Problem 4-16 Calculating Rates of Return [LO 3] In March 2015, Daniela Motor Fin

Question

Problem 4-16 Calculating Rates of Return [LO 3]

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 $1,000 in March 2055, but investors would receive nothing until then. Investors paid DMF $350 for each of these securities; so they gave up $350 in March 2015, for the promise of a $1,000 payment 40 years later.
  
a. Assuming you purchased the bond for $350, what rate of return would you earn if you held the bond for 40 years until it matured with a value $1,000? (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 2026. DMF agreed to pay an annual interest rate of 1.4 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 2026, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2055. What annual rate of return will you earn over the last 29 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             %

Explanation / Answer

a.

Rate of return = (Maturity value / Purchased value)^(1/Years) -1 = ($1000/$350)^(1/40) -1 = 2.66%

b.

Bond value = 350 x (1+1.4%)^11 = 407.835991 = $407.84

c.

Bond value calculate in part b. will be point of reference in denominator below:

Rate of return = (1000/407.835991)^(1/29) -1 = 3.14%

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