Question

Question 1: A banker must earn at least a 2.7% return after expected inflation on short term loans. The inflation rate for the past 6 months has averaged 3.5%. The expected inflation rate for the next twelve months is 7.3%. Nominal interest rates for short term loans were 7.1% last month. What is the minimum nominal interest rate that he should charge for a one year loan?

Question 2: Fred bought a $1000 face value bond issued by Zest Corporation for $1200. The bond matures in 2020 and pays him an annual interest payment of $70. What is Fred's current yield with this bond?

Question 3: A year ago, you purchased a $1000 face value bond for $1,006. A year later you sold the bond for $989 after receiving a coupon payment of $49. What was your rate of capital gain?

Question 4: You need to determine the market value of a $5,000 face value bond maturing in 5 years. The market yield for this type of bond is 4.7%. What is its market value?

Answer 1

1)

Expected rate of inflation=$\pi =$7.3%

Real rate of return=r=2.7%

According to fisher equation

Nominal Rate of return,i=real expected rate of return+expected inflation rate

i=r+$\pi =$2.7%+7.3%=10%

Minimum nominal rate of interest=10%

2)

Price of bond=Po=$1200

Interest payment=C=$70

Current yield=C/Po=70/1200=5.83%

Current yield is 5.83%

3)

Purchase price of bond=Po=$1006

Sale price of bond=P₁=$989

Capital Gain=(P₁-Po)/Po=(989-1006)/1006=-1.69%

Capital Gain=-1.69%

4)

Face value of bond=FV=$5000

Market yield=i=4.7%

Number of periods=n=5 years

Market value of bond=Present value of $5000 to be received after 5 year=FV/(1+i)^n

Market value of bond=5000/(1+4.7%)^5=$3974.08