Name: Score:
55 Multiple choice questions
,Term 1 of 55
1. Consider a zero-coupon bond with a yield to maturity (YTM) of 5%, a face value of $1000, and a
maturity date 10 years from today. What are you willing to pay for this bond today? What will you
be willing to pay for this bond 3 years from today?
What should stock price be today?
P0 = 1.25*1.04/.05 = $26
Po=(D1)/(r-g)= Do(1+g)/(r-g)
(Div PMT) *(1+r))/(r-g) = Price
b. (3 points) What are the dividend yield and capital gains yield?
CGY = .04; DY = .05
a) Bond Value = (50/.06)*(1-1/1.06^30) + 1000/1.06^30 = $862.35
b) Bond Value = (50/.06)(1-1/1.06^10) + (50/.04)(1-1/1.04^20)/1.06^10) + 1000/(1.06^10*1.04^20) =
$1002.27
Bond Value (Today) = 1000/1.05^10 = $613.91
Bond Value (3 years) = 1000/1.05^7 = $613.91*1.05^3 = $710.68
Bond Value (today) = (40/.05)*(1-1/1.05^5) + 1000/1.05^5 = $956.71
Bond Value (1 year from now) = (40/.05)*(1-1/1.05^4) + 1000/1.05^4 = $964.54
Percentage Change (Capital Gains Yield CGY) = (964.54-956.71)/956.71 = .0082 or .82%
Current Yield (year 1) = 40/956.71 = .0418 or 4.18%
NOTE: CGY + Current Yield = .82 + 4.18 = 5% = YTM
Bond Value (2 years from now) = (40/.05)*(1-1/1.05^3) + 1000/1.05^3 = $972.77
CGY = (972.77 - 964.54)/964.54 = .0085 or .85%
Current Yield (year 2) = 40/964.54 = .0415 or 4.15%
NOTE: CGY + Current Yield = .85 + 4.15 = 5% = YTM
,Term 2 of 55
7. Consider a bond that promises to make coupon payments of $150 per year for the next 7 years
and coupon payments of $350 per year for the remaining lifetime of the bond. The face value is
$1200. The bond matures in 20 years and YTM is 9%. What is the value of the bond?
CHEAT SHEET
Today: (70/.05)*(1-1/1.05^5)+(1000/(1.05)^5)=1086.614
1 year: (70/.05)*(1-1/1.05^4)+(1000/(1.05)^4)=1070.9267
CGY=-1.44%
CY=6.44%
YTM=5%
(6.44-1.44)
2 years: (70/.05)*(1-1/1.05^3)+(1000/(1.05)^3)=1054.53
P0 = (41.2/1.15) + (41.2ˆ2/1.15^2) + (41.2^21.4/1.15^3) + (41.2^21.4^2/1.15^4) + (41.2^21.4^3/1.15^5) +
(41.2^21.4^4/1.15^6) + (41.2^21.4^5/1.15^7) + (41.2^21.4^51.03/((.15 - .03)1.15^7) = 149.32
(Divided 1+g/1+r) + (Dividend 1 +g ^years for 20% growth/1+r ^ years) + (Dividend 1 + g^years
1+g^years/1 + g^years)
$4 included every time
20% growth for 1 year, 2 years then locked in at 2 after that
40% growth after 2 years (year 3), t increases until it hits 5
Once t hits 5, 3% forever kicks in, s0 51.03. Then divided by 15% required return - 3% 1+r ^
total years
a) P0 = (1.251.2/1.16) + (1.251.2^2/1.16^2) + (1.251.2^3/1.16^3) + (1.251.2^31.04/((.16 - .04)1.16^3) =
16.01
b) DY0 = 1.25*1.2/16.01 = .094; CGY0 = .16 - .094 = .066
, P1 = 16.01*1.066 = 17.07
DY1 = 1.25*1.2^2/17.07 = .1241; CGY1 = .16 - .1241 = .0359
BV0 = (150/.09)(1-1/1.09^7) + (350/.09)(1-1/1.09^13)/1.09^7 + 1200/1.09^20 = $2402.53
(C first 7/YTM) (1-1/1+YTM)^years + (Cremainder/YTM) (1-1/1+YTM)^(Remaining 13
years)/(1+YTM)^7 years) + (Face value/1+YTM) ^Total years
(1666.66)(.453) + (3888.88)(.6738)/(1.828) + (214.11)
754.997 + 1433.44 + 214.11 = $2402.53
55 Multiple choice questions
,Term 1 of 55
1. Consider a zero-coupon bond with a yield to maturity (YTM) of 5%, a face value of $1000, and a
maturity date 10 years from today. What are you willing to pay for this bond today? What will you
be willing to pay for this bond 3 years from today?
