1.

Where: i = interest rate per annum (yield to maturity or YTM), m = number of coupons per year, and n = number of years to maturity.

d: Discuss the diffulties of estimating the expected cash flows for some types of bonds and identify the bonds for which estimating the expected cash flows is difficult.

Normally, estimating the cash flow stream of a high-quality option-free bond is relatively straight forward, as the amount and timing of the coupons and principal payments are known with a high degree of certainty. Remove that certainty, and difficulties will arise in estimating the cash flow stream of a bond. Aside from normal credit risks, the following three conditions could lead to difficulties in forecasting the future cash flow stream of even high-quality issues:

The presence of embedded options, such as call features and sinking fund provisions - in which case, the length of the cash flow stream (life of the bond) cannot be determined with certainty.

The use of a variable, rather than a fixed, coupon rate - in which case, the future annual or semi-annual coupon payments cannot be determined with certainty.

The presence of a conversion or exchange privilege, so you're dealing with a convertible (or exchangeable) bond, rather than a straight bond - in which case, it's difficult to know how long it will be before the bond is converted into stock.

e: Compute the value of a bond, given the expected cash flows and the appropriate discount rates.

Example: Annual coupons. Suppose that we have a 10-year, $1,000 par value, 6% annual coupon bond. The cash value of each coupon is: CPN= ($1,000 * 0.06)/1 = $60. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 10, PMT = 60, FV = 1000, I/Y = 8; CPT PV = 865.80. This value would typically be quoted as 86.58, meaning 86.58% of par value, or $865.80.

Bond value = [60 / (1.08)1] + [60 / (1.08)2] + [60 + 100 / (1.08)3] = $865.80

Example: Semiannual coupons. Suppose that we have a 10-year, $1,000 par value, 6% semiannual coupon bond. The cash value of each coupon is: CPN = ($1,000 * 0.06)/2 = $30. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 20, PMT = 30, FV = 1000, I/Y = 4; CPT PV = 864.10. Note that the coupons constitute an annuity.

f: Explain how the value of a bond changes if the discount rate increases or decreases and compute the change in value that is attributable to the rate change.

The required yield to maturity can change dramatically during the life of a bond. These changes can be market wide (i.e., the general level of interest rates in the economy) or specific to the issue (e.g., a change in credit quality). However, for a standard, option-free bond the cash flows will not change during the life of the bond. Changes in required yield are reflected in the bond’s price.

Where: i = interest rate per annum (yield to maturity or YTM), m = number of coupons per year, and n = number of years to maturity.

d: Discuss the diffulties of estimating the expected cash flows for some types of bonds and identify the bonds for which estimating the expected cash flows is difficult.

Normally, estimating the cash flow stream of a high-quality option-free bond is relatively straight forward, as the amount and timing of the coupons and principal payments are known with a high degree of certainty. Remove that certainty, and difficulties will arise in estimating the cash flow stream of a bond. Aside from normal credit risks, the following three conditions could lead to difficulties in forecasting the future cash flow stream of even high-quality issues:

The presence of embedded options, such as call features and sinking fund provisions - in which case, the length of the cash flow stream (life of the bond) cannot be determined with certainty.

The use of a variable, rather than a fixed, coupon rate - in which case, the future annual or semi-annual coupon payments cannot be determined with certainty.

The presence of a conversion or exchange privilege, so you're dealing with a convertible (or exchangeable) bond, rather than a straight bond - in which case, it's difficult to know how long it will be before the bond is converted into stock.

e: Compute the value of a bond, given the expected cash flows and the appropriate discount rates.

Example: Annual coupons. Suppose that we have a 10-year, $1,000 par value, 6% annual coupon bond. The cash value of each coupon is: CPN= ($1,000 * 0.06)/1 = $60. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 10, PMT = 60, FV = 1000, I/Y = 8; CPT PV = 865.80. This value would typically be quoted as 86.58, meaning 86.58% of par value, or $865.80.

Bond value = [60 / (1.08)1] + [60 / (1.08)2] + [60 + 100 / (1.08)3] = $865.80

Example: Semiannual coupons. Suppose that we have a 10-year, $1,000 par value, 6% semiannual coupon bond. The cash value of each coupon is: CPN = ($1,000 * 0.06)/2 = $30. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 20, PMT = 30, FV = 1000, I/Y = 4; CPT PV = 864.10. Note that the coupons constitute an annuity.

f: Explain how the value of a bond changes if the discount rate increases or decreases and compute the change in value that is attributable to the rate change.

The required yield to maturity can change dramatically during the life of a bond. These changes can be market wide (i.e., the general level of interest rates in the economy) or specific to the issue (e.g., a change in credit quality). However, for a standard, option-free bond the cash flows will not change during the life of the bond. Changes in required yield are reflected in the bond’s price.