Guermillos Finance
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Week 4 Problems
Ch 4:
A9: (Rate of Return) After graduation, Adrian moved across the country to Brownsville and bought a small house for $208,000. Bill moved to Columbus a house for $195,000. Four years later they both sold their houses. Adrian netted $256,000 when she sold her house and Bill netted $168,000 on his.
A. What annual rate of return did Adrian realize on her house?
N=4
R=?
PV= -$208000
PMT=0
FV= $256000
PV= C(1/(1+r)⁴
208000=256000(1/(1+r)⁴
208000/256000=1/(1+r)⁴
0.8125=1/(1+r)⁴
(1+r)^4=1/0.8125
∜(+r)^4=∜1.23077
(1+r)=1.05328
R=1.05328-1
R=0.05328
R=5.33%
B. What annual rate of return did Bill realize on his house?
N=4
R=?
PV= -$195000
PMT=0
FV= $168000
PV= C(1/(1+r)⁴
195000=168000(1/(1+r)⁴
195000/168000=1/(1+r)⁴
1.16071=1/(1+r)⁴
(1+r)⁴=1/1.16071
(1+r)⁴=0.861538
∜(1+r)=∜0.861538
(1+r)=0.963427
R=0.963427-1
R=-0.036573
R= -3.66%
A11: (Calculating the PV and FV of an annuity) Assume an ordinary annuity of $500 at end of each of the next three years.
A. What is the present value discounted at 10%?
N=3
R=?
PV=?
R=10%
PMT=$500
FV= 0
PV= $500 x [1- 1/(1.10)^3]/.10
PV=$1243.43
B. What is the future value at end of year 3 if cash flows can be invested at 10%?
N=3
R=?
PV=0
R=10%
PMT= $500
FV=?
FV=$500x[(1.1)^3-1]/0.1
FV=$1655
Ch 5:
A1: (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bonds rate is 7.4%. What is the fair value of this bond?
Formula: Present value of maturity + Present value of coupon payment
Present value of maturity= 1000(1+9%)^-10
Present value of maturity= 422.41
Present value of coupon payments= 75(1-(1+9%)^-10)/9%
Present value of coupon payments= 481.32
Fair value of bond= 422.41 and 481.32= $903.73
A10: (Dividend discount model) Assume RHM is expected to pay a total cash...
Ch 4:
A9: (Rate of Return) After graduation, Adrian moved across the country to Brownsville and bought a small house for $208,000. Bill moved to Columbus a house for $195,000. Four years later they both sold their houses. Adrian netted $256,000 when she sold her house and Bill netted $168,000 on his.
A. What annual rate of return did Adrian realize on her house?
N=4
R=?
PV= -$208000
PMT=0
FV= $256000
PV= C(1/(1+r)⁴
208000=256000(1/(1+r)⁴
208000/256000=1/(1+r)⁴
0.8125=1/(1+r)⁴
(1+r)^4=1/0.8125
∜(+r)^4=∜1.23077
(1+r)=1.05328
R=1.05328-1
R=0.05328
R=5.33%
B. What annual rate of return did Bill realize on his house?
N=4
R=?
PV= -$195000
PMT=0
FV= $168000
PV= C(1/(1+r)⁴
195000=168000(1/(1+r)⁴
195000/168000=1/(1+r)⁴
1.16071=1/(1+r)⁴
(1+r)⁴=1/1.16071
(1+r)⁴=0.861538
∜(1+r)=∜0.861538
(1+r)=0.963427
R=0.963427-1
R=-0.036573
R= -3.66%
A11: (Calculating the PV and FV of an annuity) Assume an ordinary annuity of $500 at end of each of the next three years.
A. What is the present value discounted at 10%?
N=3
R=?
PV=?
R=10%
PMT=$500
FV= 0
PV= $500 x [1- 1/(1.10)^3]/.10
PV=$1243.43
B. What is the future value at end of year 3 if cash flows can be invested at 10%?
N=3
R=?
PV=0
R=10%
PMT= $500
FV=?
FV=$500x[(1.1)^3-1]/0.1
FV=$1655
Ch 5:
A1: (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bonds rate is 7.4%. What is the fair value of this bond?
Formula: Present value of maturity + Present value of coupon payment
Present value of maturity= 1000(1+9%)^-10
Present value of maturity= 422.41
Present value of coupon payments= 75(1-(1+9%)^-10)/9%
Present value of coupon payments= 481.32
Fair value of bond= 422.41 and 481.32= $903.73
A10: (Dividend discount model) Assume RHM is expected to pay a total cash...