Question

Bond Returns:

A 15-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. After one year, assuming the the yield to maturity (discount rate) remains the same as previous, calculate the following returns between the two years:

1) Current yield

2) Capital gains yield

3) Total returns

Hint:

• solve the rate (yield to maturity) for the 25-year bond.
• with the same yield to maturity, solve the price for the bond with shorter maturity.
• Show all your work for full credit.

year	0	1
rate	??	10%
nper	15	14
pmt	85	85
pv	-925	??
fv	1000	1000
type	0	0
excel	rate	pv
calculation	??	??
price	??	??	<-- from calculation
coupon		??	<-- from bond specifications
current yield		??	<-- coupon / last price
capital gains yield		??	<-- % change in price
Total return		??	<-- current yield + capital yield

Answer 1

$85 [$1,000 x 8.5%) 1 Annual coupon payment Bond's current price $925 Current yield (Annual coupon/Price) 9.19% [$85 / $925] 2) & 3) First, bond's YTM shall be calculated: # of years left to maturity, NPER 15 $85 [$1,000 x 8.5%) $925 Annual coupon Payment, PMT Bond's current price, PV 1,000 [Terminal (last) cash flow-->Par value of the bond] o-0 if paid at the end of each year; 1 if paid at the beginning of each year 9.4556% [Ref: NOTE Bond's maturity value at the end, FV Annual coupon type, TYPE Bond's yield to maturity (YTM) NOTE: Bond's yield to maturity is calculated using EXCEL FUNCTION RATE(nper,pmt,pv,fv,type) where nper-15; pmt-85; pv-925; fv--1000; Here, pmt &fv are negative as they denote cash inflows; Value for pv is positive because it denotes cash outflow; type 0 as coupon are paid at the end of each year only.

1 # of years left to maturity, NPER 15 -84*8.5% [$1,000 x 8.5%) 2 Annual coupon Payment, PMT 3 Bond's current price, PV $925 $1,000 [Terminal (last) cash flow->Par value of the bond] 0 0 if paid at the end of each year; 1 if paid at the beginning of each year 4 Bond's maturity value at the end, FV 5 Annual coupon type, TYPE Bond's yield to maturity (YTM) -RATE(B1,-B2,B3,-B4,B5) [Ref: NOTE] 6 1-year later Annual market rate, RATE 9.4556% As calculated above] # of years to maturity, NPER 14 [15-1] $85 [$1,000 x 8.5%) Annual coupon payment, PMT $1,000 [Terminal (last) cash flow - ->Par value of the bond] Maturity value at the end, FV Annual coupon type, TYPE 0 0 if paid at the end of each year; 1 if paid at the beginning of each vear $927.46 [Ref: NOTE] Bond price after 1 year Bond's current price $925.00 $2.46 [$927.46 $925] Change in bond price in one year Annual coupon received in one year $85.00 [$1,000 x 8.5%) Total returns earned over 1 year $87.46 0.27% [$2.46/$925] 2) Capital gain yield

3) Total returns (Holding period return) 9.46%[9.19% +0.27%) NOTE Bond price after 1 year is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate:9.4556%; nper-14; pmt-85; fv=-1000; type =0. Here, value for pmt & fv are negative as they denote cash inflows; type-0 as coupons paid at the end of each year only 1 Annual market rate, RATE 9.4556% As calculated above -15-1 [15-1] 2 # of years to maturity, NPER :84*8.5% [$1,000 x 8.5%) 3 Annual coupon payment, PMT $1,000 [Terminal (last) cash flow - ->Par value of the bond] 4 Maturity value at the end, FV 5 Annual coupon type, TYPE 00 if paid at the end of each year; 1 if paid at the beginning of each year 6 Bond price after 1 year -PV(B1,B2,-B3,-B4,B5) [Ref: NOTE] 7 Bond's current price $925.00 8 Change in bond price in one year -B6-B7 -83 [$1,000 x 8.5%) 9 Annual coupon received in one year 10 Total returns earned over 1 year -SUM(B8:B9) 12 2) Capital gain yield B8/B7 13