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Chapter 14 0 Saved Help Save & Exit Submit Check my work 12 A 2-year bond with par value $1,000 making annual coupon payments of $122 is priced at $1,000. a. What is the yield to maturity of the bond? (Round your answer to 1 decimal place.) points Yield to maturity % eBook Print References b. What will be the realized compound yield to maturity if the 1-year interest rate next year turns out to be (i) 8%, (ii) 9%, (iii) 10%? (Round your answers to 2 decimal places.) r Realized YTM 8% 9% 10%

Answer 1

PART A: Calculating Yield to Maturity

The yield to maturity is the effective yield on a bond on the basis of the expected coupons and reinvestment of the received coupons till maturity. The same can be calculated as given below:

Par Value	$1000	Given
Price = Initial Investment	$1000	Given
Coupon	$122	Annual Frequency
Tenor of Bond = n	2	Years
Coupon Rate	12.20%	Calculated as = 122 / 1000
Re-invest. Rate of coupon	12.20%	Same as coupon rate
Particular	Year 1	Reinvestment	CF at end of Year 2
1st Coupon	122	122 * (1 + 12.2%)	136.88
2nd Coupon + Principal			1122.00
Total Investment Value			1258.88

• The coupon received at the end of Year 1 is reinvested for another year at the same rate i.e. 12.2% giving $ 136.88 [= 122 * (1 + 12.2%)] at the end of two years.
• Hence, at the end of two years, we received, $ 136.88 and $ 1122 (i.e. the coupon for second year along with the principal)

The overall yield can be calculated as:

YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1

Hence, YTM = (1258.88 / 1000 ) ^ (1/2) – 1

YTM = 12.2%

PART B: Realized YTM is the interest rate changes i.e. The Re-investment rate of coupon changes

When Re-investment rate of coupon = 8%

Particular	Year 1	Reinvestment	Total
1st Coupon	122	122 * (1 + 8%)	131.76
2nd Coupon + Principal			1122
Total Cash Flows			1253.76

• The coupon received at the end of Year 1 is reinvested for another year at the same rate i.e. 8% giving $ 131.76 [= 122 * (1 + 8%)] at the end of two years.
• Hence, at the end of two years, we received, $ 131.76 and $ 1122 (i.e. the coupon for second year along with the principal)

The overall yield can be calculated as:

YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1

Hence, YTM = (1253.76 / 1000 ) ^ (1/2) – 1

YTM = 11.97%

When Re-investment rate of coupon = 9%

Particular	Year 1	Reinvestment	Total
1st Coupon	122	122 * (1 + 9%)	132.98
2nd Coupon + Principal			1122
Total Cash Flows			1254.98

• The coupon received at the end of Year 1 is reinvested for another year at the same rate i.e. 9% giving $ 132.98 [122 * (1 + 9%)] at the end of two years.
• Hence, at the end of two years, we received, $ 132.98 and $ 1122 (i.e. the coupon for second year along with the principal)

The overall yield can be calculated as:

YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1

Hence, YTM = (1254.98 / 1000 ) ^ (1/2) – 1

YTM = 12.03%

When Re-investment rate of coupon = 10%

Particular	Year 1	Reinvestment	Total
1st Coupon	122	122 * (1 + 10%)	134.2
2nd Coupon + Principal			1122
Total Cash Flows			1256.2

• The coupon received at the end of Year 1 is reinvested for another year at the same rate i.e. 10% giving $ 134.2 [= 122 * (1 + 10%)] at the end of two years.
• Hence, at the end of two years, we received, $ 134.2 and $ 1122 (i.e. the coupon for second year along with the principal)

The overall yield can be calculated as:

YTM = (Investment value at end of tenor / Initial Investment) ^ (1 / n) – 1

Hence, YTM = (1256.2 / 1000 ) ^ (1/2) – 1

YTM = 12.08%

r	Realized YTM
8%	11.97%
9%	12.03%
10%	12.08%