What should stock price be today?
P0 = 1.25*1.04/.05 = $26
Po=(D1)/(r-g)= Do(1+g)/(r-g)
(Div PMT) *(1+r))/(r-g) = Price
b. (3 points) What are the dividend yield and capital gains yield?
CGY = .04; DY = .05
a) Bond Value = (50/.06)*(1-1/1.06^30) + 1000/1.06^30 = $862.35
b) Bond Value = (50/.06)(1-1/1.06^10) + (50/.04)(1-1/1.04^20)/1.06^10) + 1000/(1.06^10*1.04^20) =
$1002.27
Bond Value (Today) = 1000/1.05^10 = $613.91
Bond Value (3 years) = 1000/1.05^7 = $613.91*1.05^3 = $710.68
Bond Value (today) = (40/.05)*(1-1/1.05^5) + 1000/1.05^5 = $956.71
Bond Value (1 year from now) = (40/.05)*(1-1/1.05^4) + 1000/1.05^4 = $964.54
Percentage Change (Capital Gains Yield CGY) = (964.54-956.71)/956.71 = .0082 or .82%
Current Yield (year 1) = 40/956.71 = .0418 or 4.18%
NOTE: CGY + Current Yield = .82 + 4.18 = 5% = YTM
Bond Value (2 years from now) = (40/.05)*(1-1/1.05^3) + 1000/1.05^3 = $972.77
CGY = (972.77 - 964.54)/964.54 = .0085 or .85%
Current Yield (year 2) = 40/964.54 = .0415 or 4.15%
NOTE: CGY + Current Yield = .85 + 4.15 = 5% = YTM
,Term 2 of 55
7. Consider a bond that promises to make coupon payments of $150 per year for the next 7 years
and coupon payments of $350 per year for the remaining lifetime of the bond. The face value is
$1200. The bond matures in 20 years and YTM is 9%. What is the value of the bond?
CHEAT SHEET
Today: (70/.05)*(1-1/1.05^5)+(1000/(1.05)^5)=1086.614
1 year: (70/.05)*(1-1/1.05^4)+(1000/(1.05)^4)=1070.9267
CGY=-1.44%
CY=6.44%
YTM=5%
(6.44-1.44)
2 years: (70/.05)*(1-1/1.05^3)+(1000/(1.05)^3)=1054.53
P0 = (41.2/1.15) + (41.2ˆ2/1.15^2) + (41.2^21.4/1.15^3) + (41.2^21.4^2/1.15^4) + (41.2^21.4^3/1.15^5) +
(41.2^21.4^4/1.15^6) + (41.2^21.4^5/1.15^7) + (41.2^21.4^51.03/((.15 - .03)1.15^7) = 149.32
(Divided 1+g/1+r) + (Dividend 1 +g ^years for 20% growth/1+r ^ years) + (Dividend 1 + g^years
1+g^years/1 + g^years)
$4 included every time
20% growth for 1 year, 2 years then locked in at 2 after that
40% growth after 2 years (year 3), t increases until it hits 5
Once t hits 5, 3% forever kicks in, s0 51.03. Then divided by 15% required return - 3% 1+r ^
total years
a) P0 = (1.251.2/1.16) + (1.251.2^2/1.16^2) + (1.251.2^3/1.16^3) + (1.251.2^31.04/((.16 - .04)1.16^3) =
16.01
b) DY0 = 1.25*1.2/16.01 = .094; CGY0 = .16 - .094 = .066
, P1 = 16.01*1.066 = 17.07
DY1 = 1.25*1.2^2/17.07 = .1241; CGY1 = .16 - .1241 = .0359
BV0 = (150/.09)(1-1/1.09^7) + (350/.09)(1-1/1.09^13)/1.09^7 + 1200/1.09^20 = $2402.53
(C first 7/YTM) (1-1/1+YTM)^years + (Cremainder/YTM) (1-1/1+YTM)^(Remaining 13
years)/(1+YTM)^7 years) + (Face value/1+YTM) ^Total years
(1666.66)(.453) + (3888.88)(.6738)/(1.828) + (214.11)
754.997 + 1433.44 + 214.11 = $2402.53
