Question

VII. Rate of Returns (RET) i suppose that you purchase a security (e.g. corporate or government bond) worth $2000 today with a coupon payment of $200. Next year, the price of the security increases to $2300. Compute the following: i. The current yield ii. The capital gain rate iii. The rate of return of the security iv. If the expected inflation rate in the economy is 5.75%, what is the real rate of return of the security? Example 2: Suppose now that you purchase another security (e.g. corporate or government bond) worth $15000 today with a coupon payment of $3500. Next year, the price of the security falls to $9800 Compute the following: i. The current yield ii. The capital loss rate iii. The rate of return of the security iv. If the expected inflation rate in the economy is 3.29%, what is the real rate of return of the security?
please provide instructions on how to fi d the answer

Answer 1

1)

Purchase Price=P=$2000

Coupon amount=C=$200

Next year's price=S=$2300

i)

Current yield is equal to the coupon payment divided by price of bond.

Current yield=C/P=200/2000=10%

ii)

Capital Gain=(Final Price-Initial Price)/Initial Price

Capital gain rate=(S-P)/P=(2300-2000)/2000=15%

iii)

Rate of return=RET=Current yield+Capital gain=10%+15%=25%

iv)

Given inflation rate=f=5.75%

By approximation formula,

Real interest rate=RET-f=(25%-5.75%)=19.25%

2)

Purchase Price=P=$15000

Coupon amount=C=$3500

Next year's price=S=$9800

i)

Current yield=C/P=3500/15000=23.3333%

ii)

Capital Gain=(Final Price-Initial Price)/Initial Price

Capital gain rate=(S-P)/P=(9800-15000)/15000=-34.6667%

ii)

Rate of return=RET=Current yield+Capital gain=23.3333%-34.6667%=-11.3334%

iv)

Given inflation rate=f=3.29%

By approximation formula,

Real interest rate=RET-f=(-11.3334%-3.29%)=-14.6234%