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...