Question

1. Septra, Inc. has a corporate bond issue outstanding that has 12 years remaining to maturity, semiannual coupon payments, a coupon rate of 12% per year and a yield-to-maturity of 7.65% per year. The next coupon payment is exactly six months away. Each bond has $1000 face value.

1. Price an individual bond.

2. The company is considering replacing this bond issue to take advantage of a decrease in interest rates. The company has the ability to ‘call’ each bond for a 10% premium over face value, i.e., each $1000 bond can be repurchased by the company for $1100. If a new 12 year bond issue can be made (at par) by the company at the same yield-to-maturity of 7.65%, should the company replace the bond? Show your work.

Answer 1

a) Semiannual yield rate, RATE # of semiannuals to maturity, NPER Semiannual coupon payment, PMT Maturity value at the end, FV Coupon payment type, TYPE Individual bond's current price 3.825% [7.65% / 2; Annual YTM is converted into Semiannual YTM] 24 [12 years x 2 semiannuals] $60 ($1,000 x 12% / 2] $1,000 [Par value of the bond] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $1,337.64 [Ref: NOTE] NOTE: Individual bond's current price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv, type) where rate=3.825%;nper=24; pmt=-60; fv=-1000; type = 0. Here, value for pmt & fv are negative as they denote cash inflows; type = 0 because coupons are paid at the end of each semiannual only. А C D E F G H 1 Semiannual yield rate, RATE = 7.65%/2 [7.65% / 2; Annual YTM is converted into Semiannual YTM] 2 # of semiannuals to maturity, NPER =12*2 [12 years x 2 semiannuals] 3 Semiannual coupon payment, PMT =1000*12%/2 ($1,000 x 12% / 2] 4 Maturity value at the end, FV $1,000 [Par value of the bond] 5 Coupon payment type, TYPE 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. 6 Individual bond's current price =PV(B1,B2,-B3,-B4,B5) [Ref: NOTE] b) Yes, the company should replace the bond as yield to maturity associated with fresh issue is less than existing yield to maturity and proposed coupon rate. Workings:

# of semiannuals left to maturity, NPER Semiannual coupon Payment, PMT Bond's current selling price, PV Bond's maturity value at the end, FV Semiannual compounding type, TYPE Bond's Semiannual yield to maturity Number of semiannuals in a year Yield to maturity if bonds are called at premium EXCEL SCREENSHOT: 24 [12 years x 2 semiannuals] $38.25 ($1,000 x 7.65% / 2] $1,100 (Given that $1,000 bond is repurchased at 10% premium for $1,100] $1,000 [Par value of the bond] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period 3.2204% [Ref: EXCEL SCREENSHOT] 6.441% [3.2204% x2] Bond's Semiannual yield to maturity is calculated using EXCEL FUNCTION RATE(nper,pmt,pv,fv,type) where nper=24; pmt=-38.25; pv=1100; fv=-1000; type=0; value for pmt is input as negative figure as it denotes cash inflow; Value for fv is also negative because it denotes cash inflow; type = 0 as coupon payments are made at the end of each semiannual only. А B C D E 1 # of semiannuals left to maturity, NPER =12*2 [12 years x 2 semiannuals] 2 Semiannual coupon Payment, PMT =1000*7.65%/2 ($1,000 x 7.65% / 2] 3 Bond's current selling price, PV $1,100 [Given that $1,000 bond is repurchased at 10% premium for $1,100] 4. Bond's maturity value at the end, FV $1,000 [Par value of the bond] 5 Semiannual compounding type, TYPE 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period 6 Bond's Semiannual yield to maturity =RATE(B1,-B2,B3,-B4,B5) [Ref: EXCEL SCREENSHOT] 7 Number of semiannuals in a year 8 Yield to maturity if bonds are called at premium =B6*B7 [3.2204% x 2]