Question

In March 2015, Daniela Motor Financing (DMF), offered some securities for sale to the public. Under the terms of the deal, DMF promised to repay the owner of one of these securities $5,000 in March 2050, but investors would receive nothing until then. Investors paid DMF $1,500 for each of these securities; so they gave up $1,500 in March 2015, for the promise of a $5,000 payment 35 years later.
  
a. Assuming you purchased the bond for $1,500, what rate of return would you earn if you held the bond for 35 years until it matured with a value $5,000? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
Rate of return             %
  
b. Suppose under the terms of the bond you could redeem the bond in 2022. DMF agreed to pay an annual interest rate of 1.2 percent until that date. How much would the bond be worth at that time? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Bond value            $
  
c. In 2022, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2050. What annual rate of return will you earn over the last 28 years? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
Rate of return             %

Answer 1

Formula to calculate rate of return on bond
Rate of return = (FV/PV)^(1/n) - 1
where FV is the future value to be received
PV is the present value
n is the number of years
a. Calculation of rate of return on bond
Rate of return =(5,000/1,500)^(1/35) - 1
Rate of return =3.33333^(1/35) - 1
Rate of return =1.034998 - 1
Rate of return = 3.50%
The rate of return on bond is 3.50%
Formula to calculate the future price of the bond
FV = PV*(1+r)^n
where FV is the future value to be received
PV is the present value
n is the number of years
r is the rate of interest
b. Calculation of future price of bond
FV = 1,500*(1+0.012)^7
FV = 1,500*(1.012^7)
FV = 1,500*1.087085
FV = 1,630.63
The price of the bond would be $1,630.63
c. Using the rate of return formula above, we get
Rate of return = (5,000/1630.63)^(1/28) - 1
Rate of return = 3.0663^(1/28) - 1
Rate of return = 1.0408 - 1
Rate of return = 4.08%
The rate of return on bond would be 4.08%