Question

(Answer as much as you can, I can post the rest if need be, PLEASE SHOW WORK, DONT USE EXCEL thanks!!)

All bonds are semi-annual.  All yield measures are stated as annual percentage rates.

1.         Suppose you buy a 10 year 9% bond that has a YTM of 11%.  What is the price of the bond?

2.         Suppose you buy a 30 year 7% bond that has a YTM of 7.5%.  What is the price of the bond?

3.         What is the YTM of a 7.5 year 12% bond that is currently selling for $1100?

4.       What is the yield to call (YTC) of a 30 year 8% bond selling for $940?  The call deferment period for the bond is 10 years.

5.       What is the yield to call (YTC) of a 20 year 9% bond selling for $1030?  The call deferment period for the bond is 5 years.

6.       What is the holding period yield on a 30 year 7% bond that we buy for $1020.  We sell the bond in 4 years for $1040.

7.       Suppose you bought a 10 year 8% bond for $975.  If you sold the bond for $940 after holding it for 2 years, what was your holding period yield?

Answer 1

1)

No of periods = 10 years * 2 = 20 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (9% / 2) * $1000

Coupon per period = $45

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

Bond Price = $45 / (1 + 11% / 2)¹ + $45 / (1 + 11% / 2)² + ...+ $45 / (1 + 11% / 2)¹⁰ + $1,000 / (1 + 11% / 2)¹⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $45 * (1 - (1 + 11% / 2)^-20) / (11% / 2) + $1,000 / (1 + 11% / 2)²⁰

Bond Price = $537.77 + $342.73

Bond Price = $880.50

2)

No of periods = 30 years * 2 = 60 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (7% / 2) * $1000

Coupon per period = $35

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

Bond Price = $35 / (1 + 7.5% / 2)¹ + $35 / (1 + 7.5% / 2)² + ...+ $35 / (1 + 7.5% / 2)⁶⁰ + $1,000 / (1 + 7.5% / 2)⁶⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $35 * (1 - (1 + 7.5% / 2)^-60) / (7.5% / 2) + $1,000 / (1 + 7.5% / 2)⁶⁰

Bond Price = $830.83 + $109.83

Bond Price = $940.66

3)

No of periods = 7.5 years * 2 = 15 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (12% / 2) * $1000

Coupon per period = $60

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

1100 = $60 / (1 + YTM / 2)¹ + $60 / (1 + YTM / 2)² + ...+ $60 / (1 + YTM / 2)¹⁵ + $1,000 / (1 + YTM / 2)¹⁵

Using Texas Internements BA 2 plus calculator

SET N = 15, PV = -1100, FV = 1000, PMT = 60

CPT --> I/Y = 5.0343

Yield to Maturity(YTM) = 2 * I/Y

Yield to Maturity(YTM) = 2 * 5.0343%

Yield to Maturity(YTM) = 10.0687%

4)

No of periods to Call = 10 years * 2 = 20 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (8% / 2) * $1000

Coupon per period = $40

Bond Price = Coupon / (1 + YTC / 2)^period + Face value / (1 + YTC / 2)^period

940 = $40 / (1 + YTC / 2)¹ + $40 / (1 + YTC / 2)² + ...+ $40 / (1 + YTC / 2)²⁰ + $1,000 / (1 + YTC / 2)²⁰

Using Texas Internements BA 2 plus calculator

SET N = 20, PV = -940, FV = 1000, PMT = 40

CPT --> I/Y = 4.4596

Yield to Call (YTC) = 2 * I/Y

Yield to Call (YTC) = 2 * 4.4596%

Yield to Call (YTC) = 8.9193%

5)

No of periods to Call = 5 years * 2 = 10 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (9% / 2) * $1000

Coupon per period = $45

Bond Price = Coupon / (1 + YTC / 2)^period + Face value / (1 + YTC / 2)^period

1030 = $45 / (1 + YTC / 2)¹ + $45 / (1 + YTC / 2)² + ...+ $45 / (1 + YTC / 2)¹⁰ + $1,000 / (1 + YTC / 2)¹⁰

Using Texas Internements BA 2 plus calculator

SET N = 10, PV = -1030, FV = 1000, PMT = 45

CPT --> I/Y = 4.1278

Yield to Call (YTC) = 2 * I/Y

Yield to Call (YTC) = 2 * 4.1278%

Yield to Call (YTC) = 8.2555%

6)

No of periods = 30 years * 2 = 60 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (7% / 2) * $1000

Coupon per period = $35

Let us compute the Yield to Maturity (YTM)

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

1020 = $35 / (1 + YTM / 2)¹ + $35 / (1 + YTM / 2)² + ...+ $35 / (1 + YTM / 2)⁶⁰ + $1,000 / (1 + YTM / 2)⁶⁰

Using Texas Internements BA 2 plus calculator

SET N = 60, PV = -1020, FV = 1000, PMT = 35

CPT --> I/Y = 3.4211

Yield to Maturity(YTM) = 2 * I/Y

Yield to Maturity(YTM) = 2 * 3.4211%

Yield to Maturity(YTM) = 6.8422%

Using the the YTM as reinvestment rate to get future value of coupons for 8 semi annual periods

Value of reinvested coupons = Coupons * ((1 + YTM / 2)^{no of periods} - 1) / (YTM / 2)

Value of reinvested coupons = $35 * ((1 + 6.8422% / 2)⁸ - 1) / (6.8422% / 2)

Value of reinvested coupons = $315.92

Holding period yield = ((Sale price + Value of reinvested coupons) / Purcahse price)^{(1 / no of years)} -1

Holding period yield = (($1040 + $315.92) / 1020)^(1/4) - 1

Holding period yield = 7.3763%

7)

No of periods = 10 years * 2 = 20 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (8% / 2) * $1000

Coupon per period = $40

Let us compute the Yield to Maturity (YTM)

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

975 = $40 / (1 + YTM / 2)¹ + $40 / (1 + YTM / 2)² + ...+ $40 / (1 + YTM / 2)²⁰ + $1,000 / (1 + YTM / 2)²⁰

Using Texas Internements BA 2 plus calculator

SET N = 20, PV = -975, FV = 1000, PMT = 40

CPT --> I/Y = 4.1870

Yield to Maturity(YTM) = 2 * I/Y

Yield to Maturity(YTM) = 2 * 4.1870

Yield to Maturity(YTM) = 8.3740%

Using the the YTM as reinvestment rate to get future value of coupons for 4 semi annual periods

Value of reinvested coupons = Coupons * ((1 + YTM / 2)^{no of periods} - 1) / (YTM / 2)

Value of reinvested coupons = $40 * ((1 + 8.3740% / 2)⁴ - 1) / (8.3740% / 2)

Value of reinvested coupons = $170.33

Holding period yield = ((Sale price + Value of reinvested coupons) / Purcahse price)^{(1 / no of years)} -1

Holding period yield = (($940 + $170.33) / $975)^(1/2) - 1

Holding period yield = 6.7146%