would be the value of this bond if it pays the coupon payment semiannually?

Problem 9.4: Bond Valuation w/Zero Coupon Payment A zero coupon bond matures in 10 years with 1,000 SAR par value. The market's required yield to maturity is 12%. What would be the value of this bond?

Problem 9:5: Bondholder’s Expected Rate of Return A bond matures in 15 years with 1,000 SAR par value. The coupon rate is 9% and the market price is 1250 SAR. What would be the expected rate of this bond?

Paper For Above Instructions

This paper aims to methodically address the bond valuation problems presented in the assignment while demonstrating the calculations necessary to arrive at the correct values.

Problem 9.1: Bond Valuation

To calculate the value of a bond, we use the formula for the present value of cash flows, which consists of the present value of the coupon payments and the present value of the par value. The formula is as follows:

Bond Value = C × [1 - (1 + r)-n] / r + F / (1 + r)n

Where:

  • C = Annual coupon payment = 1000 SAR × 8% = 80 SAR
  • r = Market yield to maturity = 12% or 0.12
  • n = Number of years to maturity = 10
  • F = Par value of the bond = 1000 SAR

Using the above formula, we can calculate the value of the bond:

Bond Value = 80 × [1 - (1 + 0.12)-10] / 0.12 + 1000 / (1 + 0.12)10

Calculating the present value of the coupon payment:

PV of Coupons = 80 × [1 - (1 + 0.12)-10] / 0.12 = 80 × 5.65 = 452 SAR

Calculating the present value of par:

PV of Par = 1000 / (1 + 0.12)10 = 1000 / 3.478 = 287 SAR

Bond Value = 452 + 287 = 739 SAR

Problem 9.2: Yield to Maturity

The yield to maturity (YTM) of a bond can be calculated using the following formula:

YTM = C + (F - P) / n / (F + P) / 2

Where:

  • C = Annual coupon payment = 1000 SAR × 8% = 80 SAR
  • F = Par value = 1000 SAR
  • P = Current market price = 850 SAR
  • n = Number of years to maturity = 8

Calculating YTM:

YTM = 80 + (1000 - 850) / 8 / (1000 + 850) / 2 = 80 + 18.75 / 925 = 0.095 = 9.5%

If the bond matures in 16 and 5 years, the YTM changes as follows:

For 16 years: YTM = 80 + (1000 - 850) / 16 / (1000 + 850) / 2 = 80 + 9.375 / 925 = 0.091 = 9.1%

For 5 years: YTM = 80 + (1000 - 850) / 5 / (1000 + 850) / 2 = 80 + 30 / 925 = 0.119 = 11.9%

Problem 9.3: Bond Valuation w/Semiannual Coupon Payment

When a bond pays semiannual coupon payments, the coupon rate and yield to maturity are divided by 2 and the number of periods is multiplied by 2. Therefore:

  • Coupon Payment = 1000 SAR × (8%/2) = 40 SAR
  • Market Yield = 12%/2 = 6% or 0.06
  • Total Periods = 10 × 2 = 20

The bond valuation formula remains the same:

Bond Value = 40 × [1 - (1 + 0.06)-20] / 0.06 + 1000 / (1 + 0.06)20

Calculating:

PV of Coupons = 40 × [1 - (1 + 0.06)-20] / 0.06 = 40 × 12.462 = 498.48 SAR

PV of Par = 1000 / (1 + 0.06)20 = 1000 / 3.207 = 311.80 SAR

Bond Value = 498.48 + 311.80 = 810.28 SAR

Problem 9.4: Bond Valuation w/Zero Coupon Payment

For a zero-coupon bond, the formula simplifies as there are no periodic coupon payments:

Bond Value = F / (1 + r)n

Where:

  • F = 1000 SAR
  • r = 12% or 0.12
  • n = 10

Calculating:

Bond Value = 1000 / (1 + 0.12)10 = 1000 / 3.478 = 287 SAR

Problem 9.5: Bondholder’s Expected Rate of Return

The expected rate of return can be calculated using the formula:

Expected Rate of Return = C + (F - P) / n / P

Where:

  • C = Annual coupon payment = 1000 SAR × 9% = 90 SAR
  • F = 1000 SAR
  • P = 1250 SAR
  • n = 15

Calculating:

Expected Rate of Return = 90 + (1000 - 1250) / 15 / 1250 = 90 - 16.67 / 1250 = 0.045 = 4.5%

References

  • Fabozzi, F. J. (2018). Bond Markets, Analysis and Strategies. Pearson.
  • Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
  • Fabozzi, F. J., & Drake, P. P. (2009). Foundations of Financial Markets and Institutions. Pearson.
  • Megginson, W. L., & Smart, S. B. (2015). Introduction to Financial Management. Cengage Learning.
  • Hillier, D., Griffin, P., & Morkor, D. (2018). Financial Management: A Global Perspective. Cengage Learning.
  • Dunbar, N. (2017). Principles of Finance. Cengage Learning.
  • Tyler, C. R. (2016). Valuing Bonds. CFA Institute Publications.
  • Richard, W. (2016). Fixed Income Analysis. Wiley.
  • Ross, S., Westerfield, R., & Jaffe, J. (2016). Corporate Finance. McGraw-Hill Education.
  • Investopedia. (2021). Yield to Maturity (YTM) Definition. Retrieved from https://www.investopedia.com/terms/y/yieldtomaturity.asp

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