Question

Bond Valuation and Changes in Maturity and Required Returns Suppose Level 10 Systems sold an issue of bonds with a 15-year maturity, a $1,000 par value, a 6% coupon rate, and semiannual interest payments.

1. Six years after the bonds were issued, the going rate of interest on bonds such as these fell to 5%. At what price would the bonds sell?

2. Suppose that, 6 years after the initial offering, the going interest rate had risen to 8%. At what price would the bonds sell?

3. Suppose that the conditions in part a existed—that is, interest rates fell to 5% 6 years after the issue date. Suppose further that the interest rate remained at 5% for the next 9 years. What would happen to the price of the bonds over time?

Answer 1

Part (a): After 6 years, Interest rate  reduced to 5%. Price is ascertained using the PV function of Excel, at $1071.766818 as follows:

Alignment Values $1,000 6% Semiannual Clipboard Font 012 - foc =PV(D11/05,09,010,02,0) А B Formula Cell Ref. 2 Face Value (FV) Given 3 Coupon rate (R) Given 4 Interest frequency Given 5 Number of coupon payments a year 6 Original term (T) Given 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t D6-D7 9 Number of future coupon payments (t) Nit D5*D6 10 Amount of coupon payment FV*R/2 D1*D2/D4 11 Interest rate (YTM) Given 12 Price (Present value) 18 $30 5% ($1,071.766818) PV

Part (b): After 6 years of issue, if interest rate is increased to 8%, price decreases to $873.407030 as follows:

Clipboard Font Allghment Values $1,000 6% Semiannual D12 fc =PV(D11/D5,D9, D10, D2,0) A Formula Cell Ref. 2 Face Value (FV) Given 3 Coupon rate (R) Given 4 Interest frequency Given 5 Number of coupon payments a year 6 Original term (T) Given 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t 06-07 9 Number of future coupon payments (t) N*t D5*D6 10 Amount of coupon payment FV*R/2 D1*D2/D4 11 Interest rate (YTM) Given 12 Price (Present value) 18 $30 8% ($873.407030) PV 13

Part (c): As per part (a), price had increased to $1071.77 on decrease in interest rate to 5% after 6 years of issue. When interest rate remains at the same level of 5% during the remaining tenure of 9 years, price gets adjusted on passage of time to reach the face value. Illustrated below

А I E F G H 1 6% $1,000 $1,000 $1,000 $1,000 $1,000 6% 6% 6% 6% Semiannual Semiannual Semiannual Semiannual Semiannual 2 15 2 15 2 Face Value (FV) 3 Coupon rate (R) 4 Interest frequency 5 Number of coupon payments a year 6 Original term (T) 7 Priod expired (years) (t) 8 Time to maturity (no. of years) (N) 9 Number of future coupon payments (t) 10 Amount of coupon payment 11 Interest rate (YTM) 12 Price (Present value) 7 16 12 0 14 $30 $30 $30 $30 18 $30 5% (1,071.77) 5% 5% 5% (1,065.28) 5% (1,000.00) (1,058.45) (1,051.29)